List of top Mathematics Questions

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

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 \( \text{tr}(A) - \text{tr}(B) = \)

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 \( D+A = \)

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

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

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

If \( ^{15}C_4 + ^{15}C_5 + ^{16}C_6 + ^{17}C_7 + ^{18}C_8 = ^{19}C_r \), then the value of \( r \) is equal to}

In a triangle with one of the angles \( 120^\circ \), the lengths of the sides form an A.P. If the length of the greatest side is 7 m, then the area of the triangle is

If \( \bar{a} = \frac{1}{\sqrt{10}}(3\hat{i} + \hat{k}) \) and \( \bar{b} = \frac{1}{7}(2\hat{i} + 3\hat{j} - 6\hat{k}) \), then the value of \( (2\bar{a} - \bar{b}) \cdot ((\bar{a} \times \bar{b}) \times (\bar{a} + 2\bar{b})) = \)}

The difference between the maximum value and minimum value of objective function \( z = 3x + 5y \) subject to \( x + 3y \le 60, x + y \ge 10, x - y \ge 0, x, y \ge 0 \) is

If \( x = e^{\tan^{-1} \left( \frac{y-x^2}{x^2} \right)} \), then \( \frac{dy}{dx} \) at \( x = 1 \) is

If \( x = \sin \theta, y = \sin^3 \theta \), then \( \frac{d^2y}{dx^2} \) at \( \theta = \frac{\pi}{6} \) is

If \( f(x) = 3x^3 + 2x^2 f'(1) + x f''(2) + f'''(3) \) then \( f(x) = ....... \)}

The rates of change of the perimeter and area of a rectangle respectively when length $x=5$ cm and breadth $y=2$ cm, if $dx/dt = -5$ cm/min and $dy/dt = 3$ cm/min, are

The angle between the line \( x = \frac{y-1}{2} = \frac{z-3}{\lambda} \) and the plane \( x + 2y + 3z = 6 \) is \( \cos^{-1} \sqrt{\frac{5}{14}} \), then the value of \( \lambda \) is

The combined equation of the tangent and normal to the curve \( xy = 15 \) at the point (5, 3) is

The sum of two nonzero numbers is 4. The minimum value of the sum of their reciprocals is

If the line \( ax + by + c = 0 \) is normal to the curve \( xy = 1 \), then}

\( \int \sqrt{x^2 + 3x} dx = \)}

Let the plane passing through point (2, 1, -1) containing line joining the points (1, 3, 2) and (1, 2, 1) makes intercepts \( p, q, r \) on co-ordinate axes, then \( p + q + r = \)}

\( \int \frac{x}{1+x^4} dx = \)}

In a triangle ABC with usual notations if \( b \sin C (b \cos C + c \cos B) = 42 \), then area of triangle ABC =}

If \( 0 \le \cos^{-1} x \le \pi \) and \( -\frac{\pi}{2} \le \sin^{-1} x \le \frac{\pi}{2} \), then at \( x = \frac{1}{5} \) the value of \( \cos(2 \cos^{-1} x + \sin^{-1} x) \) is

Number of switches in alternative equivalent simple circuit for the circuit is (are)

\( \int \frac{(5 \sin \theta - 2) \cos \theta}{(5 - \cos^2 \theta - 4 \sin \theta)} d\theta = \)}