List of top Questions asked in MET- 2021

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

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

The ratio in which the segment joining \((2,1)\) and \((0,-2)\) is divided by the line \(2x - 3y + 4 = 0\) is

The equation to the line through the point of intersection of \(x - y + 1 = 0\), \(3x + 2y + 4 = 0\) and perpendicular to \(x - 4y = 0\) is

The eccentricity of the conic \(9x^2 - 16y^2 = 144\) is

The value of \(\lim_{\theta \to 0} \frac{\tan\theta}{\theta}\) is

A line cuts off on the coordinate axes positive intercepts whose sum is 4. If it passes through \((9/2,-5)\), its equation is

\(\lim_{x\to0} \frac{\sin3x - \sin x}{\sin x}\) is

If \(\sec A - \tan A + a = 0\), then \(\sin A\) is equal to

If \(A(-1,2)\), \(B(5,1)\), \(C(6,5)\) are the vertices of a parallelogram \(ABCD\). The equation to the diagonal through \(B\) is

The point on the line \(y = x\) equidistant from \((4,0)\) and \((5,1)\) is

If \(A, B, C\) are the angles of a triangle, then \(\cos B + \cos C - \cos A + 1\) is equal to

In a simple regular graph, total degree is 28. If the graph has more than one cycle in it, then the degree of each vertex is

\(\cot^2\left(\frac{\pi}{4} + \frac{\theta}{2}\right)\) is equal to

\(\frac{\cos\theta}{1-\tan\theta} + \frac{\sin\theta}{1-\cot\theta}\) is equal to

If \(\sin\theta = -\frac{24}{25}\) and \(\theta\) is in the 4th quadrant, \(7\tan\theta + 25\cos\theta\) is equal to

\(\cos\frac{\pi}{12} + \cos\frac{17\pi}{12} + \cos\frac{11\pi}{12}\) is equal to

The middle term of \(\left(\sqrt{x} - \frac{1}{\sqrt{x}}\right)^6\) is

The value of \(\frac{C(n,2){(n+1)!}\) is}

The coefficient of \(x\) in the expansion of \((1 + x + x^2 + x^3)^{-3\) is}

In the usual notation, \(\frac{^nC_1}{2} + \frac{^nC_2}{3} + \cdots + \frac{^nC_n}{n+1}\) is equal to

The sum of the first n terms of two AP's are in the ratio \((2n+3):(3n-1)\). The ratio of their 5th terms is