1980 (AIEEE / IIT-JEE, in the JEE Main bank) questions

Mathematics

1. Two events A and B have probabilities 0.25 and 0.50, respectively. The probability that both A and B occur simultaneously is 0.14. Then, the probability that neither A nor B occurs, is

   Probability · with solution

2. Given the four lines with the equations x + 2y - 3 = 0, 3x + 4y - 7 = 0, 2x + 3y - 4 = 0, 4x + 5y - 6 = 0, then

   Straight Lines and Pair of Lines

3. The different letters of an alphabet are given. Words with five letters are formed from these given letters. Then, the number of words which have at least one letter repeated, is

   Permutations and Combinations · with solution

4. Two circles x^2 + y^2 = 6 and x^2 + y^2 - 6x + 8 = 0 are given. Then the equation of the circle through their points of intersection and the point (1, 1) is

   Circles · with solution

5. The value of the expression ^47C_4 + sum_j=1^5 ^52-jC_3 is

   Permutations and Combinations · with solution

6. Given A = sin^2θ + cos^4θ, then for all real values of θ

   Trigonometry · with solution

7. The probability that an event A happens in one trial of an experiment, is 0.4. Three independent trials of the experiments are performed. The probability that the event A happens atleast once, is

   Probability · with solution

8. Given positive integers r > 1, n > 2 and the coefficient of (3r)th and (r + 2)th terms in the binomial expansion of (1 + x)^2n are equal. Then,

   Binomial Theorem · with solution

9. Both the roots of the equation (x-b)(x-c) + (x-a)(x-c) + (x-a)(x-b) = 0 are always

   Complex Numbers and Quadratic Equations · with solution

10. The point (4, 1) undergoes the following three transformations successively I. Reflection about the line y = x. II. Transformation through a distance 2 units along the positive direction of X-axis. III. Rotation through…

    Straight Lines and Pair of Lines · with solution