CUET (UG) entrance exam Question Bank Solutions

If `y = log_2 log_2(x)` then `(dy)/(dx)` =

Let (h, k) be a fixed point where h > 0, k > 0. A straight line passing through this point cuts the positive direction of the coordinate axes at the points P and Q. Then the minimum area of the ΔOPQ. O being the origin, is

The equation of curve through the point (1, 0), if the slope of the tangent to t e curve at any point (x, y) is `(y - 1)/(x^2 + x)`, is

A man is moving away from a tower 41.6 m high at a rate of 2 m/s. If the eye level of the man is 1.6 m above the ground, then the rate at which the angle of elevation of the top of the tower changes, when he is at a distance of 30 m from the foot of the tower, is

Evaluate: `int  (1 - cos x)/(cos x(1 + cos x))  dx`

Equation of a common tangent to the circle, x² + y² – 6x = 0 and the parabola, y² = 4x, is:

If a² + b² + c² = – 2 and f(x) = `|(1 + a^2x, (1 + b^2)x, (1 + c^2)x),((1 + a^2)x, 1 + b^2x, (1 + c^2)x),((1 + a^2)x, (1 + b^2)x, 1 + c^2x)|` then f(x) is a polynomial of degree

The altitude through vertex C of a triangle ABC, with position vectors of vertices `veca, vecb, vecc` respectively is:

`d/(dx)(tan^-1  (sqrt(1 + x^2) - 1)/x)` is equal to:

The differential equation (1 + y²)x dx – (1 + x²)y dy = 0 represents a family of:

If `veca, vecb, vecc` are vectors such that `[veca, vecb, vecc]` = 4, then `[veca xx vecb, vecb xx vecc, vecc xx veca]` =

The area included between the parabolas y² = 4a(x +a) and y² = 4b(x – a), b > a > 0, is

`tan^-1  1/2 + tan^-1  2/11` is equal to

The Simplest form of `cot^-1 (1/sqrt(x^2 - 1))`, |x| > 1 is

What is the value of cos (sec^–1x + cosec^–1x), |x| ≥ 1

Find the value of `cos^-1 (1/2) + 2sin^-1 (1/2) ->`:-

What is the simplest form of `tan^-1  sqrt(1 - x^2 - 1)/x, x ≠ 0`

The value of `tan^-1 (x/y) - tan^-1  (x - y)/(x + y)` is equal to

`sin^-1(1 - x) - 2sin^-1 x = pi/2`, tan 'x' is equal to

A matrix is said to be a column matrix if it has