JEE Main 2023 questions
415 questions, by subject. Each opens with its options and answer.
Mathematics
- Three rotten apples are mixed accidently with seven good apples and four apples are drawn one by one without replacement. Let the random variable X denote the number of rotten apples. If μ and σ^2 represent mean and…
Probability · with solution
- The value of sum_r=0^22 ^22C_r \ ^23C_r is
Permutations and Combinations · with solution
- The equations of the sides AB and AC of a triangle ABC are (λ + 1)x + λ y = 4 and λ x + (1 - λ)y + λ = 0 respectively. Its vertex A is on the y-axis and its orthocentre is (1,2). The length of the tangent from the point…
Conic Sections
- The distance of the point P (4, 6, –2) from the line passing through the point (–3, 2, 3) and parallel to a line with direction ratios 3, 3, –1 is equal to :
Three Dimensional Geometry · with solution
- The number of numbers, strictly between 5000 and 10000 can be formed using the digits 1,3,5,7,9 without repetition, is
Permutations and Combinations · with solution
- Let x = 2 be a root of the equation x^2 + px + q = 0 and f(x) = begincases (1 - cos(x^2 - 4px + q^2 + 8q + 16))/((x - 2p)^4), & x ≠ 2p \ 0, & x = 2p endcases Then lim_x → 2p^- [f(x)], where [·] denotes greatest integer…
Limits Continuity and Differentiability · with solution
- Let A = beginbmatrix frac1√(10) & frac3√(10) \ frac-3√(10) & frac1√(10) endbmatrix and B = beginbmatrix 1 & -i \ 0 & 1 endbmatrix, where i = √(-1). If M = A^T B A, then the inverse of the matrix AM^2023A^T is
Matrices and Determinants
- Let f(x) = begincases x^2 sin (1/x ) & , x ≠ 0 \ 0 & , x = 0 endcases Then at x = 0
Limits Continuity and Differentiability · with solution
- Let p and q be two statements. Then ~(p wedge (p ⇒ ~ q)) is equivalent to
Mathematical Reasoning
- The mean and variance of the marks obtained by the students in a test are 10 and 4 respectively. Later, the marks of one of the students is increased from 8 to 12. If the new mean of the marks is 10.2, then their new…
Statistics · with solution
- Let T and C respectively be the transverse and conjugate axes of the hyperbola 16x^2 - y^2 + 64x + 4y + 44 = 0. Then the area of the region above the parabola x^2 = y + 4, below the transverse axis T and on the right of…
Definite Integrals and Areas · with solution
- Let A = \(x, y) ∈ R^2 : y ≥ 0, 2x ≤ y ≤ √(4-(x-1)^2)\ and B = \(x, y) ∈ R × R : 0 ≤ y ≤ min \2x, √(4-(x-1)^2) \\. Then the ratio of the area of A to the area of B is
Definite Integrals and Areas
- Let y = y(x) be the solution of the differential equation x^3 dy + (xy - 1) dx = 0, x > 0, y (1/2 ) = 3 - e. Then y(1) is equal to
Differential Equations
- Let y = y(x) be the solution of the differential equation (x^2 - 3y^2) dx + 3xy dy = 0, y(1) = 1. Then 6y^2(e) is equal to
Differential Equations
- The statement (p wedge (~ q)) ⇒ (p ⇒ (~ q)) is
Mathematical Reasoning
- Let Δ be the area of the region \(x,y) ∈ R^2 : x^2 + y^2 ≤ 21, y^2 ≤ 4x, x ≥ 1 \. Then 1/2 (Δ - 21sin^-1frac2√(7) ) is equal to
Definite Integrals and Areas
- Let f(x) = 2x^n + λ, λ ∈ R, n ∈ N, and f(4) = 133, f(5) = 255. Then the sum of all the positive integer divisors of (f(3) - f(2)) is
Sets Relations and Functions · with solution
- The compound statement (~(P wedge Q)) vee ((~ P) wedge Q) ⇒ ((~ P) wedge (~ Q)) is equivalent to
Mathematical Reasoning · with solution
- The number of real solutions of the equation 3 (x^2 + 1/(x^2) ) - 2 (x + 1/x ) + 5 = 0, is
Complex Numbers and Quadratic Equations · with solution
- Let S_1 and S_2 be respectively the sets of all a ∈ R - \0\ for which the system of linear equations ax + 2ay - 3az = 1 (2a+1)x + (2a+3)y + (a+1)z = 2 (3a+5)x + (a+5)y + (a+2)z = 3 has unique solution and infinitely…
Matrices and Determinants
- Let [x] denote the greatest integer ≤ x. Consider the function f(x) = max\x^2, 1+[x]\. Then the value of the integral int_0^2 f(x) dx is
Definite Integrals and Areas · with solution
- If f(x) = dfrac2^2x2^2x+2, x ∈ R, then f (1/2023 ) + f (2/2023 ) + … + f (2022/2023 ) is equal to
Definite Integrals and Areas · with solution
- Let x, y, z > 1 and A = beginbmatrix 1 & log_x y & log_x z \ log_y x & 2 & log_y z \ log_z x & log_z y & 3 endbmatrix. Then |adj(adj A^2)| is equal to
Matrices and Determinants
- Let A, B, C be 3 × 3 matrices such that A is symmetric and B and C are skew-symmetric. Consider the statements (S1) A^13 B^26 - B^26 A^13 is symmetric (S2) A^26 C^13 - C^13 A^26 is symmetric Then,
Matrices and Determinants · with solution
- If the vectors a = λi + muj + 4k, b = -2i + 4j - 2k and c = 2i + 3j + k are coplanar and the projection of a on the vector b is √(54) units, then the sum of all possible values of λ + μ is equal to
Vector Algebra
- The relation R = \(a,b): gcd(a,b) = 1, 2a ≠ b, a, b ∈ Z\ is :
Sets Relations and Functions
- If the system of equations x + 2y + 3z = 3 4x + 3y - 4z = 4 8x + 4y - λ z = 9 + μ has infinitely many solutions, then the ordered pair (λ, μ) is equal to :
Matrices and Determinants · with solution
- Let x = 2 be a local minima of the function f(x) = 2x^4 - 18x^2 + 8x + 12, x ∈ (-4, 4). If M is local maximum value of the function f in (-4, 4), then M =
Application of Derivatives
- The shortest distance between the lines x + 1 = 2y = -12z and x = y + 2 = 6z - 6 is
Three Dimensional Geometry
- A light ray emits from the origin making an angle 30° with the positive x-axis. After getting reflected by the line x + y = 1, if this ray intersects x-axis at Q, then the abscissa of Q is
Straight Lines and Pair of Lines
- Let a = -i - j + k, a · b = 1 and a × b = i - j. Then a - 6b is equal to
Vector Algebra · with solution
- Let Ω be the sample space and A ⊂eq Ω be an event. Given below are two statements : (S1) : If P(A) = 0, then A = emptyset (S2) : If P(A) = 1, then A = Ω Then
Probability · with solution
- The locus of the mid points of the chords of the circle C_1:(x-4)^2+(y-5)^2=4 which subtend an angle θ_i at the centre of the circle C_1, is a circle of radius r_i. If θ_1=(π)/3, θ_3=(2π)/3 and r_1^2=r_2^2+r_3^2, then…
Circles
- Let f(x) = ∫ 2x/((x^2+1)(x^2+3)) dx. If f(3) = 1/2(log_e 5 - log_e 6), then f(4) is equal to
Indefinite Integration
- If the function f(x) = begincases (1+|cos x|)(λ)/(|cos x|), & 0 < x < (π)/2 \ μ, & x = (π)/2 \ dfraccot 6xe^cot 4x, & (π)/2 < x < π endcases is continuous at x = (π)/2, then 9λ + 6log_e μ + μ^6 - e^6λ is equal to
Limits Continuity and Differentiability
- Let f: R arrow R be a function such that f(x) = (x^2 + 2x + 1)/(x^2 + 1). Then
Sets Relations and Functions · with solution
- The distance of the point (7, -3, -4) from the plane passing through the points (2, -3, 1), (-1, 1, -2) and (3, -4, 2) is:
Three Dimensional Geometry · with solution
- Let the plane containing the line of intersection of the planes P1 : x + (λ + 4)y + z = 1 and P2 : 2x + y + z = 2 pass through the points (0, 1, 0) and (1, 0, 1). Then the distance of the point (2λ, λ, -λ) from the…
Three Dimensional Geometry · with solution
- The vector a = -i + 2j + k is rotated through a right angle, passing through the y-axis in its way and the resulting vector is b. Then the projection of 3a + √(2) b on c = 5i + 4j + 3k is:
Vector Algebra
- The integral 16int_1^2 dx/(x^3(x^2+2)^2) is equal to
Definite Integrals and Areas
- Let y = f(x) be the solution of the differential equation y(x+1)dx - x^2 dy = 0, y(1) = e. Then lim_x → 0^+ f(x) is equal to
Differential Equations · with solution
- The distance of the point (-1, 9, -16) from the plane 2x + 3y - z = 5 measured parallel to the line (x+4)/3 = (2-y)/4 = (z-3)/12 is
Three Dimensional Geometry · with solution
- Let the six numbers a_1, a_2, a_3, a_4, a_5, a_6, be in A.P. and a_1 + a_3 = 10. If the mean of these six numbers is 19/2 and their variance is σ^2, then 8σ^2 is equal to :
Statistics · with solution
- The points of intersection of the line ax + by = 0, (a ≠ b) and the circle x^2 + y^2 - 2x = 0 are A(α, 0) and B(1, β). The image of the circle with AB as a diameter in the line x + y + 2 = 0 is :
Circles
- The equations of two sides of a variable triangle are x = 0 and y = 3, and its third side is a tangent to the parabola y^2 = 6x. The locus of its circumcentre is:
Conic Sections
- Consider the following system of equations ax + 2y + z = 1 2ax + 3y + z = 1 3x + ay + 2z = β for some α, β ∈ R. Then which of the following is NOT correct.
