List of practice Questions

If all the letters of the word MOST are permuted and the words (with or without meaning) thus obtained are arranged in the dictionary order then the rank of the word STOM when counted from the rank of the word MOST, is

The constant term in the expansion of \( \left(1+\frac{1}{x}\right)^{20} \left(30x(1+x)^{29} + (1+x)^{30}\right) \) is

\( \omega \) is a complex cube root of unity and \( Z \) is a complex number satisfying \( |Z-1| \le 2 \). The possible values of \( r \) such that \( |Z-1| \le 2 \) and \( |\omega Z - 1 - \omega^2| = r \) have no common solution are

If \( |Z|=2 \), \( Z_1 = \frac{Z}{2}e^{i\alpha} \) and \( \theta \) is the amp(Z), then \( \frac{Z_1^n - Z_1^{-n}}{Z_1^n + Z_1^{-n}} = \)

In Argand plane, no value of \( \sqrt[3]{1-i\sqrt{3}} \) lie in

If \( l \) is the maximum value of \( -3x^2+4x+1 \) and \( m \) is the minimum value of \( 3x^2+4x+1 \), then the equation of the hyperbola having foci at \( (l,0), (7m,0) \) and eccentricity as 2 is

If the equation \( x^2 - 3ax + a^2 - 2a - K = 0 \) has different real roots for every rational number \( a \), then \( K \) lies in the interval

The inverse of the function \( y = \frac{10^x - 10^{-x}}{10^x + 10^{-x}} + 1 \) is \( x = \)

The value of the greatest positive integer \( k \), such that \( 49^k + 1 \) is a factor of \( 48(49^{125} + 49^{124} + \dots + 49^2 + 49 + 1) \) is

If \( \left| \begin{matrix} 1 & 2 & 3-\lambda \\ 0 & -1-\lambda & 2 \\ 1-\lambda & 1 & 3 \end{matrix} \right| = A\lambda^3 + B\lambda^2 + C\lambda + D \), then \( D+A = \)

If \( A+2B = \begin{bmatrix} 1 & 2 & 0 \\ 6 & -3 & 3 \\ -5 & 3 & 1 \end{bmatrix} \) and \( 2A-B = \begin{bmatrix} 2 & -1 & 5 \\ 2 & -1 & 6 \\0 & 1 & 2 \end{bmatrix} \), then \( \text{tr}(A) - \text{tr}(B) = \)

A, C are \( 3 \times 3 \) matrices. B, D are \( 3 \times 1 \) matrices. If \( AX=B \) has a unique solution and \( CX=D \) has an infinite number of solutions, then

A and B are two non-square matrices. If \( P = A + B \), \( Q = A^TB \), \( R = AB^T \), then the matrices whose order is equal to the order of A are

If \( f: \mathbb{R}-\{0\} \to \mathbb{R} \) is defined by \( 3f(x) + 4f\left(\frac{1}{x}\right) = \frac{2-x}{x} \), then \( f(3) = \)

A metal rod of area of cross-section \(3 \text{cm}^2\) is stretched along its length by applying a force of \(9 \times 10^4 \text{N}\). If the Young's modulus of the material of the rod is \(2 \times 10^{11} \text{Nm}^{-2}\), the energy stored per unit volume in the stretched rod is

Suppose we throw a dice once. Then, which one of the following is/are correct?
(A) The probability of getting a number greater than 4 is \( \frac{1}{3} \).
(B) The probability of getting a number greater than or equal to 4 is \( \frac{1}{3} \).
(C) The probability of getting a number less than or equal to 3 is \( \frac{1}{2} \).
(D) The probability of getting a number less than or equal to 6 is 1.
Choose the correct answer from the options given below:

Which of the following statements is incorrect for Chandrayaan-3?

The river which flows through the Grand Canyon of India, also known as the Gandikota Gorge is

Observe the following data (\(\Delta_i H_1\), \(\Delta_i H_2\) and \(\Delta_{eg}H\) represent the first, second ionisation enthalpies and electron gain enthalpy respectively).

Using the data identify the most reactive metal.

Match the following

The correct answer is

Monochromatic light of wavelength 6000 Å incidents on a small angled prism. If the angle of the prism is 6°, the refractive indices of the material of the prism for violet and red lights are respectively 1.52 and 1.48, then the angle of dispersion produced for this incident light is

Let $\vec{a} = \hat{i} + 2\hat{j} + 2\hat{k}$ and $\vec{b} = 2\hat{i} - \hat{j} + p\hat{k}$ be two vectors. If $(\vec{a}, \vec{b}) = 60^\circ$, then $p =$