List of top Questions asked in MET

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

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

The eccentricity of the conic \(9x^2 - 16y^2 = 144\) 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 ratio in which the segment joining \((2,1)\) and \((0,-2)\) is divided by the line \(2x - 3y + 4 = 0\) 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

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 \(\sec A - \tan A + a = 0\), then \(\sin A\) 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

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

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

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

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}

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

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

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

If \(\log_3 2\), \(\log_3(2x-5)\) and \(\log_3(2x-\tfrac{7}{2})\) are in AP, then the value of \(x\) is

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

The sum of the series \(0.2 + 0.004 + 0.00006 + 0.0000008 + \dots\) is