List of top Mathematics Questions asked in MET

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

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

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

Which of the following statement is not tautology?

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

The locus of the point \(z\) satisfying \(\arg\left(\frac{z-1}{z+1}\right) = k\) (where \(k\) is non-zero) 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 binary representation of 60 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

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

If \(z = \frac{-2}{1 + \sqrt{3}i}\) then the value of \(\arg(z)\) 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

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

The number of real solutions of the equation \(1 + |e^x - 1| = e^x(e^x - 2)\) is

If \(z = x + iy\), \(z^{1/3} = a - ib\) then \(\frac{x}{a} - \frac{y}{b} = k(a^2 - b^2)\), where \(k\) is equal to

Let \(f(x) = x^p \cos(1/x)\) when \(x \neq 0\) and \(f(x) = 0\), when \(x = 0\). Then \(f(x)\) will be differentiable at \(x = 0\), if

The derivative of \(f(x) = 3|2 + x|\) at the point \(x_0 = -3\) is

Derivative of the function \(f(x) = \log_5(\log_7 x)\), \(x>7\) is

If \(u = x^2 + y^2\) and \(x = s + 3t\), \(y = 2s - t\) then \(\frac{d^2 u}{ds^2}\) is equal to