Matrices and Determinants
- Let u = i - j - 2k, v = 2i + j - k, v · w = 2 and v × w = u + λ v. Then u · w is equal to
Vector Algebra
- The set of all values of a for which lim_x → a([x-5]-[2x+2])=0, where [α] denotes the greatest integer less than or equal to α is equal to
Limits Continuity and Differentiability
- Let f:(0,1) → R be a function defined by f(x) = dfrac11-e^-x, and g(x) = (f(-x) - f(x)). Consider two statements (I) g is an increasing function in (0, 1) (II) g is one-one in (0, 1) Then,
Limits Continuity and Differentiability · with solution
- Let f(θ) = 3 (sin^4 ((3π)/2 - θ ) + sin^4(3π + θ) ) - 2(1 - sin^2 2θ) and S = \θ ∈ [0, π] : f'(θ) = -frac√(3)2 \. If 4β = sum_θ ∈ S θ, then f(β) is equal to
Trigonometry
- Let PQR be a triangle. The points A, B and C are on the sides QR, RP and PQ respectively such that QA/AR = RB/BP = PC/CQ = 1/2. Then (Area(Δ PQR))/(Area(Δ ABC)) is equal to
Vector Algebra
- If f(x) = x^3 - x^2 f'(1) + xf''(2) - f'''(3), x ∈ R, then
Limits Continuity and Differentiability · with solution
- Let y(x) = (1+x)(1+x^2)(1+x^4)(1+x^8)(1+x^16). Then y' - y'' at x = -1 is equal to:
Limits Continuity and Differentiability
- Let Δ, ∇ ∈ \wedge, vee\ be such that (p → q) Δ (p ∇ q) is a tautology. Then
Mathematical Reasoning · with solution
- Let the tangents at the points A(4,-11) and B(8,-5) on the circle x^2 + y^2 - 3x + 10y - 15 = 0, intersect at the point C. Then the radius of the circle, whose centre is C and the line joining A and B is its tangent, is…
Circles
- The foot of perpendicular of the point (2, 0, 5) on the line (x+1)/2 = (y-1)/5 = (z+1)/(-1) is (α, β, γ). Then, which of the following is NOT correct?
Three Dimensional Geometry · with solution
- The equation x^2 - 4x + [x] + 3 = x[x], where [x] denotes the greatest integer function, has:
Limits Continuity and Differentiability · with solution
- Let f(x) be a function such that f(x + y) = f(x) · f(y) for all x, y ∈ N. If f(1) = 3 and sum_k=1^n f(k) = 3279, then the value of n is
Sequences and Series
- Let α and β be real numbers. Consider a 3 × 3 matrix A such that A^2 = 3A + α I. If A^4 = 21A + β I, then
Matrices and Determinants · with solution
- Let N denote the number that turns up when a fair die is rolled. If the probability that the system of equations x + y + z = 1 2x + Ny + 2z = 2 3x + 3y + Nz = 3 has unique solution is k/6, then the sum of value of k and…
Probability · with solution
- The value of ((1+sin(2π)/9+icos(2π)/9)/(1+sin(2π)/9-icos(2π)/9) )^3 is
Complex Numbers and Quadratic Equations · with solution
- Let f: R → R be a function defined by f(x) = log_√(2)[√(2)(sin x - cos x) + m - 2], for some m, such that the range of f is [0, 2]. Then the value of m is
Trigonometry
- If the four points, whose position vectors are 3i - 4j + 2k, i + 2j - k, -2i - j + 3k and 5i - 2aj + 4k are coplanar, then a is equal to
Vector Algebra · with solution
- If p, q and r are three propositions, then which of the following combination of truth values of p, q and r makes the logical expression \(p vee q) wedge ((~ p) vee r)\ arrow ((~ q) vee r) false?
Mathematical Reasoning · with solution
- tan^-1 (dfrac1+√(3)3+√(3) ) + sec^-1 (sqrtdfrac8+4√(3)6+3√(3) ) is equal to :
Inverse Trigonometric Functions · with solution
- The number of integers, greater than 7000 that can be formed, using the digits 3,5,6,7,8 without repetition, is
Permutations and Combinations · with solution
- Consider the lines L_1 and L_2 given by L_1 : (x-1)/2 = (y-3)/1 = (z-2)/2 L_2 : (x-2)/1 = (y-2)/2 = (z-3)/3 A line L_3 having direction ratios 1, -1, -2, intersects L_1 and L_2 at the points P and Q respectively. Then…
Three Dimensional Geometry
- If A and B are two non-zero n × n matrices such that A^2 + B = A^2 B, then
Matrices and Determinants
- int_frac3√(2)4^frac3√(3)4 frac48√(9-4x^2) dx is equal to
Definite Integrals and Areas · with solution
- The value of lim_n → ∞ dfrac1+2-3+4+5-6+......+(3n-2)+(3n-1)-3n√(2n^4+4n+3)-√(n^4+5n+4) is:
Limits Continuity and Differentiability
- Let the function f(x) = 2x^3 + (2p-7)x^2 + 3(2p-9)x - 6 have a maxima for some value of x 0. Then, the set of all values of p is
Application of Derivatives
- Let B and C be the two points on the line y + x = 0 such that B and C are symmetric with respect to the origin. Suppose A is a point on y - 2x = 2 such that triangle ABC is an equilateral triangle. Then, the area of the…
Straight Lines and Pair of Lines · with solution
- The area enclosed by the curves y^2 + 4x = 4 and y - 2x = 2 is :
Definite Integrals and Areas
- Let α = 4i + 3j + 5k and β = i + 2j - 4k. Let β_1 be parallel to α and β_2 be perpendicular to α. If β = β_1 + β_2, then the value of 5β_2 · (i + j + k) is
Vector Algebra · with solution
- Let y = y(x) be the solution curve of the differential equation dy/dx = y/x (1 + xy^2(1 + log_e x) ), x > 0, y(1) = 3. Then (y^2(x))/9 is equal to :
Differential Equations
- Let z be a complex number such that |(z-2i)/(z+i) | = 2, z ≠ -i. Then z lies on the circle of radius 2 and centre
Complex Numbers and Quadratic Equations · with solution
- Let N be the sum of the numbers appeared when two fair dice are rolled and let the probability that N-2, √(3N), N+2 are in geometric progression be k/48. Then the value of k is
Probability · with solution
- Let λ ≠ 0 be a real number. Let α, β be the roots of the equation 14x^2 - 31x + 3λ = 0 and α, γ be the roots of the equation 35x^2 - 53x + 4λ = 0. Then (3α)/(β) and (4α)/(γ) are the roots of the equation
Complex Numbers and Quadratic Equations
- Let a tangent to the curve y^2 = 24x meet the curve xy = 2 at the points A and B. Then the mid points of such line segments AB lie on a parabola with the
Conic Sections · with solution
- Let A be a 3 × 3 matrix such that |adj(adj(adj A))| = 12^4. Then |A^-1 adj A| is equal to
Matrices and Determinants
- If a_r is the coefficient of x^10-r in the Binomial expansion of (1+x)^10, then displaystylesum_r=1^10 r^3 (dfraca_ra_r-1 )^2 is equal to
Binomial Theorem
- The number of functions f: \1,2,3,4\ arrow \a ∈ Z : |a| ≤ 8\ satisfying f(n) + 1/n f(n+1) = 1, forall n ∈ \1,2,3\ is
Sets Relations and Functions · with solution
- Let f(x) = x + a/(π^2 - 4)sin x + b/(π^2 - 4)cos x, x ∈ R be a function which satisfies f(x) = x + displaystyleint_0^π/2 sin(x+y) f(y) dy. Then (a+b) is equal to
Definite Integrals and Areas
- lim_t → 0 (1^1/(sin^2 t) + 2^1/(sin^2 t) + … + n^1/(sin^2 t) )^sin^2 t is equal to
Limits Continuity and Differentiability
- If the foot of the perpendicular drawn from (1, 9, 7) to the line passing through the point (3, 2, 1) and parallel to the planes x + 2y + z = 0 and 3y - z = 3 is (α, β, γ), then α + β + γ is equal to
Three Dimensional Geometry · with solution
- Let z_1 = 2 + 3i and z_2 = 3 + 4i. The set S = \ z ∈ C : |z - z_1|^2 - |z - z_2|^2 = |z_1 - z_2|^2 \ represents a
Straight Lines and Pair of Lines · with solution
- Let y = y(t) be a solution of the differential equation dy/dt + α y = γ e^-β t where, α > 0, β > 0 and γ > 0. Then lim_t → ∞ y(t)
Differential Equations · with solution
- For two non-zero complex numbers z_1 and z_2, if Re(z_1 z_2) = 0 and Re(z_1 + z_2) = 0, then which of the following are possible? A. Im(z_1) > 0 and Im(z_2) > 0 B. Im(z_1) 0 C. Im(z_1) > 0 and Im(z_2) < 0 D. Im(z_1) < 0…
Complex Numbers and Quadratic Equations · with solution
- For three positive integers p, q, r, x^pq^2 = y^qr = z^p^2r and r = pq + 1 such that 3, 3log_y x, 3log_z y, 7log_x z are in A.P. with common difference 1/2. Then r - p - q is equal to
Sequences and Series
- The number of square matrices of order 5 with entries from the set \0, 1\, such that the sum of all the elements in each row is 1 and the sum of all the elements in each column is also 1, is
Permutations and Combinations · with solution
- Let a, b and c be three non zero vectors such that b · c = 0 and a × (b × c) = dfracb - c2. If d be a vector such that b · d = a · b, then (a × b) · (c × d) is equal to
Vector Algebra · with solution
- The domain of f(x) = dfraclog_(x+1)(x-2)e^2log_e x - (2x+3), x ∈ R is
Sets Relations and Functions · with solution
- Let p, q ∈ R and (1-√(3)i )^200 = 2^199(p+iq), i = √(-1). Then p + q + q^2 and p - q + q^2 are roots of the equation.
Complex Numbers and Quadratic Equations · with solution
- If (^30C_1)^2 + 2(^30C_2)^2 + 3(^30C_3)^2 + ... + 30 (^30C_30)^2 = (α 60!)/((30!)^2) then α is equal to :
Binomial Theorem
- The minimum value of the function f(x) = int_0^2 e^|x-t| dt is :
Definite Integrals and Areas
- sum_k=0^6 51-k C_3 is equal to
Binomial Theorem · with solution
- The value of 8/(π) int_0^(π)/2 dfrac(cos x)^2023(sin x)^2023 + (cos x)^2023 dx is __________
Definite Integrals and Areas · with solution
- If dfrac1^3 + 2^3 + 3^3 + … up to n terms1·3 + 2·5 + 3·7 + … up to n terms = 9/5, then the value of n is
Sequences and Series · with solution
- Let x and y be distinct integers where 1 ≤ x ≤ 25 and 1 ≤ y ≤ 25. Then, the number of ways of choosing x and y, such that x + y is divisible by 5, is __________.
Permutations and Combinations
- If int_1^e [log_e x] dx = m/n log_e ( (e^2)/c ), where m and n are coprime natural numbers, then m^2 + n^2 - 5 is equal to
Definite Integrals and Areas
- Let the coefficients of three consecutive terms in the binomial expansion of (1+2x)^n be in the ratio 2:5:8. Then the coefficient of the term, which is in the middle of these three terms, is _______.
Binomial Theorem · with solution
- If all the six digit numbers x_1 x_2 x_3 x_4 x_5 x_6 with 0 < x_1 < x_2 < x_3 < x_4 < x_5 < x_6 are arranged in the increasing order, then the sum of the digits in the 72^nd number is ________.
