CUET (UG) entrance exam Question Bank Solutions

If P(A) = `6/11`, P(B) = `5/11` and P(A ∪ B) = `7/11`, then what will be the value of P(A ∩ B)

Determine P(E/F) if mother father and son line up at random for a tamily pictur. E = son on one end F. Father in middle.

Given that two numbers appearing on throwing two dice are different. Find the probability of the event the sum of numbers on the dice is 4.

If `tan^-1x + tan^-1y + tan^-1z = pi/2`, then

Tangent is drawn to the ellipse `x^2/27 + y^2 = 1` at the point `(3sqrt(3) cos theta, sin theta), 0 < 0 < 1`. The sum of the intercepts on the axes made by the tangent is minimum if 0 is equal to

The value of the integral `int_(-1)^2 [x]  dx` is 

Find the 5^th term of expansion of `(x^2 + 1/x)^10`?

Which of the statements describe the solution set for `-2(x + 8) = - 2x + 20`?

If `y = (x + sqrt(1 + x^2))^n`, then `(1 + x^2) (d^2y)/(dx^2) + x (dy)/(dx)` is

The rate of increase of bacteria in a certain culture is proportional to the number present. If it doubles in 5 hours then in 25 hours, its number would be

`int (sin^8x - cos^8x)/(1 - 2sin^2x cos^2x) dx` is equal to

`int_0^oo (dx)/((x^2 + a^2)(x^2 + b^2))` is

For positive numbers x, y, z the numerical value of the determinant `|(1, log_x y, log_x z),(log_y x, 3, log_y z),(log_z x, log_z y, 5)|` is

For positive numbers x, y, z, the numerical value of the determinant `|(1, log_x y, log_x z),(log_y x, 1, log_y z),(log_z x, log_z y, 1)|` is

`d/(dx)[sin^-1(xsqrt(1 - x) - sqrt(x)sqrt(1 - x^2))]` is equal to

The value of determinant `|(sin^2 13°, sin^2 77°, tan135°),(sin^2 77°, tan135°, sin^2 13°),(tan135°, sin^2 13°, sin^2 77°)|` is

The number of common tangents to the circles x² + y² – 4x – 6x – 12 = 0 and x² + y² + 6x + 18y + 26 = 0 is

If sin y = x sin (a + y), then value of dy/dx is

A signal which can be green or red with probability 4/5 and 1/5 respectively, is received by station A and then trasmitted to station B. The probability of each station receiving the signal correctly is 3/4. If the signal received at station B is given, then the probability that the original signal is green, is

Tangent and normal are drawn at P(16, 16) on the parabola y² = 16x, which intersect the axis of the parabola at A and B, respectively. If C is the centre of the circle through the points P, A and B and ∠CPB = θ, then a value of tan θ is: