List of top Questions asked in MET

Fill in the blanks with correct prepositions.

Look at the underlined part of the given sentence. Below the sentence are given three possible substitutions for the underlined part. If any of substitutions; (a), (b) or (c) is better than the underlined part, choose that substitution as your response. If none of the substitution improves the sentence, choose (d) as your response. Thus, a ‘No improvement’ response will be signified by the letter (d).
Rohit assured Sunita that he would look at her work while she was on leave.

Look at the underlined part of the given sentence. Below the sentence are given three possible substitutions for the underlined part. If any of substitutions; (a), (b) or (c) is better than the underlined part, choose that substitution as your response. If none of the substitution improves the sentence, choose (d) as your response. Thus, a ‘No improvement’ response will be signified by the letter (d).
Newton wanted to know why did the apple fall to the ground.

Look at the underlined part of the given sentence. Below the sentence are given three possible substitutions for the underlined part. If any of substitutions; (a), (b) or (c) is better than the underlined part, choose that substitution as your response. If none of the substitution improves the sentence, choose (d) as your response. Thus, a ‘No improvement’ response will be signified by the letter (d).
He has been working off and on for several years to compile a dictionary.

Look at the underlined part of the given sentence. Below the sentence are given three possible substitutions for the underlined part. If any of substitutions; (a), (b) or (c) is better than the underlined part, choose that substitution as your response. If none of the substitution improves the sentence, choose (d) as your response. Thus, a ‘No improvement’ response will be signified by the letter (d).
It is no good to cry over spilt milk.

A line passing through origin and is perpendicular to two given lines \(2x + y + 6 = 0\) and \(4x + 2y - 9 = 0\). The ratio in which the origin divides this line, is

The intercepts on the straight line \(y = mx\) by the lines \(y = 2\) and \(y = 6\) is less than 5, then \(m\) belongs to

The number of positive integers satisfying the inequality \(^{n+1}C_{n-1} + ^{n}C_{n-1} \leq 50\) is

The locus of the mid-points of the chords of the circle \(x^2 + y^2 = 16\) which are tangent to the hyperbola \(9x^2 - 16y^2 = 144\) is

All the chords of the hyperbola \(3x^2 - 2y^2 - 4x + y = 0\), subtending a right angle at the origin pass through the fixed point

The vector equation of the plane through the point \(\hat{i} + \hat{j} - 2\hat{k}\) and perpendicular to the line of intersection of the planes \(\mathbf{r} \cdot (\hat{i} - \hat{j} + 3\hat{k}) = 1\) and \(\mathbf{r} \cdot (4\hat{i} - 2\hat{j} + 2\hat{k}) = 2\) is

\(\int \cos^{-3/7} x \sin^{-11/7} x \, dx\) is equal to

If \(P = \begin{bmatrix} \frac{\sqrt{3}}{2} & \frac{1}{2} -\frac{1}{2} & \frac{\sqrt{3}}{2} \end{bmatrix}\), \(A = \begin{bmatrix} 1 & 1 0 & 1 \end{bmatrix}\), and \(Q = PAP'\), then \(P'Q^{2005}P\) is

A vector perpendicular to the plane containing the points \(A(1, 1, -2)\), \(B(2, 0, -1)\), \(C(0, 2, 1)\) is

The number of values of \(x\), where \(f(x) = \cos x + \cos 2x\) attains its maximum 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

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

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

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

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

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