Permutations and Combinations · with solution
- Let a tangent to the curve 9x^2 + 16y^2 = 144 intersect the coordinate axes at the points A and B. Then, the minimum length of the line segment AB is __________
Application of Derivatives · with solution
- Let f be a differentiable function defined on [0, (π)/2 ] such that f(x) > 0 and f(x) + int_0^x f(t)√(1 - (log_e f(t) )^2) dt = e, forall x ∈ [0, (π)/2 ] Then (6log_e f ((π)/6 ) )^2 is equal to __________.
Differential Equations · with solution
- Let a ∈ R, and let α, β be the roots of the equation x^2 + 60^1/4x + a = 0. If α^4 + β^4 = -30, then the product of all possible values of a is _______
Complex Numbers and Quadratic Equations · with solution
- Suppose f is a function satisfying f(x+y) = f(x) + f(y) for all x, y ∈ N and f(1) = 1/5. If sum_n=1^m (f(n))/(n(n+1)(n+2)) = 1/12, then m is equal to _______
Sequences and Series · with solution
- The value of 12int_0^3 |x^2 - 3x + 2 | dx is ___________
Definite Integrals and Areas
- The equations of the sides AB, BC and CA of a triangle ABC are: 2x + y = 0, x + py = 21a, (a ≠ 0) and x - y = 3 respectively. Let P(2, a) be the centroid of triangle ABC. Then (BC)^2 is equal to
Straight Lines and Pair of Lines
- If the shortest distance between the line joining the points (1, 2, 3) and (2, 3, 4), and the line (x-1)/2 = (y+1)/(-1) = (z-2)/0 is a, then 28a^2 is equal to ______.
Three Dimensional Geometry · with solution
- For the two positive numbers a, b, if a, b and 1/18 are in a geometric progression, while 1/a, 10 and 1/b are in an arithmetic progression, then 16a + 12b is equal to ___________.
Sequences and Series · with solution
- Let f: R arrow R be a differentiable function that satisfies the relation f(x+y) = f(x) + f(y) - 1, forall x, y ∈ R. If f'(0) = 2, then |f(-2)| is equal to
Limits Continuity and Differentiability · with solution
- A boy needs to select five courses from 12 available courses, out of which 5 courses are language courses. If he can choose at most two language courses, then the number of ways he can choose five courses is __________
Permutations and Combinations · with solution
- If the shortest between the lines fracx+√(6)2 = fracy-√(6)3 = fracz-√(6)4 and (x-λ)/3 = fracy-2√(6)4 = fracz+2√(6)5 is 6, then the square of sum of all possible values of λ is
Three Dimensional Geometry · with solution
- Let the equation of the plane passing through the line x - 2y - z - 5 = 0 = x + y + 3z - 5 and parallel to the line x + y + 2z - 7 = 0 = 2x + 3y + z - 2 be ax + by + cz = 65. Then the distance of the point (a, b, c)…
Three Dimensional Geometry
- Let a_1, a_2, a_3, … be a GP of increasing positive numbers. If the product of fourth and sixth terms is 9 and the sum of fifth and seventh terms is 24, then a_1 a_9 + a_2 a_4 a_9 + a_5 + a_7 is equal to ________.
Sequences and Series · with solution
- The number of 9 digit numbers, that can be formed using all the digits of the number 123412341 so that the even digits occupy only even places, is __________
Permutations and Combinations
- Let S = \θ ∈ [0, 2π) : tan(π cosθ) + tan(π sinθ) = 0\. Then displaystylesum_θ ∈ S sin^2 (θ + (π)/4 ) is equal to __________.
Trigonometry
- The remainder when (2023)^2023 is divided by 35 is __________
Binomial Theorem
- Suppose Anil's mother wants to give 5 whole fruits to Anil from a basket of 7 red apples, 5 white apples and 8 oranges. If in the selected 5 fruits, at least 2 oranges, at least one red apple and at least one white…
Permutations and Combinations · with solution
- Let a, b and c be three non-zero non-coplanar vectors. Let the position vectors of four points A, B, C and D be a - b + c, λa - 3b + 4c, -a + 2b - 3c and 2a - 4b + 6c respectively. If overrightarrowAB, overrightarrowAC…
Vector Algebra · with solution
- Let λ ∈ R and let the equation E be |x|^2 - 2|x| + |λ - 3| = 0. Then the largest element in the set S = \x + λ : x is an integer solution of E\ is
Complex Numbers and Quadratic Equations
- The minimum number of elements that must be added to the relation R = \(a, b), (b, c), (b, d)\ on the set \a, b, c, d\ so that it is an equivalence relation, is ______.
Sets Relations and Functions
- The vertices of a hyperbola H are (± 6, 0) and its eccentricity is dfrac√(5)2. Let N be the normal to H at a point in the first quadrant and parallel to the line √(2)x + y = 2√(2). If d is the length of the line segment…
Conic Sections
- Let the co-ordinates of one vertex of triangle ABC be A(0, 2, a) and the other two vertices lie on the line (x+a)/5 = (y-1)/2 = (z+4)/3. For a ∈ Z, if the area of triangle ABC is 21 sq. units and the line segment BC has…
Three Dimensional Geometry
- The 4^th term of GP is 500 and its common ratio is 1/m, m ∈ N. Let S_n denote the sum of the first n terms of this GP. If S_6 > S_5 + 1 and S_7 < S_6 + 1/2, then the number of possible values of m is
Sequences and Series · with solution
- Three urns A, B and C contain 4 red, 6 black; 5 red, 5 black; and λ red, 4 black balls respectively. One of the urns is selected at random and a ball is drawn. If the ball drawn is red and the probability that it is…
Probability · with solution
- Points P(-3, 2), Q(9, 10) and R(a, 4) lie on a circle C with PR as its diameter. The tangents to C at the points Q and R intersect at the point S. If S lies on the line 2x - ky = 1, then k is equal to
Circles
- If the co-efficient of x^9 in (ax^3 + 1/(β x) )^11 and the co-efficient of x^-9 in (ax - 1/(β x^3) )^11 are equal, then (αβ)^2 is equal to ________.
Binomial Theorem · with solution
- Suppose sum_r=0^2023 r^2 · ^2023C_r = 2023 × α × 2^2022. Then the value of α is _______
Binomial Theorem
- Let S = \1, 2, 3, 5, 7, 10, 11\. The number of non-empty subsets of S that have the sum of all elements a multiple of 3, is _________.
Permutations and Combinations
- If m and n respectively are the numbers of positive and negative values of θ in the interval [-π, π] that satisfy the equation cos 2θ cos (θ)/2 = cos 3θ cos (9θ)/2, then mn is equal to _______.
Trigonometry · with solution
- 25% of the population are smokers. A smoker has 27 times more chances to develop lung cancer than a non smoker. A person is diagnosed with lung cancer and the probability that that person is a smoker is k/10. Then the…
Probability
- Let the equation of the plane P containing the line x + 10 = (8-y)/2 = z be ax + by + 3z = 2(a+b) and the distance of the plane P from the point (1, 27, 7) be c. Then a^2 + b^2 + c^2 is equal to _______.
Three Dimensional Geometry · with solution
- Let A_1, A_2, A_3 be the three A.P. with the same common difference d and having their first terms as A, A+1, A+2, respectively. Let a, b, c be the 7^th, 9^th, 17^th terms of A_1, A_2, A_3, respectively such that…
Sequences and Series
- Five digit numbers are formed using the digits 1, 2, 3, 5, 7 with repetitions and are written in descending order with serial numbers. For example, the number 77777 has serial number 1. Then the serial number of 35337 is
Permutations and Combinations · with solution
- If the area of the region bounded by the curves y^2 - 2y = -x, x + y = 0 is A, then 8A is equal to
Definite Integrals and Areas
- For some a, b, c ∈ N, let f(x) = ax - 3 and g(x) = x^b + c, x ∈ R. If (fog)^-1(x) = ((x-7)/2 )^1/3, then (fog)(ac) + (gof)(b) is equal to __________.
Sets Relations and Functions
- A triangle is formed by X-axis, Y-axis and the line 3x + 4y = 60. Then the number of points P(a, b) which lie strictly inside the triangle, where a is an integer and b is a multiple of a, is ___.
Straight Lines and Pair of Lines
Chemistry
- "A" obtained by Ostwald's method involving air oxidation of NH_3, upon further air oxidation produces "B". "B" on hydration forms an oxoacid of Nitrogen along with evolution of "A". The oxoacid also produces "A" and…
p-Block Elements · with solution
- The magnetic moment of a transition metal compound has been calculated to be 3.87 B.M. The metal ion is
d- and f-Block Elements · with solution
- Which one amongst the following are good oxidizing agents? A. Sm^2+ B. Ce^2+ C. Ce^4+ D. Tb^4+ Choose the most appropriate answer from the options given below:
d- and f-Block Elements · with solution
- The correct order in aqueous medium of basic strength in case of methyl substituted amines is :
Amines and Nitrogen Compounds
- Potassium dichromate acts as a strong oxidizing agent in acidic solution. During this process, the oxidation state changes from
d- and f-Block Elements · with solution
- Find out the major product from the following reaction. undersetΔoversetH_2SO_4 (Concentrated)→ [figure]
Alcohols Phenols and Ethers
- The reaction representing the Mond process for metal refining is 2K[Au(CN)_2] + Zn →[Δ] K_2[Zn(CN)_4] + 2Au
General Principles of Metallurgy · with solution
- Assertion A : Hydrolysis of an alkyl chloride is a slow reaction but in the presence of NaI, the rate of the hydrolysis increases. Reason R : I^- is a good nucleophile as well as a good leaving group. In the light of…
Haloalkanes and Haloarenes · with solution
- Which of the following cannot be explained by crystal field theory?
Coordination Compounds · with solution
- Inert gases have positive electron gain enthalpy. Its correct order is
Periodic Classification
- During the borax bead test with CuSO_4, a blue green colour of the bead was observed in oxidising flame due to the formation of
Practical Chemistry · with solution
- Match List I with List II | LIST I | LIST II | |---|---| | Coordination entity | Wavelength of light absorbed in nm | | A. [CoCl(NH_3)_5]^2+ | I. 310 | | B. [Co(NH_3)_6]^3+ | II. 475 | | C. [Co(CN)_6]^3- | III. 535 | |…
Coordination Compounds · with solution
- K_2Cr_2O_7 paper acidified with dilute H_2SO_4 turns green when exposed to
Practical Chemistry
- In the cumene to phenol preparation in presence of air, the intermediate is
Alcohols Phenols and Ethers
- Statement I : Dipole moment is a vector quantity and by convention it is depicted by a small arrow with tail on the negative centre and head pointing towards the positive centre. Statement II : The crossed arrow of the…
Chemical Bonding · with solution
- Compound that will give positive Lassaigne's test for both nitrogen and halogen is:
Practical Chemistry · with solution
- Statement I : For colloidal particles, the values of colligative properties are of small order as compared to values shown by true solutions at same concentration. Statement II : For colloidal particles, the potential…
Surface Chemistry · with solution
- Find out the major products from the following reactions. [figure]
Basic Principles of Organic Chemistry
- Which of the following statements is incorrect for antibiotics?
