List of top Mathematics Questions

If \[ A = \begin{bmatrix} 2 & -1 \\ -1 & 2 \end{bmatrix}, \] such that \[ A^2 - 4A + 3I = 0, \] then \( A^{-1} \) is

If \[ | \mathbf{a} \times \mathbf{b} \times \mathbf{c} | = 4, \] then the volume of the parallelepiped with coterminous edges \[ \mathbf{a} + 2\mathbf{b}, \quad \mathbf{b} + 2\mathbf{c}, \quad \mathbf{c} + 2\mathbf{a} \] is

If \[ x = \log t, \quad y + 1 = \frac{1}{t}, \] then \[ e^{-x} \frac{d^2 x}{dy^2} + \frac{dx}{dy} = \]

If \[ \sec x + \tan x = 3, \quad x \in \left( 0, \frac{\pi}{2} \right), \] then \( \sin x = \)

If \( \theta \) is a parameter, then the parametric equations of the circle \[ x^2 + y^2 - 6x + 4y - 3 = 0 \] are given by

Evaluate the integral \[ \int_0^{\frac{\pi}{2}} \frac{\sin x \cos x}{1 + \sin^4 x} \, dx = \]

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

If \[ \mathbf{a} = \frac{1}{\sqrt{10}} (3i + k), \quad \mathbf{b} = \frac{1}{7} (2i + 3j - 6k), \quad \text{then the value of} \] \[ (2\mathbf{a} - \mathbf{b}) \cdot \left[ (\mathbf{a} \times \mathbf{b}) \times (\mathbf{a} + 2\mathbf{b}) \right] \]

The displacement of a particle at the time \( t \) is given by \[ s = \sqrt{1 + t}, \quad \text{then its acceleration } a \text{ is proportional to} \]

Two cards are drawn from a pack of well shuffled 52 playing cards one by one without replacement. Then the probability that both cards are queens is

The statement pattern \[ [(p \vee q) \wedge \neg p] \wedge (\neg q) \] is

If \[ y = \tan^{-1}(\sec x + \tan x), \quad \text{then} \quad \frac{dy}{dx} = \]

Degree of the differential equation \[ \frac{dy}{dx} e^x + \left( \frac{dy}{dx} \right)^3 = x \]

The solution of the differential equation \[ x^2 \frac{dy}{dx} = y^2 + xy \]

If \( Z = 7x + y \) subject to \[ 5x + y \geq 5, \quad x + y \geq 3, \quad x \geq 0, \quad y \geq 0, \quad \text{then the minimum value of } Z \text{ is} \]

If \( \cos 2\theta = \sin \alpha \), then \( \theta = \)

The maximum value of the function \[ y = e^{5 + \sqrt{3} \sin x + \cos x} \]

Evaluate the integral \[ \int \frac{dx}{\sqrt{5 + 4x - x^2}} = \]

Evaluate the integral \[ \int \frac{dx}{\sqrt{(x - 1)(x - 2)}} = \text{?}

The equation of the circle whose end points of a diameter are the centres of the circles \[ x^2 + y^2 + 2x - 4y + 1 = 0 \quad \text{and} \quad x^2 + y^2 - 8x + 6y + 17 = 0 \] is

The area of the region bounded by the curve \( y = 4x - x^2 \) and the x-axis is

If \[ f(x) = \left[ \tan \left( \frac{\pi}{4} + x \right) \right]^{\frac{1}{x}} \quad \text{if} \quad x \neq 0 \] \[ f(x) = k \quad \text{if} \quad x = 0 \] is continuous at \( x = 0 \), then \( k = \)

The equation of a line passing through the point \( (2, 4, 6) \) and parallel to the line \[ 3x + 4 = 4y - 1 = 1 - 4z \] is

Evaluate the integral \[ \int \frac{(1 + \log x)}{\cos^2(\log x)} \, dx \]

If \[ \tan u = \frac{\sqrt{1 - x}}{\sqrt{1 + x}}, \quad \cos v = 4x^3 - 3x, \quad \text{then} \quad \frac{du}{dv} = \text{?}