2010 (AIEEE / IIT-JEE, in the JEE Main bank) questions
9 questions, by subject. Each opens with its options and answer.
Mathematics
- For r = 0, 1, …, 10, if A_r, B_r and C_r denote respectively the coefficient of x^r in the expansions of (1+x)^10, (1+x)^20 and (1+x)^30. Then, sum_r=1^10 A_r (B_10B_r - C_10A_r) is equal to
Binomial Theorem
- If the angles A, B and C of a triangle are in an arithmetic progression and if a, b and c denote the lengths of the sides opposite to A, B and C respectively, then the value of the expression a/csin 2C + c/asin 2A is
Trigonometry · with solution
- Two adjacent sides of a parallelogram ABCD are given by AB = 2i + 10j + 11k and AD = -i + 2j + 2k. The side AD is rotated by an acute angle α in the plane of the parallelogram so that AD becomes AD'. If AD' makes a…
Vector Algebra · with solution
- Let P, Q, R and S be the points on the plane with position vectors -2i - j, 4i, 3i + 3j and -3i + 2j, respectively. The quadrilateral PQRS must be a
Vector Algebra · with solution
- Let ω be a complex cube root of unity with ω ≠ 1. A fair die is thrown three times. If r_1, r_2 and r_3 are the numbers obtained on the die, then the probability that ω^r_1 + ω^r_2 + ω^r_3 = 0, is
Probability
- The number of 3 × 3 matrices A whose entries are either 0 or 1 and for which the system A beginbmatrix x \ y \ z endbmatrix = beginbmatrix 1 \ 0 \ 0 endbmatrix has exactly two distinct solutions, is
Matrices and Determinants
- Let f, g and h be real-valued functions defined on the interval [0, 1] by f(x) = e^x^2 + e^-x^2, g(x) = xe^x^2 + e^-x^2 and h(x) = x^2e^x^2 + e^-x^2. If a, b and c denote respectively, the absolute maximum of f, g and h…
Application of Derivatives
- If the distance of the point P(1, -2, 1) from the plane x + 2y - 2z = α, where α > 0, is 5, then the foot of the perpendicular from P to the plane is
Three Dimensional Geometry
Physics
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