1982 (AIEEE / IIT-JEE, in the JEE Main bank) questions

Mathematics

1. Eight chairs are numbered 1 to 8. Two women and three men wish to occupy one chair each. First the women choose the chairs from amongst the chairs marked 1 to 4 and then the men select the chairs from amongst the…

   Permutations and Combinations

2. The third term of a geometric progression is 4. The product of the first five terms is

   Sequences and Series · with solution

3. For non-zero vectors a, b, c, |(a × b) · c|= |a||b||c| holds, if and only if

   Vector Algebra · with solution

4. If x_1, x_2, …, x_n are any real numbers and n is any positive integer, then

   Sequences and Series

5. If A and B are two independent events such that P(A) > 0, and P(B) ≠ 1, then P(A/B) is equal to

   Probability · with solution

6. The inequality |z-4| < |z-2| represents the region given by

   Complex Numbers and Quadratic Equations

7. If z = (dfrac√(3)2 + i/2 )^5 + (dfrac√(3)2 - i/2 )^5, then

   Complex Numbers and Quadratic Equations

8. There exists a function f(x) satisfying f(0)=1, f'(0)=-1, f(x)>0, forall x and

   Limits Continuity and Differentiability

9. If p, q and r are any real numbers, then

   Application of Derivatives · with solution

10. The number of real solutions of the equation |x|^2 - 3|x| + 2 = 0 is

    Complex Numbers and Quadratic Equations · with solution