Chemistry in Everyday Life
- Correct statement about smog is:
Environmental Chemistry · with solution
- 'A' and 'B' formed in the following set of reactions are: [figure]
Basic Principles of Organic Chemistry
- Identify the correct statements about alkali metals. A. The order of standard reduction potential (M^+ | M) for alkali metal ions is Na > Rb > Li. B. CsI is highly soluble in water. C. Lithium carbonate is highly stable…
Hydrogen and s-Block Elements · with solution
- The variation of the rate of an enzyme catalyzed reaction with substrate concentration is correctly represented by graph [figure]
Surface Chemistry
- Which one among the following metals is the weakest reducing agent?
Redox and Electrochemistry · with solution
- The correct order of hydration enthalpies is (A) K^+ (B) Rb^+ (C) Mg^2+ (D) Ca^+ (E) Ca^2+ Choose the correct answer from the options given below:
Hydrogen and s-Block Elements · with solution
- Given below are two statements: Statement I : Noradrenaline is a neurotransmitter. Statement II : Low level of noradrenaline is not the cause of depression in human. In the light of the above statements, choose the…
Chemistry in Everyday Life · with solution
- In which of the following reactions the hydrogen peroxide acts as a reducing agent?
Hydrogen and s-Block Elements · with solution
- Match List I with List II | LIST I (Elements) | LIST II (Colour imparted to the flame) | |---|---| | A. K | I. Brick Red | | B. Ca | II. Violet | | C. Sr | III. Apple Green | | D. Ba | IV. Crimson Red | Choose the…
Hydrogen and s-Block Elements · with solution
- Match List I with List II | LIST I | LIST II | |---|---| | A. Cobalt catalyst | I. (H_2 + Cl_2) production | | B. Syngas | II. Water gas production | | C. Nickel catalyst | III. Coal gasification | | D. Brine solution |…
Hydrogen and s-Block Elements · with solution
- The standard electrode potential (M^3+/M^2+) for V, Cr, Mn & Co are -0.26 V, -0.41 V, +1.57 V and +1.97 V, respectively. The metal ions which can liberate H_2 from a dilute acid are
d- and f-Block Elements · with solution
- Which of the following represents the correct order of metallic character of the given elements?
Periodic Classification · with solution
- Reaction of BeO with ammonia and hydrogen fluoride gives A which on thermal decomposition gives BeF_2 and NH_4F. What is 'A' ?
Hydrogen and s-Block Elements · with solution
- The metal which is extracted by oxidation and subsequent reduction from its ore is:
General Principles of Metallurgy
- The compound P (shown below) is converted to PhCOOH (Q) and PhCH_2OH (R): [figure] The correct sequence of reagents for the preparation of Q and R is:
Aldehydes Ketones and Acids
- Given below are two statements: Statement I : In froth floatation method a rotating paddle agitates the mixture to drive air out of it. Statement II : Iron pyrites are generally avoided for extraction of iron due to…
General Principles of Metallurgy · with solution
- Number of cyclic tripeptides formed with 2 amino acids A and B is:
Biomolecules · with solution
- Order of Covalent bond: A. KF > KI ; LiF > KF B. KF KF C. SnCl_4 > SnCl_2 ; CuCl > NaCl D. LiF > KF ; CuCl NaCl Choose the correct answer from the options given below:
Chemical Bonding · with solution
- Given below are two statements: Statement I : Pure Aniline and other arylamines are usually colourless. Statement II : Arylamines get coloured on storage due to atmospheric reduction In the light of the above…
Amines and Nitrogen Compounds · with solution
- Compound A reacts with NH_4Cl and forms a compound B. Compound B reacts with H_2O and excess of CO_2 to form compound C which on passing through or reaction with saturated NaCl solution forms sodium hydrogen carbonate.…
Some Basic Concepts of Chemistry · with solution
- For 1 mol of gas, the plot of pV vs. p is shown below. p is the pressure and V is the volume of the gas What is the value of compressibility factor at point A? [figure]
States of Matter · with solution
- Given below are two statements, one is labelled as Assertion A and the other is labelled as Reason R Assertion A: The alkali metals and their salts impart characteristic colour to reducing flame. Reason R: Alkali metals…
Hydrogen and s-Block Elements · with solution
- Which of the following is true about freons?
Environmental Chemistry · with solution
- Given below are two statements: Statement I : H_2N-containing compound under Clemmensen reduction conditions will give HOOC-containing compound Statement II : Cl-containing ketone under Wolff-Kishner reduction condition…
Basic Principles of Organic Chemistry
- Match List I with List II | LIST I (Name of polymer) | LIST II (Uses) | |---|---| | A. Glyptal | I. Flexible pipes | | B. Neoprene | II. Synthetic wool | | C. Acrilan | III. Paints and Lacquers | | D. LDP | IV. Gaskets…
Coordination Compounds
- Match List I with List II. | List I | List II | |---|---| | Antimicrobials | Names | | (A) Narrow Spectrum Antibiotic | (I) Furacin | | (B) Antiseptic | (II) Sulphur dioxide | | (C) Disinfectants | (III) Penicillin G |…
Chemistry in Everyday Life · with solution
- An ammoniacal metal salt solution gives a brilliant red precipitate on addition of dimethylglyoxime. The metal ion is:
d- and f-Block Elements · with solution
- Given below are two statements, one is labelled as Assertion A and the other is labelled as Reason R Assertion A: Beryllium has less negative value of reduction potential compared to the other alkaline earth metals.…
Hydrogen and s-Block Elements · with solution
- The compound which will have the lowest rate towards nucleophilic aromatic substitution on treatment with OH^- is
Haloalkanes and Haloarenes
- Identify the correct order for the given property for following compounds. (A) Boiling Point: frownCl frownCl > frownCl Choose the correct answer from the option given below: [figure]
Basic Principles of Organic Chemistry
- Which of the Phosphorus oxoacid can create silver mirror from AgNO_3 solution?
p-Block Elements · with solution
- Correct statement is:
Coordination Compounds · with solution
- What is the mass ratio of ethylene glycol (C_2H_6O_2, molar mass = 62 g/mol) required for making 500 g of 0.25 molal aqueous solution and 250 mL of 0.25 molal aqueous solution?
Solutions · with solution
- Identify the product formed (A and E) [figure]
Basic Principles of Organic Chemistry
- Chiral complex from the following is: Here en = ethylene diamine
Coordination Compounds · with solution
- Match List I with List II | LIST I (Amines) | LIST II (pK_b) | |---|---| | A. Aniline | I. 3.25 | | B. Ethanamine | II. 3.00 | | C. N-Ethylethanamine | III. 9.38 | | D. N, N-Diethylethanamine | IV. 3.29 | Choose the…
Amines and Nitrogen Compounds · with solution
- Match List I with List II | LIST I | LIST II | |---|---| | A. Chlorophyll | I. Na_2CO_3 | | B. Soda ash | II. CaSO_4 | | C. Dentistry, Ornamental work | III. Mg^2+ | | D. Used in white washing | IV. Ca(OH)_2 | Choose…
Hydrogen and s-Block Elements · with solution
- Reaction of thionyl chloride with white phosphorus forms a compound [A], which on hydrolysis gives [B], a dibasic acid. [A] and [B] are respectively
p-Block Elements · with solution
- Which of the following salt solutions would coagulate the colloid solution formed when FeCl_3 is added to NaOH solution, at the fastest rate?
Surface Chemistry · with solution
- Increasing order of stability of the resonance structures is: [figure] Choose the correct answer from the options given below:
Chemical Bonding
- Match List I with List II | LIST I (Type) | LIST II (Name) | |---|---| | A. Antifertility drug | I. Norethindrone | | B. Tranquilizer | II. Meprobomate | | C. Antihistamine | III. Seldane | | D. Antibiotic | IV.…
Chemistry in Everyday Life · with solution
- 'A' in the given reaction is [figure]
Aldehydes Ketones and Acids
- Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R : Assertion A : Acetal / Ketal is stable in basic medium. Reason R : The high leaving tendency of alkoxide ion gives…
Aldehydes Ketones and Acids · with solution
- Match List I with List II | | LIST I (Isomeric pairs) | LIST II (Type of isomers) | |---|---|---| | A. | Propanamine and N-Methylethanamine | I. Metamers | | B. | Hexan-2-one and Hexan-3-one | II. Positional isomers | |…
Basic Principles of Organic Chemistry · with solution
- The bond dissociation energy is highest for
Chemical Bonding · with solution
- Match List I with List II | LIST I | | LIST II | |---|---|---| | A. | Reverberatory furnace | I. Pig Iron | | B. | Electrolytic cell | II. Aluminum | | C. | Blast furnace | III. Silicon | | D. | Zone Refining furnace |…
General Principles of Metallurgy · with solution
- Choose the correct representation of conductometric titration of benzoic acid vs sodium hydroxide.
Practical Chemistry
- '25 volume' hydrogen peroxide means
Solutions · with solution
- The shortest wavelength of hydrogen atom in Lyman series is λ. The longest wavelength in Balmer series of He^+ is
Atomic Structure · with solution
- Given below are two statements, one is labelled as Assertion A and the other is labelled as Reason R Assertion A : Benzene is more stable than hypothetical cyclohexatriene Reason R : The delocalized π electron cloud is…
Hydrocarbons · with solution
- Which one of the following reactions does not occur during extraction of copper?
