List of top Questions asked in MET

If \(0 < \alpha, \beta, \gamma < \frac{\pi}{2}\), such that \(\alpha + \beta + \gamma = \frac{\pi}{2}\) and \(\cot \alpha, \cot \beta, \cot \gamma\) are in AP, then the value of \(\cot \alpha \cot \gamma\) is

In a \(\triangle ABC\), if \(b = 2\), \(\angle B = 30^\circ\), then the area of the circumcircle of \(\triangle ABC\) (in sq units) is

The sum of the series \(\frac{3}{4 \times 8} - \frac{3 \times 5}{4 \times 8 \times 12} + \frac{3 \times 5 \times 7}{4 \times 8 \times 12 \times 16} - \cdots\) is

The value of \(\int_0^\pi |\sin 3\theta| \, d\theta\) is

The value of \(\int \frac{\cos x + \sin x}{\cos x + x \sin x} \, dx\) is

Tangent to the ellipse \(\frac{x^2}{32} + \frac{y^2}{18} = 1\) having slope \(-\frac{3}{4}\) meet the coordinate axis at A and B. Then, the area of \(\triangle AOB\), where O is the origin, is

The value of \(\lim_{x \to \pi/6} \frac{\sin x + \sin 2x - 1}{\sin 2x - \sin 3x + 1}\) is

If \(\sin A + \cos B = a\) and \(\sin B + \cos A = b\), then \(\sin(A + B)\) is equal to

In a \(\triangle ABC\), if \(\sin A \sin B = \frac{ab}{c^2}\), then the triangle is

The direction cosines \(l, m, n\) of two lines are connected by the relations \(l + m + n = 0\) and \(lm = 0\), then the angle between them is

The foci of the conic section \(25x^2 + 16y^2 - 150x - 175 = 0\) are

If \(x - 2y = 4\), then the minimum value of \(xy\) is

If \( \mathbf{b} \) and \( \mathbf{c} \) are any two non-collinear unit vectors and \( \mathbf{a} \) is any vector, then \[ (\mathbf{a} \cdot \mathbf{b})\mathbf{b} + (\mathbf{a} \cdot \mathbf{c})\mathbf{c} + \frac{(\mathbf{a} \cdot (\mathbf{b} \times \mathbf{c}))}{|\mathbf{b} \times \mathbf{c}|^2} (\mathbf{b} \times \mathbf{c}) \] is equal to:

If \(\theta\) is the semi-vertical angle of a cone of maximum volume and given slant height, then \(\tan \theta\) is given by

The period of the function \[ f(x) = \begin{vmatrix} \sin x & \cos x & \sin x \cos x \\ \sin x & \cos x & \sin x \\ \cos x & \sin x & \sin x \end{vmatrix} \] is:

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

If \(Q\) is the image of the point \(P(2, 3, 4)\) under the reflection in the plane \(x - 2y + 5z = 6\), then the equation of the line \(PQ\) is

The equation of the plane passing through the line of intersection of the planes \(x + y + z = 6\) and \(2x + 3y + 4z + 5 = 0\) and perpendicular to the plane \(4x + 5y + 3z = 8\) is

\(1 + \frac{2}{2!} + \frac{3}{3!} + \frac{4}{4!} + \cdots \infty\) equals

The number of values of \(x\), where \(f(x) = \cos x + \cos 2x\) attains its maximum is

A vector perpendicular to the plane containing the points \(A(1, 1, -2)\), \(B(2, 0, -1)\), \(C(0, 2, 1)\) is

If \(P = \begin{bmatrix} \frac{\sqrt{3}}{2} & \frac{1}{2} -\frac{1}{2} & \frac{\sqrt{3}}{2} \end{bmatrix}\), \(A = \begin{bmatrix} 1 & 1 0 & 1 \end{bmatrix}\), and \(Q = PAP'\), then \(P'Q^{2005}P\) is

\(\int \cos^{-3/7} x \sin^{-11/7} x \, dx\) is equal to

All the chords of the hyperbola \(3x^2 - 2y^2 - 4x + y = 0\), subtending a right angle at the origin pass through the fixed point

The vector equation of the plane through the point \(\hat{i} + \hat{j} - 2\hat{k}\) and perpendicular to the line of intersection of the planes \(\mathbf{r} \cdot (\hat{i} - \hat{j} + 3\hat{k}) = 1\) and \(\mathbf{r} \cdot (4\hat{i} - 2\hat{j} + 2\hat{k}) = 2\) is