List of practice Questions

A batsman hits a cricket ball of mass 0.15 kg travelling at a speed of 54 kmph. The ball reverses its direction. The impulse imparted to the ball in kgms\(^{-1}\) is

A car moves at a speed of 72 kmph, under a force of 600 N. The power output of the car is

A body of mass 2 kg at rest starts to move under the action of an applied horizontal force of 7 N on a table with coefficient of kinetic friction, 0.1. The kinetic energy of the body in 10 seconds is (\(g = 10 \text{ ms}^{-2}\))

A particle starting with an initial velocity \(2 \text{ ms}^{-1}\) moves with a uniform linear acceleration \(2 \text{ ms}^{-2}\). The particle velocities at the end of the 5 seconds and 10 seconds of its motion from the start, are in the ratio

If the solution of the differential equation \(\frac{dy}{dx} = \frac{\alpha x^2 + 4x - 4}{2y - 4}\), when \(y(1) = 3\), is \(y^2 - 4y = x^3 + 2x^2 - 4x + c\), then the value of \(\alpha\) is equal to

The integrating factor of the differential equation \(\frac{dy}{dx} + \frac{2y}{20 - x} = 10\) is

If the constraints of a Linear Programming Problem are : \(x + y \leq 6, 2x + y \leq 8, x \geq 0, y \geq 0\), then a corner point of the feasible region is

Which of the following is not the unit of pressure ?

For a given mass m, linear velocity v, linear displacement s, linear acceleration a and time t, the dimensionally INCORRECT expression for power P is

The value of \(\int 16x^3 \log_e x dx\) is equal to

The value of \(\int_0^3 |3x^2 - 3| dx\) is equal to

The area of the region bounded by \(y = \sqrt{x}, y = -x\), and \(x = 4\) (in square units) is

A ladder AB, of length 13m, has one end A on a levelled horizontal ground and the other end B resting against a vertical wall. If the end A begins to slip away from the wall with constant speed 0.25 m/s, and the end B slips down the wall, then the speed of the end B, when B has reached a height of 5m above the ground, is

Let \(f(x) = -x^3 + 9x^2 - \alpha x - 13\), where \(x \in \mathbb{R}\) and \(\alpha\) is a constant. If the function \(f\) is increasing only in the interval (1,5), then the value of \(\alpha\) is equal to

\(\int \frac{\sec x \sqrt{\sec x}}{\sqrt{\sin x} + \sqrt{\cos x}} dx = \)

If \(y = \sin\left(\tan^{-1}\left(\frac{1}{\sqrt{x^2 - 1}}\right)\right), x > 1\), then \(\frac{dy}{dx} =\)

If \(s = \sqrt{t + 1}, x = \log s\) and \(y = 6x + 3\), then \(\frac{dy}{dt} =\)

If \(y = \sqrt{x} + 2\cos(\sqrt{x})\), then the value of \(\frac{dy}{dx}\) at \(x = \frac{\pi^2}{4}\) is equal to

If \(f(x) = x - 7, g(x) = 11 - x\), and \(h(x) = f(x)g(x)\), then the maximum value of \(h\) is

The direction ratios of a straight line \(L_1\) are 2,-1,2 and that of another straight line \(L_2\) are 3,6,-2. Then the angle between \(L_1\) and \(L_2\) is

A committee of 4 people is selected from the members of a school council which consists of 5 students, 4 teachers and 3 administrators. The probability that the committee has no teachers is

The events A and B are such that \(P(A)=0.7, P(B')=0.8\) and \(P(A \cup B) = 0.8\). Then \(P(A' \cup B')\) is equal to

The following set of data is given: 72, 72, 74, 80, 82, 82, 86, 88, 92, 92. The mean deviation from the median is

The 10 letters of the word STATISTICS are arranged randomly. The probability that the 10-letter arrangement starts with CAT is

The projection of \(\vec{b}\) on \(\vec{a}\) is 12. If the angle between \(\vec{a}\) and \(\vec{b}\) is \(60^\circ\), then \(|\vec{b}| =\)