CUET (UG) entrance exam Question Bank Solutions

The value of k for which the system of equations x + ky + 3z = 0, 4x + 3y + kz = 0, 2x + y + 2z = 0 has nontrivial solution is

Let A = `((cos^2x, sin^2x),(sin^2x, cos^2x))` and B = `((sin^2x, cos^2x),(cos^2x, sin^2x))`. Then the determinant of the matrix A + B is

If A is a finite set consisting of n elements, then the number of reflexive relations on A is

The function f: N → N, where

f(n) = `{{:(1/2(n + 1), "If n is sold"),(1/2n, "if n is even"):}` is

If 0 < P(A) < 1, 0 < P(B) < 1 and P(A ∪ B) = P(A) + P(B) – P(A)P(B), then 

The value of f(0) for the function `f(x) = 1/x[log(1 + x) - log(1 - x)]` to be continuous at x = 0 should be

If `f`: R → {0, 1} is a continuous surjection map then `f^(-1) (0) ∩ f^(-1) (1)` is:

The relation > (greater than) on the set of real numbers is

Which one of the following relations on the set of real numbers R is an equivalence relation?

Form the point of intersection (P) of lines given by x₂ – y² – 2x + 2y = 0, points A, B, C, Dare taken on the lines at a distance of `2sqrt(2)` units to form a quadrilateral whose area is A₁ and the area of the quadrilateral formed by joining the circumcentres of ΔPAB, ΔPBC, ΔPCD, ΔPDA is A₂, then `A_1/A_2` equals

On the set N of all natural numbers, define the relation R by a R b, if GCD of a and b is 2. Then, R is

In a group of 52 persons, 16 drink tea but not coffee, while 33 drink tea. How many persons drink coffee but not tea?

The number of surjective functions from A to B where A = {1, 2, 3, 4} and B = {a, b} is

A real value of x satisfies `((3 - 4ix)/(3 + 4ix))` = α – iβ (α, β ∈ R), if α² + β² is equal to

There are 600 student in a school. If 400 of them can speak Telugu, 300 can speak Hindi, then the number of students who can speak both Telugu and Hindi is:

If `f(x) = {{:(-x^2",", "when"  x ≤ 0),(5x - 4",", "when"  0 < x ≤ 1),(4x^2 - 3x",", "when"  1 < x < 2),(3x + 4",", "when"  x ≥ 2):}`, then

Let f(x) = `{{:(5^(1/x), x < 0),(lambda[x], x ≥ 0):}` and λ ∈ R, then at x = 0

A market research group conducted a survey of 2000 consumers and reported that 1720 consumers like product P₁ and 1450 consumers like product P₂. What is the least number that must have liked both the products?

A relation in a set 'A' is known as empty relation:-

A relation 'R' in a set 'A' is called a universal relation, if each element of' A' is related to :-