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JEE 2020 Mathematics : Sets and Functions

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Question 1

Let S = {1, 2, …., 20}. A subset B of S is said to be “nice”, if the sum of the elements of B is 203. Then the probability that a randomly chosen subset of S is “nice” is:

Question 2

Let A and B be 2 sets. Then,

is?

Question 3

Let A and B be 2 sets such that

and A U X = B U X, then which of the following is true?

Question 4

If A = {x : x is a prime factor of 240} and B = {y : y is a prime factors of 512}, then which is true?

Question 5

If P(S) denotes the set of all subsets of a given set S, then the number of one-to-one functions from the set S = {1, 2, 3} to the set P(S) is

Question 6

If X = {8ⁿ-7n – 1: n ∈ N} and Y = {49(n – 1): n ∈ N}, then and

Question 7

Consider the following relation R on the set of real square matrices of order 3.

R = {(A, B) |A = P^-1 BP for some invertible matrix P}.

Statement -1:

R is equivalence relation.

Statement - 2:

For any two invertible 3 × 3 matrices M and N, (MN)^-1 = N^-¹ M^-1.

Question 8

If the function f given by f(x) = x³ – 3(a – 2)x² + 3ax + 7, for some aϵR is increasing in (0, 1] and decreasing in [1, 5), then a root of the equation,

is :

Question 9

Let function f = (0,∞ )→ (0,∞) be defined by

. Then f is :

Question 10

then

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May 26JEE & BITSAT