List of practice Questions

A sequence of frames from an animation is given below, where one frame is missing. Select the one from the given options to complete the sequence. 

At what time of the day was this photograph taken in Central India? 

A cube is shown with its shadow. Identify the one with the correct shadow. 

Identify the tool used to create the letters shown below. 

Identify the state to which the given image belongs.

Identify the person from the photograph shown below. 

Identify the skin texture of elephant from the images given below.

Identify the logo of State Bank of India.

If \( f(x) = \left\{ \begin{array}{ll} mx + 1, & \text{for } x \leq \frac{\pi}{2}, \\ \sin x + n, & \text{for } x>\frac{\pi}{2}, \end{array} \right. \) is continuous at \( x = \frac{\pi}{2} \), then:
The value of the determinant \[ \begin{vmatrix} \cos \alpha & -\sin \alpha & 1 \\ \sin \alpha & \cos \alpha & 1 \\ \cos(\alpha + \beta) & -\sin(\alpha + \beta) & 1 \end{vmatrix} \] is:
The domain of the function \[ f(x) = \frac{\sqrt{4 - x^2}}{\sin^{-1}(2 - x)} \] is:
The general solution of the differential equation \[ (1 + y^2) \, dx + (1 + x^2) \, dy = 0 \] is:
The order and degree of the differential equation \[ \rho = \frac{\left[ 1 + \left( \frac{dy}{dx} \right)^2 \right]^{3/2}}{\frac{d^2y}{dx^2}}, \] are respectively:
The relation \( R \) defined on the set of natural numbers as \( (a, b) : a \) differs from \( b \) by 3 is given by:
The sum of the series \[ 1 + \frac{1^2 + 2^2}{2!} + \frac{1^2 + 2^2 + 3^2}{3!} + \frac{1^2 + 2^2 + 3^2 + 4^2}{4!} + \dots \] is:
The coefficient of \( x^n \) in the expansion of \( \log_a(1 + x) \) is:
If a plane meets the coordinate axes at \( A \), \( B \), and \( C \) in such a way that the centroid of \( \triangle ABC \) is at the point \( (1, 2, 3) \), then the equation of the plane is:
The area lying in the first quadrant and bounded by the circle \( x^2 + y^2 = 4 \), the line \( x = \sqrt{3}y \), and the \( x \)-axis is:
The value of \[ \lim_{x \to \infty} \left( \frac{\pi}{2} - \tan^{-1} x \right)^{1/x} \] is:
\[ \int \frac{dx}{\sin x - \cos x + \sqrt{2}} = ? \]
The value of the integral \[ I = \int_0^1 \frac{\sqrt{1 - x}}{\sqrt{1 + x}} \, dx \] is:
The value of the integral \[ I = \int_0^1 \left| x - \frac{1}{2} \right| \, dx \] is:
The eccentricity of the ellipse, which meets the straight line \( \frac{x}{7} + \frac{y}{2} = 1 \) on the axis of \( x \) and the straight line \( \frac{x}{3} - \frac{y}{5} = 1 \) on the axis of \( y \), and whose axes lie along the axes of coordinates, is:
If \[ \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \quad (a>b) \] and \[ x^2 - y^2 = c^2 \] cut at right angles, then:
The equation of the conic with focus at \( (1, -1) \), directrix along \( x - y + 1 = 0 \), and eccentricity \( \sqrt{2} \) is: