List of top Questions asked in MET- 2019

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

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

The number of integral solution of \(\frac{x + 1}{x^2 + 2}>\frac{1}{4}\) 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 \(3^x + 2^{2x} \ge 5^x\), then the solution set for \(x\) 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

The triangle PQR of which the angles P, Q, R satisfy \(\cos P = \sin Q = 2 \sin R\) is

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

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

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

The binary representation of 60 is

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

If P(3,4,5), Q(4,6,3), R(-1,2,4), S(1,0,5), then the projection of RS on PQ is

If a line makes \(\alpha, \beta, \gamma\) with the positive direction of x, y and z-axes respectively. Then, \(\cos^2\alpha + \cos^2\beta + \cos^2\gamma\) is equal to

The locus of the point \(z\) satisfying \(\arg\left(\frac{z-1}{z+1}\right) = k\) (where \(k\) is non-zero) is

If the equation \(x^2 + px + q = 0\) and \(x^2 + qx + p = 0\) have a common root then \(p + q + 1\) is equal to

Let \(\omega\) is an imaginary cube root of unity, then the value of \(2(1+\omega)(1+\omega^2) + 3(2\omega+1)(2\omega^2+1) + \cdots + (n+1)(n\omega+1)(n\omega^2+1)\) is

The value of \(a \ge b\) for which the sum of the cubes of the roots of \(x^2 - (a - 2)x + (a - 3) = 0\) assumes the least value, is

Let \(z_1, z_2, z_3\) be three vertices of an equilateral triangle circumscribing the circle \(|z| = 1/2\). If \(z_1 = 1/2 + i\sqrt{3}/2\) and \(z_1, z_2, z_3\) were in anticlockwise sense, then \(z_2\) is