General Principles of Metallurgy · with solution
- Given below are two statements, one is labelled as Assertion A and the other is labelled as Reason R Assertion A : Carbon forms two important oxides - CO and CO_2. CO is neutral whereas CO_2 is acidic in nature Reason R…
p-Block Elements · with solution
- The magnetic behavior of Li_2O, Na_2O_2 and KO_2, respectively, are
Hydrogen and s-Block Elements · with solution
- Decreasing order of the hydrogen bonding in following forms of water is correctly represented by A. Liquid water B. Ice C. Impure water Choose the correct answer from the options given below:
Hydrogen and s-Block Elements · with solution
- The number of s-electrons present in an ion with 55 protons in its unipositive state is
Atomic Structure
- A cubic solid is made up of two elements X and Y. Atoms of X are present on every alternate corner and one at the center of cube. Y is at 1/3rd of the total faces. The empirical formula of the compound is
States of Matter
- The isomeric deuterated bromide with molecular formula C_4H_8DBr having two chiral carbon atoms is
Haloalkanes and Haloarenes · with solution
- When the hydrogen ion concentration [H^+] changes by a factor of 1000, the value of pH of the solution ________
Equilibrium · with solution
- The major product 'P' for the following sequence of reactions is: PhoversetOoverset|C - oversetOoverset|C - NH_2 →beginarrayl1) Zn/Hg\ HCl\ 2) LiAlH_4\ 3) H_3O^+endarray 'P' major product [figure]
Hydrocarbons
- The primary and secondary valencies of cobalt respectively in [Co(NH_3)_5Cl]Cl_2 are:
Coordination Compounds
- The hybridization and magnetic behaviour of cobalt ion in [Co(NH_3)_6]^3+ complex, respectively is
Coordination Compounds · with solution
- Match the List-I with List-II : | List-I | List-II | |---|---| | Cations | Group reagents | | A arrow Pb^2+, Cu^2+ | i) H_2S gas in presence of dilute HCl | | B arrow Al^3+, Fe^3+ | ii) (NH_4)_2CO_3 in presence of…
Practical Chemistry
- A chloride salt solution acidified with dil.HNO_3 gives a curdy white precipitate, [A], on addition of AgNO_3. [A] on treatment with NH_4OH gives a clear solution, B. A and B are respectively
Practical Chemistry · with solution
- Which of the given compounds can enhance the efficiency of hydrogen storage tank?
Hydrogen and s-Block Elements · with solution
- The electric potential at the centre of two concentric half rings of radii R_1 and R_2, having same linear charge density λ is : [figure]
Atomic Structure
- A student has studied the decomposition of a gas AB_3 at 25°C. He obtained the following data. | p (mm Hg) | 50 | 100 | 200 | 400 | |---|---|---|---|---| | relative t_1/2 (s) | 4 | 2 | 1 | 0.5 | The order of the…
Chemical Kinetics · with solution
- Some reactions of NO_2 relevant to photochemical smog formation are NO_2 →[sunlight] X + Y X →[A] B Identify A, B, X and Y
Environmental Chemistry · with solution
- A. Ammonium salts produce haze in atmosphere. B. Ozone gets produced when atmospheric oxygen reacts with chlorine radicals. C. Polychlorinated biphenyls act as cleansing solvents. D. 'Blue baby' syndrome occurs due to…
Environmental Chemistry · with solution
- Match List I with List II. | List I | List II | |---|---| | Reaction | Reagents | | (A) Hoffmann Degradation | (I) Conc.KOH, Δ | | (B) Clemenson reduction | (II) CHCl_3, NaOH/H_2O^oplus | | (C) Cannizaro reaction |…
Amines and Nitrogen Compounds · with solution
- In the depression of freezing point experiment A. Vapour pressure of the solution is less than that of pure solvent B. Vapour pressure of the solution is more than that of pure solvent C. Only solute molecules solidify…
Solutions · with solution
- What is the number of unpaired electron(s) in the highest occupied molecular orbital of the following species : N_2 ; N_2^+ ; O_2 ; O_2^+ ?
Chemical Bonding · with solution
- Which of the following conformations will be the most stable ?
Basic Principles of Organic Chemistry
- The increasing order of pK_a for the following phenols is (A) 2, 4 - Dinitrophenol (B) 4 - Nitrophenol (C) 2, 4, 5 - Trimethylphenol (D) Phenol (E) 3-Chlorophenol Choose the correct answer from the option given below:
Alcohols Phenols and Ethers · with solution
- Compound (X) undergoes following sequence of reactions to give the Lactone (Y). [figure] Compound (X) is
Aldehydes Ketones and Acids
- Choose the correct colour of the product for the following reaction. [figure] + 1-Naphthyl amine arrow
Amines and Nitrogen Compounds · with solution
- Match items of Row I with those of Row II. Row I: [figure] Row II: (i) α-D-(-)-Fructofuranose, (ii) β-D-(-)-Fructofuranose (iii) α-D-(-) Glucopyranose, (iv) β-D-(-)-Glucopyranose Correct match is
Biomolecules
- Given below are two statements, one is labelled as Assertion A and the other is labelled as Reason R Assertion A : Butylated hydroxy anisole when added to butter increases its shelf life. Reason R : Butylated hydroxy…
Chemistry in Everyday Life · with solution
- Following figure shows dependence of molar conductance of two electrolytes on concentration. Am is the limiting molar conductance. The number of incorrect statement(s) from the following is ______ (A) Am for electrolyte…
Redox and Electrochemistry · with solution
- Number of moles of AgCl formed in the following reaction is __________ [figure]
Coordination Compounds
- Sum of π – bonds present in peroxodisulphuric acid and pyrosulphuric acid is __________
p-Block Elements · with solution
- How many of the following metal ions have similar value of spin only magnetic moment in gaseous state? (Given: Atomic number : V, 23; Cr, 24; Fe, 26; Ni, 28) V^3+, Cr^3+, Fe^2+, Ni^3+
d- and f-Block Elements · with solution
- Number of hydrogen atoms per molecule of a hydrocarbon A having 85.8 % carbon is ___________ (Given: Molar mass of A = 84 g mol^-1)
Basic Principles of Organic Chemistry · with solution
- Total number of moles of AgCl precipitated on addition of excess of AgNO_3 to one mole each of the following complexes [Co(NH_3)_4Cl_2]Cl, [Ni(H_2O)_6]Cl_2, [Pt(NH_3)_3Cl_2]Cl, and [Pd(NH_3)_4]Cl_2 is
Coordination Compounds · with solution
- Consider the following reaction approaching equilibrium at 27°C and 1 atm pressure A+B leftharpoons C+D The standard Gibbs's energy change (Δ_r G°) at 27°C is (–) __________ kJ mol^-1 (Nearest integer). (Given: R = 8.3…
Chemical Thermodynamics · with solution
- 5 g of NaOH was dissolved in deionized water to prepare a 450 mL stock solution. What volume (in mL) of this solution would be required to prepare 500 mL of 0.1 M solution? Given: Molar Mass of Na, O and H is 23, 16 and…
Solutions · with solution
- The number of units, which are used to express concentration of solutions from the following is Mass percent, Mole, Mole fraction, Molarity, ppm, Molality
Solutions · with solution
- An athlete is given 100 g of glucose (C_6H_12O_6) for energy. This is equivalent to 1800 kJ of energy. The 50% of this energy gained is utilized by the athlete for sports activities at the event. In order to avoid…
Chemical Thermodynamics · with solution
- The number of pairs of the solutions having the same value of the osmotic pressure from the following is ________. (Assume 100% ionization) A. 0.500 M C_2H_5OH (aq) and 0.25 M KBr (aq) B. 0.100 M K_4[Fe(CN)_6] (aq) and…
Solutions
- Following chromatogram was developed by adsorption of compound 'A' on a 6 cm TLC glass plate. Retardation factor of the compound 'A' is _______ × 10^-1. [figure]
Practical Chemistry · with solution
- The number of correct statement/s from the following is __________ A. Larger the activation energy, smaller is the value of the rate constant. B. The higher is the activation energy, higher is the value of the…
Chemical Kinetics
- Maximum number of isomeric monochloro derivatives which can be obtained from 2,2,5,5-tetramethylhexane by chlorination is __________
Haloalkanes and Haloarenes
- Based on the given figure, the number of correct statement/s is/are ___________ A. Surface tension is the outcome of equal attractive and repulsive forces acting on the liquid molecule in bulk. B. Surface tension is due…
States of Matter · with solution
- The sum of bridging carbonyls in W(CO)_6 and Mn_2(CO)_10 is ________
Coordination Compounds · with solution
- At 298 K, a 1 litre solution containing 10 mmol of Cr_2O_7^2- and 100 mmol of Cr^3+ shows a pH of 3.0. Given: Cr_2O_7^2- arrow Cr^3+; E° = 1.330V and (2.303 RT)/F = 0.059 V The potential for the half cell reaction is x…
Redox and Electrochemistry · with solution
- Following figure shows spectrum of an ideal black body at four different temperatures. The number of correct statement/s from the following is __________ A. T_4 > T_3 > T_2 > T_1 B. The black body consists of particles…
Atomic Structure
- The number of molecules or ions from the following, which do not have odd number of electrons are ___________. (A) NO_2 (B) ICl_2^- (C) BrF_3 (D) ClO_2 (E) NO_2^+ (F) NO
Chemical Bonding · with solution
- Uracil is a base present in RNA with the following structure. % of N in uracil is ___________ [figure] Given : Molar mass N = 14 g mol^-1 O = 16 g mol^-1 C = 12 g mol^-1 H = 1 g mol^-1
Some Basic Concepts of Chemistry
- The total number of lone pairs of electrons on oxygen atoms of ozone is __________.
p-Block Elements
- 28.0 L of CO_2 is produced on complete combustion of 16.8 L gaseous mixture of ethene and methane at 25°C and 1 atm. Heat evolved during the combustion process is _________ kJ. Given : Δ H_c (CH_4) = -900 kJ mol^-1 Δ…
Chemical Thermodynamics · with solution
- Water decomposes at 2300 K H_2O(g) arrow H_2(g) + 1/2O_2(g) The percent of water decomposing at 2300 K and 1 bar is __________ (Nearest integer). Equilibrium constant for the reaction is 2 × 10^-3 at 2300 K.
Equilibrium · with solution
- The dissociation constant of acetic acid is x × 10^-5. When 25 mL of 0.2 M CH_3COONa solution is mixed with 25 mL of 0.02 M CH_3COOH solution, the pH of the resultant solution is found to be equal to 5. The value of x…
Equilibrium
- Consider the cell Pt(s) mid H_2(g) (1 atm) mid H^+(aq, [H^+]=1) ∥ Fe^3+(aq), Fe^2+(aq) mid Pt(s) Given E°_Fe^3+/Fe^2+ = 0.771 V and E°_H^+/1/2H_2 = 0 V, T = 298 K If the potential of the cell is 0.712 V, the ratio of…
Redox and Electrochemistry
- The number of given orbitals which have electron density along the axis is p_x, p_y, p_z, d_xy, d_xz, d_yz, d_x^2-y^2, d_z^2, s
Atomic Structure · with solution
- Millimoles of calcium hydroxide required to produce 100 mL of the aqueous solution of pH 12 is x × 10^-1. The value of x is _________ (Nearest integer). Assume complete dissociation.
