List of top Mathematics Questions asked in MET

The direction cosines of any normal to the xy-plane are

If \(\int f(x) dx = F(x)\), then \(\int x^3 f(x^2) dx\) is equal to

If the distance between the foci of an ellipse is 6 and the length of the minor axis is 8, then the eccentricity is

The approximate value of \(\int_1^5 x^2 dx\) using trapezoidal rule with \(n = 4\) is

If \(n \in \mathbb{N}\), then \(|\sin nx|\)

Which is the correct order for a given number \(\alpha\) in increasing order?

The vertex connectivity of any tree is

The maximum value of \(3\cos\theta + 4\sin\theta\) is

If \(\mathbf{a}, \mathbf{b}\) and \(\mathbf{c}\) are non-collinear vectors such that for some scalars \(x, y, z\), \(x\mathbf{a} + y\mathbf{b} + z\mathbf{c} = \mathbf{0}\), then

In \(\triangle ABC\), \(\frac{b - c}{r_1} + \frac{c - a}{r_2} + \frac{a - b}{r_3}\) is equal to

\(\cos^{-1}\{\cos 2\cot^{-1}(\sqrt{2} - 1)\}\) is equal to

One mapping (function) is selected at random from all the mappings of the set \(A = \{1, 2, 3, \dots, n\}\) into itself. The probability that the mapping selected is one-one, is

The function \(f(x) = [x]\cos\left[\frac{2x - 1}{2}\right]\pi\), where \([\,\cdot\,]\) denotes the greatest integer function, is discontinuous at

If \(\mathbf{a} = -\hat{\mathbf{i}} + 2\hat{\mathbf{j}} - \hat{\mathbf{k}}\), \(\mathbf{b} = \hat{\mathbf{i}} + \hat{\mathbf{j}} - 3\hat{\mathbf{k}}\) and \(\mathbf{c} = -4\hat{\mathbf{i}} - \hat{\mathbf{k}}\), then \(\mathbf{a} \times (\mathbf{b} \times \mathbf{c}) + (\mathbf{a} \cdot \mathbf{b})\mathbf{c}\) is

A perpendicular is drawn from the point P(2, 4, -1) to the line \(\frac{x + 5}{1} = \frac{y + 3}{4} = \frac{z - 6}{-9}\). The equation of the perpendicular from P to the given line is

The number of five digits numbers that can be formed without any restriction is

If \(f(x) = \cos[\pi^2]x + \cos[-\pi^2]x\), then

The range of \(f(x) = \sec\left(\frac{\pi}{4}\cos^2 x\right)\), \(-\infty<x<\infty\) is

The domain of the function \(f(x) = \frac{\sin^{-1}(3 - x)}{\log(|x| - 2)}\) is

The remainder obtained when \(1! + 2! + \cdots + 200!\) is divided by 14 is

Equation \(x * a = b\) has in group \((G, *)\)

If \(z_1, z_2\) and \(z_3\) are complex number such that \(|z_1| = |z_2| = |z_3| = \left|\frac{1}{z_1} + \frac{1}{z_2} + \frac{1}{z_3}\right| = 1\) then \(|z_1 + z_2 + z_3|\) is

If \(f(x) = (a - x^n)^{1/n}\), where \(a>0\) and \(n\) is a positive integer, then \(f[f(x)]\) is equal to

A function \(f(x) = \frac{x^2 - 3x + 2}{x^2 + 2x - 3}\) is

The number of integral solution of \(\frac{x + 1}{x^2 + 2}>\frac{1}{4}\) is