List of top Questions asked in MET- 2021

The term independent of \( x \) in the expansion of \( \left( 2x^4 - \frac{1}{x^2} \right)^{12} \) is

The middle term in the expansion of \( \left(x - \frac{1}{2y}\right)^{10} \) is

If \( \frac{C(2n,3)}{C(n,2)} = \frac{44}{3} \), then \( n \) is equal to

\( \sum_{n=1}^{\infty} \frac{(-1)^{n-1}}{n+1} \) is equal to

\(\vec{a}=\frac{1}{7}(2\hat{i}+3\hat{j}+6\hat{k}),\; \vec{b}=\frac{1}{7}(3\hat{i}-\lambda \hat{j}+2\hat{k})\). If \(\vec{a}\perp \vec{b}\), find \(\lambda\)

A bar magnet has a magnetic moment equal to \(5 \times 10^{-5}\,\text{Wb}\cdot\text{m}\). It is suspended in a magnetising field equal to \(8\pi \times 10^{-4}\,\text{A}\cdot\text{m}^{-1}\). The magnet vibrates with a period \(15\,\text{s}\). The moment of inertia of the magnet is:

The value of \(\{(\vec{a} \times \vec{b})^2 + (\vec{a}\cdot \vec{b})^2\\div a^2 b^2\) 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

If \(\alpha,\beta,\gamma\) are direction angles, then \(\sin^2\alpha+\sin^2\beta+\sin^2\gamma\) is

\([\vec{a} + \vec{b},\; \vec{b} + \vec{c},\; \vec{c} + \vec{a}]\) is equal to

The area enclosed between the curves \(y^2 = 2x\) and \(x^2 = 2y\) is

\(\int_0^1 \sin^{-1}x \, dx\) is

Differential equation of family \(y=a\cos \mu x + b\sin \mu x\) is

The value of \(|\vec{a} \times \vec{b} + \vec{b} \times \vec{a}|\) is

\(\int_1^e \frac{\log x}{x} \, dx\) is

The function \(\sin x(1+\cos x)\), \(0 \le x \le \pi/2\), has maximum value when \(x\) is

\(\int_0^1 x(1-x)^{12 dx\) is equal to}

\(\int_{-\pi/2}^{\pi/2} |\sin x| dx\) 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

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

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