Equilibrium · with solution
- For independent processes at 300 K | Process | Δ H/kJ mol^-1 | Δ S/J K^-1 | |---------|------------------------|----------------------| | A | -25 | -80 | | B | -22 | 40 | | C | 25 | -50 | | D | 22 | 20 | The number of…
Chemical Thermodynamics · with solution
- The total pressure observed by mixing two liquids A and B is 350 mm Hg when their mole fractions are 0.7 and 0.3 respectively. The total pressure becomes 410 mm Hg if the mole fractions are changed to 0.2 and 0.8…
Solutions
- The number of incorrect statement/s from the following is/are ____ A. Water vapours are adsorbed by anhydrous calcium chloride. B. There is a decrease in surface energy during adsorption. C. As the adsorption proceeds,…
Surface Chemistry · with solution
- Solid Lead nitrate is dissolved in 1 litre of water. The solution was found to boil at 100.15° C. When 0.2 mol of NaCl is added to the resulting solution, it was observed that the solution froze at -0.8° C. The…
Solutions
- When Fe_0.93O is heated in presence of oxygen, it converts to Fe_2O_3. The number of correct statement/s from the following is __________ A. The equivalent weight of Fe_0.93O is dfracMolecular weight0.79 B. The number…
Redox and Electrochemistry · with solution
- The osmotic pressure of solutions of PVC in cyclohexanone at 300 K are plotted on the graph. The molar mass of PVC is __________ g mol^-1 (Nearest integer) [figure] (Given : R = 0.083 L atm K^-1 mol^-1)
Solutions
- Number of compounds giving (i) red colouration with ceric ammonium nitrate and also (ii) positive iodoform test from the following is [figure]
Alcohols Phenols and Ethers
- If wavelength of the first line of the Paschen series of hydrogen atom is 720 nm, then the wavelength of the second line of this series is __________ nm. (Nearest integer)
Atomic Structure
- The number of statement/s which are the characteristics of physisorption is ________ A. It is highly specific in nature B. Enthalpy of adsorption is high C. It decreases with increase in temperature D. It results into…
Surface Chemistry · with solution
- A litre of buffer solution contains 0.1 mole of each of NH_3 and NH_4Cl. On the addition of 0.02 mole of HCl by dissolving gaseous HCl, the pH of the solution is found to be __________ × 10^-3 (Nearest integer) [Given :…
Equilibrium
- Pt(s)|H_2(g)(1 bar)|H^+(aq)(1 M)||M^3+(aq),M^2+(aq)|Pt(s) The E_cell for the given cell is 0.1115 V at 298 K when dfrac[M^2+(aq)][M^3+(aq)] = 10^a The value of a is ___________ Given : E^θ_M^3+/M^2+ = 0.2 V 2.303RT/F =…
Redox and Electrochemistry · with solution
- For certain chemical reaction X→Y, the rate of formation of product is plotted against the time as shown in the figure. The number of correct statement/s from the following is _____. (A) Over all order of this reaction…
Chemical Kinetics · with solution
- 17 mg of a hydrocarbon (M.F. C_10H_16) takes up 8.40 mL of the H_2 gas measured at 0°C and 760 mm of Hg. Ozonolysis of the same hydrocarbon yields CH_3-oversetdisplaystyle Ooversetdisplaystyle \|C-CH_3,…
Hydrocarbons · with solution
- The d-electronic configuration of [CoCl_4]^2- in tetrahedral crystal field is e^m t_2^n. Sum of "m" and "number of unpaired electrons" is _________
Coordination Compounds · with solution
- The number of statement/s, which are correct with respect to the compression of carbon dioxide from point (a) in the Andrews isotherm from the following is ___________ [figure]
States of Matter
- The number of paramagnetic species from the following is ___________. [Ni(CN)_4]^2-, [Ni(CO)_4], [NiCl_4]^2-, [Fe(CN)_6]^4-, [Cu(NH_3)_4]^2+ [Fe(CN)_6]^3- and [Fe(H_2O)_6]^2+
Coordination Compounds · with solution
Physics
- A stone is projected at angle 30° to the horizontal. The ratio of kinetic energy of the stone at point of projection to its kinetic energy at the highest point of flight will be -
Work Energy and Power · with solution
- From the photoelectric effect experiment, following observations are made. Identify which of these are correct. A. The stopping potential depends only on the work function of the metal. B. The saturation current…
Dual Nature of Radiation · with solution
- A body of mass 200g is tied to a spring of spring constant 12.5 N/m, while the other end of spring is fixed at point O. If the body moves about O in a circular path on a smooth horizontal surface with constant angular…
Rotational Motion · with solution
- The root mean square velocity of molecules of gas is
Kinetic Theory of Gases · with solution
- According to law of equipartition of energy the molar specific heat of a diatomic gas at constant volume where the molecule has one additional vibrational mode is:-
Kinetic Theory of Gases · with solution
- The light rays from an object have been reflected towards an observer from a standard flat mirror, the image observed by the observer are:- A. Real B. Erect C. Smaller in size then object D. Laterally inverted Select…
Ray Optics · with solution
- Match List I with List II: | List I (Physical Quantity) | List II (Dimensional Formula) | |---|---| | A. Pressure gradient | I. [M^0L^2T^-2] | | B. Energy density | II. [M^1L^-1T^-2] | | C. Electric Field | III.…
Units and Measurements · with solution
- Given below are two statements : Statement I : If the Brewster's angle for the light propagating from air to glass is θ_B, then the Brewster's angle for the light propagating from glass to air is (π)/2 - θ_B Statement…
Wave Optics · with solution
- Match List I with List II | LIST I | | LIST II | |---|---|---| | A. | AM Broadcast | I. 88–108 MHz | | B. | FM Broadcast | II. 540–1600 kHz | | C. | Television | III. 3.7–4.2 GHz | | D. | Satellite Communication | IV.…
Electromagnetic Waves · with solution
- Match List I with List II | List I | List II | |---|---| | A. Surface tension | I. kg m^-1s^-1 | | B. Pressure | II. kg ms^-1 | | C. Viscosity | III. kg m^-1s^-2 | | D. Impulse | IV. kg s^-2 | Choose the correct answer…
Units and Measurements
- A particle executes simple harmonic motion between x = -A and x = A. If time taken by particle to go from x = 0 to A/2 is 2 s; then time taken by particle in going from x = A/2 to A is
Oscillations and Waves · with solution
- Find the mutual inductance in the arrangement, when a small circular loop of wire of radius 'R' is placed inside a large square loop of wire of side L (L gg R). The loops are coplanar and their centres coincide :…
Electromagnetic Induction and AC · with solution
- Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R Assertion A : Photodiodes are preferably operated in reverse bias condition for light intensity measurement. Reason R…
Semiconductor Electronics · with solution
- The frequency (v) of an oscillating liquid drop may depend upon radius (r) of the drop, density (ρ) of liquid and the surface tension (s) of the liquid as : v = r^a ρ^b s^c. The values of a, b and c respectively are
Units and Measurements · with solution
- Match List I with List II | List I (Current configuration) | List II (Magnitude of Magnetic Field at point O) | |---|---| | A. [straight wire with circular loop of radius r at center, current I] | I. B_0 = (mu_0 I)/(4π…
Units and Measurements
- If the height of transmitting and receiving antennas are 80 m each, the maximum line of sight distance will be: Given: Earth's radius = 6.4 × 10^6 m
Electromagnetic Waves · with solution
- Match List I with List II | | LIST I | | LIST II | |---|---|---|---| | A | Isothermal Process | I | Work done by the gas decreases internal energy | | B | Adiabatic Process | II | No change in internal energy | | C |…
Thermodynamics · with solution
- A circular loop of radius r is carrying current I A. The ratio of magnetic field at the center of circular loop and at a distance r from the center of the loop on its axis is:
Magnetism and Moving Charges
- Assume that the earth is a solid sphere of uniform density and a tunnel is dug along its diameter throughout the earth. It is found that when a particle is released in this tunnel, it executes a simple harmonic motion.…
Oscillations and Waves · with solution
- In a cuboid of dimension 2L × 2L × L, a charge q is placed at the center of the surface S having area of 4L^2. The flux through the opposite surface to S is given by
Electrostatics · with solution
- In E and K represent electric field and propagation vectors of the EM waves in vacuum, then magnetic field vector is given by: (ω - angular frequency):
Electromagnetic Waves · with solution
- If the distance of the earth from Sun is 1.5 × 10^6 km. Then the distance of an imaginary planet from Sun, if its period of revolution is 2.83 years is :
Gravitation · with solution
- A message signal of frequency 5 kHz is used to modulate a carrier signal of frequency 2 MHz. The bandwidth for amplitude modulation is:
Semiconductor Electronics
- The resistance of a wire is 5 Ω. Its new resistance in ohm if stretched to 5 times of its original length will be:
Current Electricity · with solution
- If a radioactive element having half-life of 30 min is undergoing beta decay, the fraction of radioactive element remains undecayed after 90 min. will be
Atoms and Nuclei · with solution
- As shown in the figure, a network of resistors is connected to a battery of 24V with an internal resistance of 3Ω. The currents through the resistors R_4 and R_5 are I_4 and I_5 respectively. The values of I_4 and I_5…
Current Electricity
- Let γ_1 be the ratio of molar specific heat at constant pressure and molar specific heat at constant volume of a monoatomic gas and γ_2 be the similar ratio of diatomic gas. Considering the diatomic gas molecule as a…
Kinetic Theory of Gases · with solution
- Consider a block kept on an inclined plane (inclined at 45°) as shown in the figure. If the force required to just push it up the incline is 2 times the force required to just prevent it from sliding down, the…
Laws of Motion · with solution
- Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R Assertion A: Photodiodes are used in forward bias usually for measuring the light intensity. Reason R: For a p-n…
Semiconductor Electronics
- Match List I with List II | | LIST I | | LIST II | |---|---|---|---| | A. | Young's Modulus (Y) | I. | [M L^-1 T^-1] | | B. | Co-efficient of Viscosity (η) | II. | [M L^2 T^-1] | | C. | Planck's Constant (h) | III. | [M…
Units and Measurements · with solution
- A block of mass m slides down the plane inclined at angle 30° with an acceleration g/4. The value of coefficient of kinetic friction will be:
Laws of Motion · with solution
- If two charges q_1 and q_2 are separated with distance 'd' and placed in a medium of dielectric constant K. What will be the equivalent distance between charges in air for the same electrostatic force?
