CUET (UG) entrance exam Question Bank Solutions for Mathematics

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:

An electric instrument consists of two units. Each unit must function independently for the instrument to operate. The probability that the first unit functions is 0.9 and that of the second unit is 0.8. The instrument is switched on and it fails to operate. If the probability that only the first unit failed and second unit is functioning is p, then 98 p is equal to

The points at which the tangent passes through the origin for the curve y = 4x³ – 2x⁵ are

Evaluate: `int_0^(pi/2) cosx/(( cos  x/2 + sin  x/2)^3) dx`

Value of `|(2, 4),(-1, 2)|` is