List of top Mathematics Questions asked in MET

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

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

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

If \(\mathbf{a} \cdot \mathbf{i} = \mathbf{a} \cdot (\mathbf{j} + \mathbf{i}) = \mathbf{a} \cdot (\mathbf{i} + \mathbf{j} + \mathbf{k})\), then \(\mathbf{a}\) is equal to

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

If \(\theta\) be the angle between the unit vectors \(\mathbf{a}\) and \(\mathbf{b}\), then \(\cos \frac{\theta}{2}\) is equal to

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

If the scalar projection of the vector \(x\mathbf{i} - \mathbf{j} + \mathbf{k}\) on the vector \(2\mathbf{i} - \mathbf{j} + 5\mathbf{k}\) is \(\frac{1}{\sqrt{30}}\) then value of \(x\) is equal to

The minimum value of the expression \(\sin \alpha + \sin \beta + \sin \gamma\) where \(\alpha, \beta, \gamma\) are real numbers satisfying \(\alpha + \beta + \gamma = \pi\) is

The value of \(\lim_{x \to \infty} \frac{x}{x + \frac{\sqrt[3]{x}}{x + \frac{\sqrt[3]{x}}{x + \dots}}}\) is

If \(f(x)\) defined by \(f(x) = \begin{cases} \frac{|x^2 - x|}{x^2 - x}, & x \neq 0, 1 \\ 1, & x = 0 \\ -1, & x = 1 \end{cases}\) then \(f(x)\) is continuous for all

The maximum value of \((\cos \alpha_1) \cdot (\cos \alpha_2) \cdots (\cos \alpha_n)\) under the restrictions \(0 \leq \alpha_1, \alpha_2, \ldots, \alpha_n \leq \frac{\pi}{2}\) and \((\cot \alpha_1) \cdot (\cot \alpha_2) \cdots (\cot \alpha_n) = 1\) is

Function \(f(x)\) is defined as \(f(x) = \begin{cases} 3x, & x<1 \\ a-b, & x = 1 \\ 4b-a, & x>1 \end{cases}\) If \(f(x)\) is continuous at \(x = 1\), but discontinuous at \(x = 2\) then the locus of the point \((a, b)\) is a straight line excluding the point where it cuts the line

The pair of lines \(\sqrt{3}x^2 - 4xy + \sqrt{3}y^2 = 0\) are rotated about the origin by \(\frac{\pi}{6}\) in the anticlockwise sense. The equation of the pair in the new position is

The value of \(\lim_{x \to 1} \frac{\sum_{k=1}^{100} x^k - 100}{x - 1}\) is

\(\sum_{k=0}^{10} {}^{20}C_k\) is equal to

If the line \(\frac{x}{a} + \frac{y}{b} = 1\) moves in such a way that \(\frac{1}{a^2} + \frac{1}{b^2} = \frac{1}{c^2}\) where \(c\) is a constant, then the locus of the foot of perpendicular from the origin on the straight line is

If the point \((a,a)\) is placed in between the lines \(|x+y| = 4\) then

The value of \(x\) in the expression \((x + x^{\log_{10}x})^5\), if the third term in the expansion is 1,000,000, is

The number of rational values of \(m\) for which the \(y\)-coordinate of the point of intersection of the lines \(3x + 2y = 10\) and \(x = my + 2\) is an integer is

A straight line cuts intercepts from the axis of coordinates the sum of the reciprocals of which is a constant \(K\). Then it always passes through a fixed point

If \(b<0\), then the roots \(x_1\) and \(x_2\) of the equation \(2x^2 + 6x + b = 0\) satisfy the condition \(\left(\frac{x_1}{x_2}\right) + \left(\frac{x_2}{x_1}\right)<K\), where \(K\) is equal to

If the roots of the equation \((a-1)(x^2 + x + 1)^2 = (a+1)(x^4 + x^2 + 1)\) are real and distinct then the value of \(a \in\)

If the sum of two of the roots of \(x^3 + px^2 + qx + r = 0\) is zero, then \(pq =\)

If \(m\) parallel lines in a plane are intersected by a family of \(n\) parallel lines, then the number of parallelograms that can be formed is