Electrostatics · with solution
- Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. Assertion A: A pendulum clock when taken to Mount Everest becomes fast. Reason R: The value of g (acceleration due to…
Oscillations and Waves · with solution
- The energy levels of an atom is shown in figure. Which one of these transitions will result in the emission of a photon of wavelength 124.1nm ? Given (h = 6.62 × 10^-34 Js) [figure]
Atoms and Nuclei · with solution
- A bicycle tyre is filled with air having pressure of 270 kPa at 27°C. The approximate pressure of the air in the tyre when the temperature increases to 36°C is
Kinetic Theory of Gases · with solution
- The maximum vertical height to which a man can throw a ball is 136 m. The maximum horizontal distance upto which he can throw the same ball is:
Kinematics · with solution
- Given below are two statements: Statement I : Acceleration due to earth's gravity decreases as you go 'up' or 'down' from earth's surface. Statement II : Acceleration due to earth's gravity is same at a height 'h' and…
Gravitation · with solution
- In an LC oscillator, if values of inductance and capacitance become twice and eight times, respectively, then the resonant frequency of oscillator becomes x times its initial resonant frequency ω_0. The value of x is:
Electromagnetic Induction and AC · with solution
- In a Young's double slit experiment, two slits are illuminated with a light of wavelength 800 nm. The line joining A_1P is perpendicular to A_1A_2 as shown in the figure. If the first minimum is detected at P, the value…
Wave Optics · with solution
- Given below are two statements: Statement I: Stopping potential in photoelectric effect does not depend on the power of the light source. Statement II: For a given metal, the maximum kinetic energy of the photoelectron…
Dual Nature of Radiation · with solution
- Given below are two statements : Statement I : The temperature of a gas is -73°C. When the gas is heated to 527°C, the root mean square speed of the molecules is doubled. Statement II : The product of pressure and…
Kinetic Theory of Gases · with solution
- A metallic rod of length 'L' is rotated with an angular speed of 'ω' normal to a uniform magnetic field 'B' about an axis passing through one end of rod as shown in figure. The induced emf will be : [figure]
Electromagnetic Induction and AC
- A wire of length 1m moving with velocity 8 m/s at right angles to a magnetic field of 2T. The magnitude of induced emf, between the ends of wire will be ___________
Electromagnetic Induction and AC · with solution
- Ratio of thermal energy released in two resistors R and 3R connected in parallel in an electric circuit is :
Current Electricity · with solution
- If two vectors P = i + 2mj + mk and Q = 4i - 2j + mk are perpendicular to each other. Then, the value of m will be :
Kinematics
- The ratio of the density of oxygen nucleus (^16_8O) and helium nucleus (^4_2He) is
Atoms and Nuclei
- The threshold wavelength for photoelectric emission from a material is 5500 Å. Photoelectrons will be emitted, when this material is illuminated with monochromatic radiation from a A. 75 W infra-red lamp B. 10 W…
Dual Nature of Radiation · with solution
- Consider the following radioactive decay process ^218_84A →[α] A_1 →[β^-] A_2 →[γ] A_3 →[α] A_4 →[β^+] A_5 →[γ] A_6 The mass number and the atomic number of A_6 are given by:
Atoms and Nuclei · with solution
- The electric field and magnetic field components of an electromagnetic wave going through vacuum is described by E_x = E_0 sin(kz - ω t) B_y = B_0 sin(kz - ω t) Then the correct relation between E_0 and B_0 is given by
Electromagnetic Waves · with solution
- The graph between two temperature scales P and Q is shown in the figure. Between upper fixed point and lower fixed point there are 150 equal divisions of scale P and 100 divisions on scale Q. The relationship for…
Thermodynamics · with solution
- A uniform metallic wire carries a current 2 A, when 3.4 V battery is connected across it. The mass of uniform metallic wire is 8.92 × 10^-3 kg, density is 8.92 × 10^3 kg/m^3 and resistivity is 1.7 × 10^-8 Ω-m. The…
Current Electricity
- Every planet revolves around the sun in an elliptical orbit:- A. The force acting on a planet is inversely proportional to square of distance from sun. B. Force acting on planet is inversely proportional to product of…
Gravitation · with solution
- A single current carrying loop of wire carrying current I flowing in anticlockwise direction seen from +ve z direction and lying in xy plane is shown in figure. The plot of j component of magnetic field (By) at a…
Magnetism and Moving Charges
- The weight of a body at the surface of earth is 18 N. The weight of the body at an altitude of 3200 km above the earth's surface is (given, radius of earth R_e = 6400 km):
Gravitation
- The logic gate equivalent to the given circuit diagram is : [figure]
Semiconductor Electronics
- A solenoid of 1200 turns is wound uniformly in a single layer on a glass tube 2 m long and 0.2 m in diameter. The magnetic intensity at the center of the solenoid when a current of 2 A flows through it is:
Magnetism and Moving Charges · with solution
- Which one of the following statement is not correct in the case of light emitting diodes? A. It is a heavily doped p-n junction. B. It emits light only when it is forward biased. C. It emits light only when it is…
Semiconductor Electronics · with solution
- A conducting circular loop of radius frac10√(π) cm is placed perpendicular to a uniform magnetic field of 0.5 T. The magnetic field is decreased to zero in 0.5 s at a steady rate. The induced emf in the circular loop at…
Electromagnetic Induction and AC · with solution
- An α-particle, a proton and an electron have the same kinetic energy. Which one of the following is correct in case of their de-Broglie wavelength:
Dual Nature of Radiation · with solution
- An object of mass 8 kg is hanging from one end of a uniform rod CD of mass 2 kg and length 1 m pivoted at its end C on a vertical wall as shown in figure. It is supported by a cable AB such that the system is in…
Laws of Motion
- Match List I with List II | | LIST I | | LIST II | |---|---|---|---| | A | Troposphere | I | Approximate 65-75 km over Earth's surface | | B | E- Part of Stratosphere | II | Approximate 300 km over Earth's surface | | C…
Electromagnetic Waves · with solution
- Two particles of equal mass 'm' move in a circle of radius 'r' under the action of their mutual gravitational attraction. The speed of each particle will be :
Gravitation · with solution
- A body of mass is taken from earth surface to the height h equal to twice the radius of earth (R_e), the increase in potential energy will be: (g = acceleration due to gravity on the surface of Earth)
Gravitation · with solution
- Two long straight wires P and Q carrying equal current 10A each were kept parallel to each other at 5 cm distance. Magnitude of magnetic force experienced by 10 cm length of wire P is F_1. If distance between wires is…
Magnetism and Moving Charges · with solution
- When a beam of white light is allowed to pass through convex lens parallel to principal axis, the different colours of light converge at different point on the principle axis after refraction. This is called :
Ray Optics · with solution
- A parallel plate capacitor has plate area 40 cm^2 and plates separation 2 mm. The space between the plates is filled with a dielectric medium of a thickness 1 mm and dielectric constant 5. The capacitance of the system…
Electrostatics
- The magnitude of magnetic induction at mid point O due to current arrangement as shown in Fig will be [figure]
Magnetism and Moving Charges
- Given below are two statements : Statement I: An elevator can go up or down with uniform speed when its weight is balanced with the tension of its cable. Statement II: Force exerted by the floor of an elevator on the…
Laws of Motion · with solution
- A long solenoid is formed by winding 70 turns cm^-1. If 2.0 A current flows, then the magnetic field produced inside the solenoid is__________ (mu_o = 4π × 10^-7 TmA^-1)
Magnetism and Moving Charges · with solution
- Electron beam used in an electron microscope, when accelerated by a voltage of 20 kV, has a de-Broglie wavelength of λ_0. If the voltage is increased to 40 kV, then the de-Broglie wavelength associated with the electron…
Dual Nature of Radiation
- For a moving coil galvanometer, the deflection in the coil is 0.05 rad when a current of 10 mA is passed through it. If the torsional constant of suspension wire is 4.0 × 10^-5 N m rad^-1, the magnetic field is 0.01T…
Magnetism and Moving Charges · with solution
- A person observes two moving trains, 'A' reaching the station and 'B' leaving the station with equal speed of 30 m/s. If both trains emit sounds with frequency 300 Hz. (Speed of sound: 330 m/s) approximate difference of…
Oscillations and Waves · with solution
- A modulating signal is a square wave, as shown in the figure. [figure] If the carrier wave is given as c(t) = 2 sin(8π t) volts, the modulation index is:
Semiconductor Electronics
- T is the time period of simple pendulum on the earth's surface. Its time period becomes x T when taken to a height R (equal to earth's radius) above the earth's surface. Then, the value of x will be:
Gravitation · with solution
- Statement I: When a Si sample is doped with Boron, it becomes P type and when doped by Arsenic it becomes N-type semi conductor such that P-type has excess holes and N-type has excess electrons. Statement II: When such…
Semiconductor Electronics · with solution
- A point charge of 10 μC is placed at the origin. At what location on the X-axis should a point charge of 40 μC be placed so that the net electric field is zero at x = 2 cm on the X-axis?
Electrostatics · with solution
- Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R. Assertion A: If dQ and dW represent the heat supplied to the system and the work done on the system respectively.…
Thermodynamics · with solution
- A travelling wave is described by the equation y(x, t) = [0.05 sin(8x - 4t)] m The velocity of the wave is : [all the quantities are in SI unit]
Oscillations and Waves · with solution
- A photon is emitted in transition from n = 4 to n = 1 level in hydrogen atom. The corresponding wavelength for this transition is (given, h = 4 × 10^-15 eVs) :
Atoms and Nuclei · with solution
- In Young's double slits experiment, the position of 5^th bright fringe from the central maximum is 5 cm. The distance between slits and screen is 1 m and wavelength of used monochromatic light is 600 nm. The separation…
Wave Optics
- The distance travelled by a particle is related to time t as x = 4t^2. The velocity of the particle at t = 5s is:-
Kinematics · with solution
- Surface tension of a soap bubble is 2.0 × 10^-2 Nm^-1. Work done to increase the radius of soap bubble from 3.5 cm to 7 cm will be: Take [π = 22/7 ]
Properties of Matter · with solution
- A 100 m long wire having cross-sectional area 6.25 × 10^-4 m^2 and Young's modulus is 10^10 Nm^-2 is subjected to a load of 250 N, then the elongation in the wire will be:
Properties of Matter · with solution
- Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A : Steel is used in the construction of buildings and bridges. Reason R : Steel is more elastic and its…
Properties of Matter · with solution
- A car travels a distance of 'x' with speed v_1 and then same distance 'x' with speed v_2 in the same direction. The average speed of the car is:
Kinematics
- Two objects are projected with same velocity 'u' however at different angles α and β with the horizontal. If α + β = 90°, the ratio of horizontal range of the first object to the 2nd object will be:
Kinematics · with solution
- Which of the following are true? A. Speed of light in vacuum is dependent on the direction of propagation. B. Speed of light in a medium is independent of the wavelength of light. C. The speed of light is independent of…
Electromagnetic Waves · with solution
- 1 g of a liquid is converted to vapour at 3 × 10^5 Pa pressure. If 10% of the heat supplied is used for increasing the volume by 1600 cm^3 during this phase change, then the increase in internal energy in the process…
Thermodynamics · with solution
- In an Isothermal change, the change in pressure and volume of a gas can be represented for three different temperature; T_3 > T_2 > T_1 as :
Thermodynamics · with solution
- A bowl filled with very hot soup cools from 98°C to 86°C in 2 minutes when the room temperature is 22°C. How long it will take to cool from 75°C to 69°C?
