CUET (UG) entrance exam Question Bank Solutions

The equation ax + by + c = 0 represents a straight line

The set of all real numbers x for which `x^2 - |x + 2| + x > 0` holds is

Determine k so that the equation 4x² + kx + 1 = 0 will have just one real solution?

If p, q, r, s are real number and pr = 2(q + s) then for the equation x² + px + q = 0 and x² + rx + s = 0 which of the following statement is true?

If `f(x) = log [e^x ((3 - x)/(3 + x))^(1/3)]`,  then `f^'(1)` is equal to

The solution of the differential equation `(1 + e^(x/y)) dx + e^(x/y) (1 + x/y) dy` = 0 is

Given f(x) = `log((1 + x)/(1 - x))` and g(x) = `(3x + x^3)/(1 + 3x^2)`, then fog(x) equals

An ellipse has OB as semi-minor axis, F and F' its focii and the angle FBF' is a right angle. Then the eccentricity of the ellipse is

Matrices A and B will be inverse of each other only if

Adjoint of each of the matrices `[(1, 2),(3, 4)]` is

Find the inverse of the matrices `[(-1, 5),(-3, 2)]`

Let A be nonsingular square matrix of order 3 × 3 Then |adj A| is equal to.

If 'A' is an invertible matrix of order 2, then det (A^-1) is equal to.

The value of `int_(- pi/2)^(pi/2) (x^3 + x cos x + tan^5x + 1)  dx` is

The value of `int_0^(pi/2) log ((4 + 3 sin x)/(4 + 3 cos x))  dx` is

A homogeneous differential equation of the `(dx)/(dy) = h(x/y)` can be solved by making the substitution.

Find the unit vector in the diret:tion of the vector `veca = hati + hatj + 2hatk`

What is the midpoint of the vector joining the point P(2, 3, 4) and Q(4, 1, –2)?

Let E₁ and E₂ be two independent events. Let P(E) denotes the probability of the occurrence of the event E. Further, let E'₁ and E'₂ denote the complements of E₁ and E₂, respectively. If P(E'₁ ∩ E₂) = `2/15` and P(E₁ ∩ E'₂) = `1/6`, then P(E₁) is

If A, B are two events such that `1/8 ≤ P(A ∩ B) ≤ 3/8` then