List of top Questions asked in MET

The projection of a line on a co-ordinate axes are 2, 3, 6. Then the length of the line is

The decimal equivalent of the binary number 10011.1 is

The binary representation of 60 is

Which of the following statement is not tautology?

The period of \(f(x) = \sin\left(\frac{\pi x}{n-1}\right) + \cos\left(\frac{\pi x}{n}\right)\), \(n \in \mathbb{Z}\), \(n>2\) is

For \(\theta>\pi/3\) the value of \(f(\theta) = \sec^2\theta + \cos^2\theta\) always lies in the interval

The radius of the circle whose arc of length 15 cm makes an angle of 3/4 radian at the centre, is

If \(f_n(x) = e^{f_{n-1}(x)}\) for all \(n \in \mathbb{N}\) and \(f_0(x) = x\) then \(\frac{d}{dx}\{f_n(x)\}\) is equal to

If \(3^x + 2^{2x} \ge 5^x\), then the solution set for \(x\) is

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

The triangle PQR of which the angles P, Q, R satisfy \(\cos P = \sin Q = 2 \sin R\) 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 locus of the point \(P(x, y)\) satisfying \(\sqrt{(x-3)^2 + (y-1)^2} + \sqrt{(x+3)^2 + (y-1)^2} = 6\) is

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

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

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

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

Three blocks of masses \(2\ \mathrm{kg}\), \(3\ \mathrm{kg}\) and \(5\ \mathrm{kg}\) are connected to each other with light string and are then placed on a frictionless surface as shown in the figure. The system is pulled by a force \(\mathrm{F} = 10\ \mathrm{N}\), then tension \(\mathrm{T_1}\) is

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

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

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