Thermodynamics
- A car is moving on a horizontal curved road with radius 50 m. The approximate maximum speed of car will be, if friction between tyres and road is 0.34. [take g = 10 ms^-2]
Laws of Motion · with solution
- Match List I with List II | LIST I | LIST II | |---|---| | A. Planck's constant (h) | I. [M^1 L^2 T^-2] | | B. Stopping potential (Vs) | II. [M^1 L^1 T^-1] | | C. Work function (Ø) | III. [M^1 L^2 T^-1] | | D. Momentum…
Units and Measurements · with solution
- A cell of emf 90 V is connected across series combination of two resistors each of 100Ω resistance. A voltmeter of resistance 400Ω is used to measure the potential difference across each resistor. The reading of the…
Current Electricity · with solution
- An electromagnetic wave is transporting energy in the negative z direction. At a certain point and certain time the direction of electric field of the wave is along positive y direction. What will be the direction of…
Electromagnetic Waves · with solution
- Match List I with List II | LIST I | | LIST II | |---|---|---| | A. Gauss's Law in Electrostatics | I. | oint E · dl = -(dφ_B)/dt | | B. Faraday's Law | II. | oint B · dA = 0 | | C. Gauss's Law in Magnetism | III. |…
Electromagnetic Waves
- As shown in the figure, three identical polaroids P_1, P_2 and P_3 are placed one after another. The pass axis of P_2 and P_3 are inclined at angle of 60° and 90° with respect to axis of P_1. The source S has an…
Wave Optics · with solution
- A block of a mass 2 kg is attached with two identical springs of spring constant 20 N/m each. The block is placed on a frictionless surface and the ends of the springs are attached to rigid supports (see figure). When…
Oscillations and Waves · with solution
- A single turn current loop in the shape of a right angle triangle with sides 5 cm, 12 cm, 13 cm is carrying a current of 2 A. The loop is in a uniform magnetic field of magnitude 0.75 T whose direction is parallel to…
Magnetism and Moving Charges · with solution
- A uniform electric field of 10 N/C is created between two parallel charged plates (as shown in figure). An electron enters the field symmetrically between the plates with a kinetic energy 0.5 eV. The length of each…
Electrostatics
- A series LCR circuit is connected to an AC source of 220 V, 50 Hz. The circuit contains a resistance R = 80Ω, an inductor of inductive reactance X_L = 70Ω, and a capacitor of capacitive reactance X_C = 130Ω. The power…
Electromagnetic Induction and AC · with solution
- A solid sphere of mass 2 kg is making pure rolling on a horizontal surface with kinetic energy 2240 J. The velocity of centre of mass of the sphere will be ______ ms^-1.
Rotational Motion · with solution
- A Spherical ball of radius 1mm and density 10.5 g/cc is dropped in glycerine of coefficient of viscosity 9.8 poise and density 1.5 g/cc. Viscous force on the ball when it attains constant velocity is 3696 × 10^-x N. The…
Properties of Matter · with solution
- A ray of light is incident from air on a glass plate having thickness √(3) cm and refractive index √(2). The angle of incidence of a ray is equal to the critical angle for glass-air interface. The lateral displacement…
Ray Optics
- Two long parallel wires carrying currents 8A and 15A in opposite directions are placed at a distance of 7cm from each other. A point P is at equidistant from both the wires such that the lines joining the point P to the…
Magnetism and Moving Charges
- In a metre bridge experiment the balance point is obtained if the gaps are closed by 2 Ω and 3 Ω. A shunt of X Ω is added to 3 Ω resistor to shift the balancing point by 22.5 cm. The value of X is ___
Current Electricity
- Vectors ai + bj + k and 2i - 3j + 4k are perpendicular to each other when 3a + 2b = 7, the ratio of a to b is x/2. The value of x is __________.
Kinematics
- A convex lens of refractive index 1.5 and focal length 18cm in air is immersed in water. The change in focal length of the lens will be __________ cm. (Given refractive index of water = 4/3)
Ray Optics
- A body of mass 1 kg collides head on elastically with a stationary body of mass 3kg. After collision, the smaller body reverses its direction of motion and moves with a speed of 2m/s. The initial speed of the smaller…
Laws of Motion · with solution
- Two simple harmonic waves having equal amplitudes of 8 cm and equal frequency of 10 Hz are moving along the same direction. The resultant amplitude is also 8 cm. The phase difference between the individual waves is…
Oscillations and Waves · with solution
- A hole is drilled in a metal sheet. At 27°C, the diameter of hole is 5 cm. When the sheet is heated to 177°C, the change in the diameter of hole is d × 10^-3 cm. The value of d will be __________ if coefficient of…
Properties of Matter · with solution
- A body of mass 1kg begins to move under the action of a time dependent force F = (i + 3t^2j) N, where i and j are the unit vectors along x and y axis. The power developed by above force, at the time t = 2s, will be…
Work Energy and Power
- A nucleus disintegrates into two smaller parts, which have their velocities in the ratio 3:2. The ratio of their nuclear sizes will be (x/3 )^1/3. The value of 'x' is:-
Atoms and Nuclei · with solution
- A certain elastic conducting material is stretched into a circular loop. It is placed with its plane perpendicular to a uniform magnetic field B = 0.8 T. When released the radius of the loop starts shrinking at a…
Electromagnetic Induction and AC · with solution
- Assume that protons and neutrons have equal masses. Mass of a nucleon is 1.6 × 10^-27 kg and radius of nucleus is 1.5 × 10^-15 A^1/3 m. The approximate ratio of the nuclear density and water density is n × 10^13. The…
Atoms and Nuclei · with solution
- The energy released per fission of nucleus of ^240X is 200 MeV. The energy released if all the atoms in 120g of pure ^240X undergo fission is __________ × 10^25 MeV. (Given N_A = 6 × 10^23)
Atoms and Nuclei · with solution
- The wavelength of the radiation emitted is λ_o when an electron jumps from the second excited state to the first excited state of hydrogen atom. If the electron jumps from the third excited state to the second orbit of…
Atoms and Nuclei · with solution
- If a solid sphere of mass 5kg and a disc of mass 4kg have the same radius. Then the ratio of moment of inertia of the disc about a tangent in its plane to the moment of inertia of the sphere about its tangent will be…
Rotational Motion · with solution
- A point charge q_1 = 4q_0 is placed at origin. Another point charge q_2 = -q_0 is placed at x = 12 cm. Charge of proton is q_0. The proton is placed on x axis so that the electrostatic force on the proton is zero. In…
Electrostatics
- A spherical body of mass 2 kg starting from rest acquires a kinetic energy of 10000 J at the end of 5^th second. The force acted on the body is __________ N.
Laws of Motion · with solution
- A parallel plate capacitor with air between the plate has a capacitance of 15pF. The separation between the plate becomes twice and the space between them is filled with a medium of dielectric constant 3.5. Then the…
Electrostatics · with solution
- A capacitor has capacitance 5μ F when it's parallel plates are separated by air medium of thickness d. A slab of material of dielectric constant 1.5 having area equal to that of plates but thickness d/2 is inserted…
Electrostatics
- A radioactive element ^210_84X emits two α-particles, one electron and two positrons. The product nucleus is represented by ^Z_PY. The value of P is
Atoms and Nuclei
- A train blowing a whistle of frequency 320 Hz approaches an observer standing on the platform at a speed of 66 m/s. The frequency observed by the observer will be (given speed of sound = 330 ms^-1) ________ Hz.
Oscillations and Waves · with solution
- As shown in the figure, a combination of a thin plano concave lens and a thin plano convex lens is used to image an object placed at infinity. The radius of curvature of both the lenses is 30 cm and refraction index of…
Ray Optics
- A mass m attached to free end of a spring executes SHM with a period of 1s. If the mass is increased by 3 kg the period of oscillation increases by one second, the value of mass m is __________ kg.
Oscillations and Waves · with solution
- If P = 3i + √(3)j + 2k and Q = 4i + √(3)j + 2.5k then. The unit vector in the direction of P × Q is 1/x (√(3)i + j - 2√(3)k ). The value of x is
Rotational Motion · with solution
- A tennis ball is dropped on to the floor from a height of 9.8 m. It rebounds to a height 5.0 m. Ball comes in contact with the floor for 0.2s. The average acceleration during contact is __________ ms^-2. (Given g = 10…
Kinematics · with solution
- Solid sphere A is rotating about an axis PQ. If the radius of the sphere is 5 cm then its radius of gyration about PQ will be √(x) cm. The value of x is __________. [figure]
Rotational Motion
- A uniform solid cylinder with radius R and length L has moment of inertia I_1, about the axis of the cylinder. A concentric solid cylinder of radius R' = R/2 and length L' = L/2 is carved out of the original cylinder.…
Rotational Motion · with solution
- In the given circuit, the equivalent resistance between the terminal A and B is ____________ Ω. [figure]
Current Electricity
- Two cells are connected between points A and B as shown. Cell 1 has emf of 12 V and internal resistance of 3Ω. Cell 2 has emf of 6V and internal resistance of 6Ω. An external resistor R of 4Ω is connected across A and…
Current Electricity
- A 0.4 kg mass takes 8s to reach ground when dropped from a certain height 'P' above surface of earth. The loss of potential energy in the last second of fall is _________ J. (Take g = 10 m/s²)
Work Energy and Power · with solution
- A stream of a positively charged particles having q/m = 2 × 10^11 C/kg and velocity v_0 = 3 × 10^7 i m/s is deflected by an electric field 1.8j kV/m. The electric field exists in a region of 10 cm along x direction. Due…
Electrostatics · with solution
- The distance between two consecutive points with phase difference of 60° in a wave of frequency 500 Hz is 6.0 m. The velocity with which wave is traveling is __________ km/s
Oscillations and Waves
- A body cools from 60°C to 40°C in 6 minutes. If, temperature of surroundings is 10°C. Then, after the next 6 minutes, its temperature will be ________°C.
Thermodynamics · with solution
- A hollow cylindrical conductor has length of 3.14 m, while its inner and outer diameters are 4 mm and 8 mm respectively. The resistance of the conductor is n × 10^-3Ω. If the resistivity of the material is 2.4 ×…
Current Electricity · with solution
- Three identical resistors with resistance R = 12Ω and two identical inductors with self inductance L = 5 mH are connected to an ideal battery with emf of 12 V as shown in figure. The current through the battery long…
Current Electricity
- I_CM is the moment of inertia of a circular disc about an axis (CM) passing through its center and perpendicular to the plane of disc. I_AB is it's moment of inertia about an axis AB perpendicular to plane and parallel…
Rotational Motion
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