List of top Mathematics Questions asked in MET

If \(\cos P = 1/7\) and \(\cos Q = 13/14\), where P and Q both are acute angles. Then the value of \(P - Q\) is

The equation \(3\cos x + 4\sin x = 6\) has ... solution.

If \(\sec^{-1}x = \csc^{-1}y\), then \(\cos^{-1}(1/x) + \cos^{-1}(1/y)\) is equal to

If n be any integer, then \(n(n+1)(2n+1)\) is:

If \(\tan\theta = -4/3\), then the value of \(\sin\theta\) is

If \(c = 2\cos\theta\), then the value of the determinant \(\Delta = \begin{vmatrix} c & 1 & 0 \\ 1 & c & 1 \\ 6 & 1 & c \end{vmatrix}\) is

The equation of the parabola whose vertex is (-1, -2), axis is vertical and which passes through the point (3, 6), is

The length of the axis of the conic \(9x^2 + 4y^2 - 6x + 4y + 1 = 0\) are

If \(f(x) = \cot^{-1}\left(\frac{3x - x^3}{1 - 3x^2}\right)\) and \(g(x) = \cos^{-1}\left(\frac{1 - x^2}{1 + x^2}\right)\), then \(\lim_{x \to a} \frac{f(x) - f(a)}{g(x) - g(a)}\), \(0<a<1/2\), is

If \(f(x) = \begin{cases} x, & 0 \le x \le 1 \\ 2x - 1, & 1<x \end{cases}\), then

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

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

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

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

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

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

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