List of practice Questions

A body slides down a smooth inclined plane having angle \( \theta \) and reaches the bottom with velocity \( v \). If a body is a sphere then its linear velocity at the bottom of the plane is

The graph of kinetic energy against the frequency \( v \) of incident light is as shown in the figure. The slope of the graph and intercept on X-axis respectively are

A simple pendulum of length \( \ell \) has a bob of mass \( m \). It executes S.H.M. of small amplitude \( A \). The maximum tension in the string is

The magnetic susceptibility of a paramagnetic material at \( -73^\circ \text{C} \) is \( 0.0075 \). Its value at \( -173^\circ \text{C} \) will be

Two wires A and B are stretched by the same load. The radius of wire A is double the radius of wire B. The stress on the wire B as compared to the stress on the wire A is

When wavelength of light used in optical instruments A and B are 4500Å and 6000Å respectively, the ratio of resolving power of A to B will be

The ratio of radii of gyration of a ring to a disc (both circular of same radii and mass), about a tangential axis perpendicular to the plane is

The work done in blowing a soap bubble of radius \( R \) is \( W \). The work done in blowing a bubble of radius \( 2R \) of the same soap solution is

The light of wavelength \( \lambda \) incident on the surface of metal having work function \( \phi \) emits the electrons. The maximum velocity of electrons emitted is

A thin uniform rod has mass \( M \) and length \( L \). The moment of inertia about an axis perpendicular to it and passing through the point at a distance \( \frac{L}{3} \) from one of its ends, will be

The integral \[ \int_0^{\frac{\pi}{2}} \log \left( \frac{\sqrt{1 - \cos 2x}}{\sqrt{1 + \cos 2x}} \right) dx \] is

The approximate value of the function \[ f(x) = x^3 - 3x + 5 \quad \text{at} \quad x = 1.99 \] is

The radius of the circle passing through the points \[ (5, 7), \quad (2, -2), \quad (-2, 0) \] is

If \[ p \rightarrow \left( \sim p \vee q \right) \text{ is false, then the truth values of } p \text{ and } q \text{ are respectively} \]

The Cartesian coordinates of the point on the parabola \[ y^2 = x \quad \text{whose parameter is} \quad \frac{-4}{3} \] are

If \[ A = \{x, y, z\}, \quad B = \{1, 2\}, \text{ then the total number of relations from set } A \text{ to set } B \text{ are} \]

A particle starting from rest moves along the circumference of a circle of radius \( r \) with angular acceleration \( \alpha \). The magnitude of the average velocity, in the time it completes the small angular displacement \( \theta \), is

If \[ \sin \theta = \frac{-12}{13}, \quad \cos \phi = \frac{-4}{5}, \quad \text{and} \quad \theta, \phi \text{ lie in the third quadrant, then } \tan(\theta - \phi) = \]

If \[ x \cos \theta + y \sin \theta = 5, \quad x \sin \theta - y \cos \theta = 3, \quad \text{then the value of} \, x^2 + y^2 \, \text{is} \]

If \[ \begin{vmatrix} a + b & b + c & c + a \\ b & c & a \\ c & a & b \end{vmatrix} \neq 0, \quad \text{then} \quad \begin{vmatrix} a + b & b + c & c + a \\ b & c & a \\ c & a & b \end{vmatrix} = \]

The equation of the tangent at \( P(-4, -4) \) on the curve \[ x^2 = -4y \] is

The angle between the line \[ \mathbf{r} = (i + j + k) + \lambda (3i + j + 3k) \] and the plane \[ \mathbf{r} \cdot (i + 2j + 3k) = 8 \] is

In a triangle ABC, if \[ \frac{\sin A - \sin C}{\cos C - \cos A} = \cot B, \text{ then A, B, C are in} \]

If \[ \int \sqrt{x - 1} \left( \frac{x^2 + 1}{x^2} \right) dx = \frac{2}{3} (x - 1)^k + c, \quad \text{then the value of } k \text{ is} \]

The probability that a bomb will miss the target is 0.2. Then the probability that out of 10 bombs dropped exactly 2 will hit the target is