List of top Mathematics Questions

If the cofactors of the elements 3, 7, and 6 of the matrix \( \begin{bmatrix} 1 & 2 & 3 \\ 4 & -1 & 7 \\ 2 & 4 & 6 \end{bmatrix} \) are \( a, b, c \) respectively, then evaluate: \[ \left[ a \ b \ c \right] \begin{bmatrix} 1 \\ 4 \\ 2 \end{bmatrix} + \left[ a \ b \ c \right] \begin{bmatrix} 3 \\ 7 \\ 6 \end{bmatrix} \]
Let \( B = \begin{bmatrix} 2 & 6 & 4 \\ 1 & 0 & 1 \\ -1 & -1 & -1 \end{bmatrix} \), \( C = \begin{bmatrix} -1 & 0 & 1 \\ 1 & 1 & 3 \\ 2 & 0 & 2 \end{bmatrix} \), and if a matrix \( A \) is such that \( BAC = I \), then \( A^{-1} = \)
If \( \det(AB) = \det(A)\det(B) \) and \( A \) is a non-singular matrix of order \( 3 \times 3 \), then \( \det(\text{adj}(A)) \) is:
Let \( S = \{ z \in \mathbb{C} : |z - 1 + i| = 1 \} \) represents:
If one root of the quadratic equation \(a(b-c)x^2+b(c-a)x+c(a-b)=0\) is 1, then the other root is
A particle moves along the curve \(\frac{x^2}{16}+\frac{y^2}{4}=1\). When the rate of change of abscissa is 4 times that of its ordinate, then the quadrant in which the particle lies is

Let \( \alpha, \beta, \) and \( \gamma \) be real numbers. Consider the following system of linear equations: 
\( x + 2y + z = 7 \)
\( x + \alpha z = 11 \)
\( 2x - 3y + \beta z = \gamma \)
Match each entry in List I to the correct entries in List II

List IList II
(P)If \( \beta = \frac{1}{2}(7\alpha - 3) \) and \( \gamma = 28 \), then the system has(1)a unique solution
(Q)If \( \beta = \frac{1}{2}(7\alpha - 3) \) and \( \gamma \neq 28 \), then the system has(2)no solution
(R)If \( \beta \neq \frac{1}{2}(7\alpha - 3) \) where \( \alpha = 1 \) and \( \gamma \neq 28 \), then the system has(3)infinitely many solutions
(S)If \( \beta \neq \frac{1}{2}(7\alpha - 3) \) where \( \alpha = 1 \) and \( \gamma = 28 \), then the system has(4)\( x = 11, y = -2 \) and \( z = 0 \) as a solution
  (5)\( x = -15, y = 4 \) and \( z = 0 \) as a solution
The distance ‘s’ in meters travelled by a particle in ‘t’ seconds is given by s = \(\frac{2t^3}{3}-18t+\frac{5}{3}.\) The acceleration when the particle comes to rest is

Number of 4-digit numbers that are less than or equal to 2800 and either divisible by 3 or by 11 , is equal to

If \( \left| \frac{z - 2}{z} \right| = 2 \), then the greatest value of \( |z| \) is:
One of the 15th roots of \( -1 \) is:
The product of the four values of \( \left( 1 + i\sqrt{3} \right)^{3/4} \) is:
If one root of the equation \( ax^2 + bx + c = 0 \) is twice another root, then the equation \( ax^2 + bx + c = 0 \) is:
If \( \alpha \) and \( \beta \) are the roots of \( x^2 - ax - b = 0 \), and \( \alpha^2 + \beta^2 \) and \( \alpha^3 + \beta^3 \) are the roots of \( Ax^2 + Bx + C = 0 \), then \( C = \ldots \)
If \( -1 \) is a twice repeated root of the equation \( ax^3 + bx^2 + cx + 1 = 0 \), then \( ax^3 + bx^2 + cx + 1 = 0 \) represents:
The minimum value of \( f(x) = \frac{x^2 - 2x + 3}{x^2 - 4x + 7} \) is:
If \( C_j = \binom{n}{j} \), then \( C_0 C_t + C_1 C_{t+1} + C_2 C_{t+2} + \dots + C_n = \)
The coefficient of the highest power of \( x \) in the expansion of \[ \left( x + \sqrt{x^2 - 1} \right)^3 + \left( x - \sqrt{x^2 - 1} \right)^8 \text{ is:} \]
The number of non-negative integral solutions of \( x_1 + x_2 + x_3 + x_4 = 10 \) is:
The number of six-digit natural numbers that can be formed with the digits 2, 3, 4, 0, 5, 6, 7, 8 is:
If \( A = \begin{pmatrix} a & b \\ c & d \end{pmatrix} \), where \( a, b, c, d \in \{-1, 1\} \), then the number of singular matrices in \( A \) is:
If \( \cot x \cot y = a \) and \( x + y = \frac{\pi}{6} \), then the quadratic equation satisfying \( \cot x \) and \( \cot y \) is:
If \( \tan A + \tan B = x \) and \( \cot A + \cot B = y \), then \( \tan(A + B) = \)
Evaluate: \[ \frac{1}{\cos 290^\circ} + \frac{1}{\sqrt{3} \sin 250^\circ} \]
If \[ \left| 1 - \cos \left( \frac{\pi}{2} - \alpha \right) + \sin \left( \frac{3\pi}{2} - \alpha \right) \right| \left[ 1 - \sin \left( \frac{3\pi}{2} - \alpha \right) - \cos \left( \frac{\pi}{2} - \alpha \right) \right] = a + b \sin \left( \frac{\pi}{4} + \alpha \right) \] then \( a^2 + b^2 = \)