List of top Mathematics Questions

\( \int_{0}^{1} \log (\frac{1}{x} - 1) dx = \)}

\( \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} (x^2 + \log (\frac{\pi - x}{\pi + x}) \cdot \cos x) dx = \)}

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

The area bounded by the curve \( y = x^2 + 3, y = x, x = 3 \) and \( y \)-axis is

If the foot of the perpendicular drawn from the origin to a plane is \( P(2, -1, 4) \), then the equation of the plane is

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

The line passing through the points \( (a, 1, 6) \) and \( (3, 4, b) \) crosses the \( yz \)-plane at \( (0, \frac{17}{2}, -\frac{13}{2}) \), then the value of \( (3a + 4b) \) is

The angle between the lines \( x = y, z = 0 \) and \( y = 0, z = 0 \) is

The differential equation whose solution is \( Ax^2 + By^2 = 1 \), where A and B are arbitrary constants is of}

Solution of \( (2y - x) \frac{dy}{dx} = 1 \) is

Let \( \bar{a}, \bar{b}, \bar{c} \) be three vectors such that \( \bar{a} + \bar{b} + \bar{c} = \bar{0}, |\bar{a}| = 3, |\bar{b}| = 4, |\bar{c}| = 5 \), then \( \bar{a} \cdot \bar{b} + \bar{b} \cdot \bar{c} + \bar{c} \cdot \bar{a} = \)}

The integrating factor of \( y + \frac{d}{dx}(xy) = x(\sin x + \log x) \) is

If \( \bar{a} = 2\hat{i} + 3\hat{j} + 4\hat{k}, \bar{b} = \hat{i} - 2\hat{j} - 2\hat{k}, \bar{c} = -\hat{i} + 4\hat{j} + 3\hat{k} \) and if \( \bar{d} \) is vector perpendicular to both \( \bar{b} \) and \( \bar{c} \), \( \bar{a} \cdot \bar{d} = 18 \), then \( |\bar{a} \times \bar{d}|^2 = \)}

A random variable X has following p.d.f. \( f(x) = kx(1 - x), 0 \le x \le 1 \) and \( P(x>a) = \frac{20}{27} \), then \( a = \)}

If \( (\cos^{-1} x)^2 - (\sin^{-1} x)^2>0 \), then}

The probability distribution of a random variable X is given by

Then the variance of X is

The rate of change of volume of spherical balloon at any instant is directly proportional to its surface area. If initially its radius is 3 cm, after 2 minutes its radius becomes 9 cm, then radius of balloon after 4 minutes is

If \( \theta \) is the angle between the lines whose direction cosines are given by \( 6mn - 2nl + 5lm = 0 \) and \( 3l + m + 5n = 0 \), then \( \sin \theta = \)}

Let \( \bar{a} = \hat{i} + \hat{j}, \bar{b} = 2\hat{i} - \hat{k}, \bar{c} = 3\hat{i} - \hat{j} + \hat{k} \), then vector \( \bar{p} \) satisfying \( \bar{p} \cdot \bar{a} = 0 \) and \( \bar{p} \times \bar{b} = \bar{c} \times \bar{b} \) is

If \( X \sim B(6, \frac{1}{2}) \), then \( P(|X - 2| \le 1) = \)}

The equation \( x^2 - 3xy + \lambda y^2 + 3x - 5y + 2 = 0 \), where \( \lambda \) is a real number represents a pair of lines. If \( \theta \) is the acute angle between the lines, then \( \frac{\text{cosec}^2 \theta}{\sqrt{10}} = \)}

If \( A = \begin{bmatrix} 1 & -1 & 1 \\ 0 & 2 & -3 \\ 2 & 1 & 0 \end{bmatrix} \), \( B = \text{adj } A \) and \( C = 5A \), then \( \frac{|\text{adj } B|}{|C|} = \)}

The number of values of \( x \) in the interval \( [0, 3\pi] \) satisfying the equation \( 2 \sin^2 x + 5 \sin x - 3 = 0 \) is

Let A = \( \lim_{x \to 0^+} (1 + \tan^2 \sqrt{x})^{\frac{1}{2x}} \), then log\(_e\) A =}

The equations of the tangents to the circle \( x^2 + y^2 = 36 \) which are perpendicular to the line \( 5x + y - 2 = 0 \) are