CUET (UG) entrance exam Question Bank Solutions for Mathematics

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

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

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`

Let `y = f(x)` be the equation of the curve, then equation of normal is

Which of the following represent the slope of normal?

Find the points on the curve `y = x^3` at which the slope of the tangent is equal to the y-coordinate of the point

The Slope of the normal to the curve `y = 2x^2 + 3 sin x` at `x` = 0 is

The line is y = x + 1 is a tangent to the curve y² = 4x at the point.

The slope of the tangentto the curve `x= t^2 + 3t - 8, y = 2t^2 - 2t - 5` at the point `(2, -1)` is

The normal at the point (1, 1) on the curve `2y + x^2` = 3 is