ExamHabit
Practise free

1989 (AIEEE / IIT-JEE, in the JEE Main bank) questions

10 questions, by subject. Each opens with its options and answer.

Mathematics

  1. Let a, b, c be real numbers, a ≠ 0. If α is a root of a^2x^2 + bx + c = 0, β is the root of a^2x^2 - bx - c = 0 and 0 < α < β, then the equation a^2x^2 + 2bx + 2c = 0 has a root γ that always satisfies

    Complex Numbers and Quadratic Equations

  2. If f(x) = 1/2 - x - 1, then on the interval [0, π]

    Limits Continuity and Differentiability

  3. A five digits number divisible by 3 is to be formed using the numbers 0, 1, 2, 3, 4 and 5, without repetition. The total number of ways this can be done, is

    Permutations and Combinations

  4. The lines 2x - 3y = 5 and 3x - 4y = 7 are diameters of a circle of area 154 sq units. Then, the equation of this circle is

    Circles

  5. If the two circles (x-1)^2 + (y-3)^2 = r^2 and x^2 + y^2 - 8x + 2y + 8 = 0 intersect in two distinct points, then

    Circles · with solution

  6. The general solution of sin x - 3sin 2x + sin 3x = cos x - 3cos 2x + cos 3x is

    Trigonometry · with solution

  7. The equation x^3/4(log_2 x)^2 + log_2 x - 5/4 = √(2) has

    Complex Numbers and Quadratic Equations · with solution

  8. If α and β are the roots of x^2 + px + q = 0 and α^4, β^4 are the roots of x^2 - rx + s = 0, then the equation x^2 - 4qx + 2q^2 - r = 0 has always

    Complex Numbers and Quadratic Equations

Chemistry

  1. The correct set of quantum numbers for the unpaired electron of chlorine atom is

    Atomic Structure · with solution

  2. The correct ground state electronic configuration of chromium atom is

    Atomic Structure · with solution

Practise JEE Main every day

Five real previous-year questions a day, graded as the exam grades. No sign-up.

Start today's five