List of top Mathematics Questions asked in MET

If \(\mathbf{a} \times \mathbf{b} = \mathbf{c}\), \(\mathbf{b} \times \mathbf{c} = \mathbf{a}\) and \(a, b, c\) be the moduli of the vectors \(\mathbf{a}, \mathbf{b}, \mathbf{c}\) respectively, then

A unit vector coplanar with \(\mathbf{i} + \mathbf{j} + 2\mathbf{k}\) and \(\mathbf{i} + 2\mathbf{j} + \mathbf{k}\) and perpendicular to \(\mathbf{i} + \mathbf{j} + \mathbf{k}\) is

Let \(A = \begin{bmatrix} 0 & \alpha \\ 0 & 0 \end{bmatrix}\) and \((A + I)^{50} - 50A = \begin{bmatrix} a & b \\ c & d \end{bmatrix}\) then the value of \(a + b + c + d\) is

For two unimodular complex numbers \(z_1\) and \(z_2\), \(\begin{bmatrix} z_1 & z_2 \\ -\bar{z}_2 & \bar{z}_1 \end{bmatrix}^{-1} \begin{bmatrix} \bar{z}_1 & -z_2 \\ \bar{z}_2 & z_1 \end{bmatrix}^{-1}\) is equal to

If \(A\) is a square matrix of order \(n\) such that \(|\operatorname{adj}(\operatorname{adj} A)| = |A|^9\), then the value of \(n\) can be

Coefficient of \(x\) in \(f(x) = \begin{vmatrix} x & (1 + \sin x)^3 & \cos x \\ 1 & \log(1 + x) & 2 \\ x^2 & (1 + x)^2 & 0 \end{vmatrix}\) is

Let \(\alpha_1, \alpha_2\) and \(\beta_1, \beta_2\) be the roots of \(ax^2 + bx + c = 0\) and \(px^2 + qx + r = 0\) respectively. If the system of equations \(\alpha_1 y + \alpha_2 z = 0\) and \(\beta_1 y + \beta_2 z = 0\) has a non-trivial solution, then

The values of \(\alpha\) for which the point \((\alpha - 1, \alpha + 1)\) lies in the larger segment of the circle \(x^2 + y^2 - x - y - 6 = 0\) made by the chord whose equation is \(x + y - 2 = 0\) is

The circles whose equations are \(x^2 + y^2 + c^2 = 2ax\) and \(x^2 + y^2 + c^2 - 2by = 0\) will touch each other externally if

The tangents to \(x^2 + y^2 = a^2\) having inclinations \(\alpha\) and \(\beta\) intersect at \(P\). If \(\cot \alpha + \cot \beta = 0\), then the locus of \(P\) is

An equilateral triangle \(SAB\) is inscribed in the parabola \(y^2 = 4ax\) having its focus at \(S\). If chord \(AB\) lies towards the left of \(S\), then side length of this triangle is

Minimum distance between the curves \(y^2 = 4x\) and \(x^2 + y^2 - 12x + 31 = 0\) is

If the line \(lx + my + n = 0\) cuts the ellipse \(\frac{x^2}{a^2} + \frac{y^2}{25} = 1\) in points whose eccentric angles differ by \(\frac{\pi}{2}\), then \(\frac{a^2 l^2 + b^2 m^2}{n^2}\) is equal to

If the tangent to ellipse \(x^2 + 2y^2 = 1\) at point \(P\left(\frac{1}{\sqrt{2}}, \frac{1}{2}\right)\) meets the auxiliary circle at the points \(R\) and \(Q\), then tangents to circle at \(Q\) and \(R\) intersect at

Which one of the following is independent of \(\alpha\) in the hyperbola \((0<\alpha<\pi/2)\) \(\frac{x^2}{\cos^2 \alpha} - \frac{y^2}{\sin^2 \alpha} = 1\)?

If \(PQ\) is a double ordinate of the hyperbola \(\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1\) such that \(OPQ\) is an equilateral triangle, \(O\) being the centre of the hyperbola, then the eccentricity \(e\) of the hyperbola satisfies

If \(iz^4 + 1 = 0\) then \(z\) can take the value

If \(\cos \alpha + \cos \beta + \cos \gamma = \sin \alpha + \sin \beta + \sin \gamma = 0\) then the value of \(\cos 3\alpha + \cos 3\beta + \cos 3\gamma\) is

If \(Q\) is real and \(z_1, z_2\) are connected by \(z_1^2 + z_2^2 + 2z_1z_2\cos \theta = 0\) then triangle with vertices \(0, z_1\) and \(z_2\) is

Let \(f(xy) = f(x) \cdot f(y)\) for all \(x, y \in \mathbb{R}\). If \(f'(1) = 2\) and \(f(4) = 4\), then \(f'(4)\) equal to

If \(y = \sqrt{(a-x)(x-b)} - (a-b)\tan^{-1}\sqrt{\frac{a-x}{x-b}}\), then \(\frac{dy}{dx}\) is equal to

If \(\sin^{-1}\left(\frac{x^2 - y^2}{x^2 + y^2}\right) = \log a\), then \(\frac{d^2y}{dx^2}\) equals

A man \(1.6\mathrm{m}\) high walks at the rate of \(30\mathrm{m/min}\) away from a lamp which is \(4\mathrm{m}\) above ground. How fast is the man's shadow lengthening?

The value \(P\) such that the length of subtangent and subnormal is equal for the curve \(y = e^{Px} + Px\) at the point \((0,1)\) is

\(AB\) is a diameter of a circle and \(C\) is any point on the circumference of the circle. Then