List of top Questions asked in MET- 2021

The system of linear equations \[ x+y+z=0,\; 2x+y-z=0,\; 3x+2y=0 \] has

The value of \( a \) for which the system \[ ax + y + z = 0,\; x + ay + z = 0,\; x + y + z = 0 \] has non-zero solutions is

In the determinant \[ \begin{vmatrix} 3 & x & -1 2 & -1 & 4 1 & y & -3 \end{vmatrix} \] the sum of the cofactors of \(x\) and \(y\) is

If \( A = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ a & b & -1 \end{bmatrix} \), then \( A^2 \) is equal to

If \(A+B+C=\pi\), then \[ \begin{vmatrix} \sin(A+B+C) & \sin B & \cos C -\sin B & 0 & \tan A \cos(A+B) & -\tan A & 0 \end{vmatrix} \] is equal to
If \(a \neq b\) and \[ \begin{vmatrix} a & a^2 & 1+a^3 b & b^2 & 1+b^3 1 & 1 & 2 \end{vmatrix} = 0, \] then \(ab\) is equal to
If \(\alpha,\beta,\gamma\) are direction angles, then \(\sin^2\alpha+\sin^2\beta+\sin^2\gamma\) is
A parallelogram is constructed on vectors \(\vec{a}=3\vec{\alpha}-\vec{\beta},\; \vec{b}=\vec{\alpha}+3\vec{\beta}\). If \(|\vec{\alpha}|=|\vec{\beta}|=2\) and angle between them is \(\pi/3\), find length of a diagonal
\([\vec{a} + \vec{b},\; \vec{b} + \vec{c},\; \vec{c} + \vec{a}]\) is equal to
The value of \(\{(\vec{a} \times \vec{b})^2 + (\vec{a}\cdot \vec{b})^2\\div a^2 b^2\) is}
\(\vec{a}=\frac{1}{7}(2\hat{i}+3\hat{j}+6\hat{k}),\; \vec{b}=\frac{1}{7}(3\hat{i}-\lambda \hat{j}+2\hat{k})\). If \(\vec{a}\perp \vec{b}\), find \(\lambda\)
The value of \(|\vec{a} \times \vec{b} + \vec{b} \times \vec{a}|\) is
Differential equation of family \(y=a\cos \mu x + b\sin \mu x\) is
The area enclosed between the curves \(y^2 = 2x\) and \(x^2 = 2y\) is
\(\int_0^1 \sin^{-1}x \, dx\) is
\(\int_1^e \frac{\log x}{x} \, dx\) is
\(\int_{-\pi/2}^{\pi/2} |\sin x| dx\) is
\(\int_0^1 x(1-x)^{12 dx\) is equal to}
The function \(\sin x(1+\cos x)\), \(0 \le x \le \pi/2\), has maximum value when \(x\) is
If \(y=\sqrt{\sin x + \sqrt{\sin x + \cdots}}\), then \(\frac{dy}{dx}\) is
The function whose derivative is equal to itself is
If \(\tan^{-1}x + \tan^{-1}y + \tan^{-1}z = \pi\), then the value of \(x+y+z-xyz\) is
\(\sin^{-1}\frac{1}{\sqrt{5}} + \cos^{-1}\frac{3}{\sqrt{10}}\) is equal to
If \[ \begin{bmatrix} a & 2 & 3 b & 5 & -1 \end{bmatrix} \begin{bmatrix} 1 & 2 3 & 4 -1 & 1 \end{bmatrix} = \begin{bmatrix} 4 & 13 12 & 11 \end{bmatrix} \] then $(a,b)$ is
Pick out the wrong statement. If \(A\) and \(B\) are square matrices of the same order, then