List of top Questions asked in MET- 2016

\(1 + \frac{2}{2!} + \frac{3}{3!} + \frac{4}{4!} + \cdots \infty\) equals

The equation of the plane through the points \((2, 3, 1)\) and \((4, -5, 3)\) parallel to X-axis is

The equation of the plane passing through the line of intersection of the planes \(x + y + z = 6\) and \(2x + 3y + 4z + 5 = 0\) and perpendicular to the plane \(4x + 5y + 3z = 8\) is

If \(Q\) is the image of the point \(P(2, 3, 4)\) under the reflection in the plane \(x - 2y + 5z = 6\), then the equation of the line \(PQ\) is

The direction cosines \(l, m, n\) of two lines are connected by the relations \(l + m + n = 0\) and \(lm = 0\), then the angle between them is

The foci of the conic section \(25x^2 + 16y^2 - 150x - 175 = 0\) are

If \(\theta\) is the semi-vertical angle of a cone of maximum volume and given slant height, then \(\tan \theta\) is given by

In a \(\triangle ABC\), if \(\sin A \sin B = \frac{ab}{c^2}\), then the triangle is

If \(x - 2y = 4\), then the minimum value of \(xy\) is

The value of \(\lim_{x \to \pi/6} \frac{\sin x + \sin 2x - 1}{\sin 2x - \sin 3x + 1}\) is

The value of \(\int \frac{\cos x + \sin x}{\cos x + x \sin x} \, dx\) is

The sum of the series \(\frac{3}{4 \times 8} - \frac{3 \times 5}{4 \times 8 \times 12} + \frac{3 \times 5 \times 7}{4 \times 8 \times 12 \times 16} - \cdots\) is

The value of \(\int_0^\pi |\sin 3\theta| \, d\theta\) is

In a \(\triangle ABC\), if \(b = 2\), \(\angle B = 30^\circ\), then the area of the circumcircle of \(\triangle ABC\) (in sq units) is

If \(\sin A + \cos B = a\) and \(\sin B + \cos A = b\), then \(\sin(A + B)\) is equal to

Tangent to the ellipse \(\frac{x^2}{32} + \frac{y^2}{18} = 1\) having slope \(-\frac{3}{4}\) meet the coordinate axis at A and B. Then, the area of \(\triangle AOB\), where O is the origin, is

The condition that the straight line \(cx - by + b^2 = 0\) may touch the circle \(x^2 + y^2 = ax + by\) is

If \(0 < \alpha, \beta, \gamma < \frac{\pi}{2}\), such that \(\alpha + \beta + \gamma = \frac{\pi}{2}\) and \(\cot \alpha, \cot \beta, \cot \gamma\) are in AP, then the value of \(\cot \alpha \cot \gamma\) is

A letter lock contains 5 rings each marked with four different letters. The number of all possible unsuccessful attempts to open the lock is

The value of \(S = \frac{1}{6} \left( \frac{\pi}{2} - \sin^2 \frac{2\pi}{7} - \cos^2 \frac{2\pi}{7} \right)\) is

If \(y^{1/m} + y^{-1/m} = 2x\), then \((x^2 - 1)y'' + xy'\) is equal to

Fifteen coupons are numbered 1, 2, …, 15, respectively. Seven coupons are selected at random one at a time with replacement. The probability that the largest number appearing on a selected coupon is 9, is

Let \(h(x) = \min(x, x^2)\), for every real number \(x\). Then,

The solution of the differential equation \(\frac{dy}{dx} = \sin(x + y) \tan(x + y) - 1\) is

The area bounded by the parabolas \(y^2 = 4a(x + a)\) and \(y^2 = -4a(x - a)\) is