List of top Mathematics Questions

If \( AX = B \), where \( A = \begin{bmatrix} 1 & -1 & 1 \\ 2 & -1 & 0 \\ 3 & 3 & -4 \end{bmatrix} \), \( B = \begin{bmatrix} 1 \\ 2 \end{bmatrix} \) and \( X = \begin{bmatrix} x \\ y \\ z \end{bmatrix} \), then \( x + y + z = \)

If the vectors \( (2\mathbf{i}-q\mathbf{j}+3\mathbf{k}) \) and \( (4\mathbf{i}-5\mathbf{j}+6\mathbf{k}) \) are collinear, then the value of \( q \) is

If \( | \vec{a} \, \vec{b} \, \vec{c} | = 3 \), then the volume of the parallelepiped with \( 2\vec{a} + \vec{b} \), \( 2\vec{b} + \vec{c} \), \( 2\vec{c} + \vec{a} \) as coterminous edges is:

The minimum value of \( Z = 5x + 8y \) subject to \[ x + y \geq 5, \quad 0 \leq x \leq 4, \quad y \geq 2, \quad x \geq 0, \quad y \geq 0 \] is

Evaluate \( \int_0^{\frac{\pi}{2}} \sin^2 x \, dx \)

If for an Arithmetic progression, 9 times the ninth term is equal to 13 times the thirteenth term, then the value of the twenty-second term is

The equation of the plane passing through the points \( (2, 3, 1), (4, -5, 3) \) and parallel to the y-axis 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

If \( A \) and \( B \) are independent events such that odds in favour of \( A \) is 2:3 and odds against \( B \) is 4:5, then \( P(A \cap B) = \)

The equation of a line passing through the point of intersection of the lines \[ x + 2y + 8 = 0 \quad \text{and} \quad 3x - y + 4 = 0 \] and having x– and y–intercepts zero is

The value of \( \sin^{-1} \left( -\frac{1}{2} \right) + \cos^{-1} \left( -\frac{\sqrt{3}}{2} \right) \) is

If the body cools from \( 135^\circ C \) to \( 80^\circ C \) at room temperature of \( 25^\circ C \) in 60 minutes, then the temperature of the body after 2 hours is

The domain of the function \( f(x) = \sqrt{x} \) is

If \( A, B, C \) are angles of a triangle ABC, then \( \tan 2A + \tan 2B + \tan 2C = \)

Which of the following have the same value:
(a) \( \sin 120^\circ \)
(b) \( \cos 930^\circ \)
(c) \( \tan 840^\circ \)
(d) \( \cot(-1110^\circ) \)

The entries in the last column of the truth table for \( \neg (p \wedge q) \) are

If the A.M. and G.M. of the roots of a quadratic equation in \( x \) are \( p \) and \( q \) respectively, then its equation is

If $\vec a,\vec b,\vec c$ are nonzero vectors along the coterminous edges of a parallelepiped with volume $7$ cubic units, then the volume of the parallelepiped with $\vec a+\vec b,\ \vec b+\vec c,\ \vec c+\vec a$ as the coterminous edges is

If the points \( A(5, k) \), \( B(-3, 1) \) and \( C(-7, -2) \) are collinear, then \( k = \)

Evaluate the integral \[ \int_{0}^{\pi} \frac{x \cos x \sin x}{\cos^3 x + \cos x}\,dx \]

For a sequence \( (t_n) \), if \( s_n = 7(3^n - 1) \), then \( t_n = \)

If the length of perpendicular drawn from the point $(4,1)$ on the line $3x - 4y + k = 0$ is $2$ units, then the values of $k$ are

The adjoint of the matrix \[ A = \begin{pmatrix} 2 & 3
-3 & 5 \end{pmatrix} \] is

If for the harmonic progression, \( t_7 = \frac{1}{10}, \, t_{12} = \frac{1}{25}, \) then \( t_{20} = \)

Let f(x) be a quadratic polynomial such that f(–1) + f(2) = 0. If one of the roots of f(x) = 0 is 3, then its other root lies in :