1987 (AIEEE / IIT-JEE, in the JEE Main bank) questions

Mathematics

1. The probability that at least one of the events A and B occurs is 0.6. If A and B occur simultaneously with probability 0.2, then P(A) + P(B) is equal to

   Probability · with solution

2. If z_1 and z_2 are two non-zero complex numbers such that |z_1 + z_2| = |z_1| + |z_2|, then arg(z_1) - arg(z_2) is equal to

   Complex Numbers and Quadratic Equations · with solution

3. The smallest positive root of the equation tan x - x = 0 lies in

   Trigonometry · with solution

4. The number of all possible triplets (a_1, a_2, a_3) such that a_1 + a_2 cos(2x) + a_3 sin^2(x) = 0, forall x is

   Trigonometry · with solution

5. If a, b, c, d and p are distinct real numbers such that (a^2 + b^2 + c^2) p^2 - 2(ab + bc + cd) p + (b^2 + c^2 + d^2) ≤ 0, then a, b, c, d

   Sequences and Series · with solution

6. The number of vectors of unit length perpendicular to vectors a = (1, 1, 0) and b = (0, 1, 1) is

   Vector Algebra · with solution

7. The set of all points, where the function f(x) = x/(1+|x|) is differentiable, is

   Limits Continuity and Differentiability · with solution