List of top Questions asked in MET- 2014

If the chords of the hyperbola $x^2 - y^2 = a^2$ touch the parabola $y^2 = -4ax$, then the locus of the middle points of these chords is

A rhombus is inscribed in the region common to the two circles \( x^2 + y^2 - 4x - 12 = 0 \) and \( x^2 - y^2 + 4x - 12 = 0 \) with two of its vertices on the line joining the centres of the circles. The area of rhombus is

If the line \( \frac{x}{a} + \frac{y}{b} = 1 \) moves such that \( \frac{1}{a^2} + \frac{1}{b^2} = \frac{1}{c^2} \), then the locus of the foot of the perpendicular from the origin to the line is

The radius of the circle passing through the foci of the ellipse \( \frac{x^2}{4} + \frac{4y^2}{7} = 1 \) and having its centre at \( \left(\frac{1}{2}, 2\right) \) is

$AB$ is a chord of the parabola $y^2 = 4ax$ with vertex $A$. $BC$ is perpendicular to $AB$ meeting axis at $C$. Projection of $BC$ on axis is

The distance of the point (3, 5) from $2x + 3y -14 = 0$ measured parallel to $x - 2y = 1$ is

If the line \( y - \sqrt{3}x + 3 = 0 \) cuts the parabola \( y^2 = x + 2 \) at \( A \) and \( B \), then \( PA \cdot PB \) where \( P = (\sqrt{3},0) \) is

If the term free from \( x \) in the expansion of \( \left(\sqrt{x} - \frac{k}{x^2}\right)^{10} \) is 405, then the value of \( k \) is

Out of 50 tickets numbered 00, 01, 02, …, 49, one ticket is drawn randomly. The probability that the ticket has the product of its digits 7, given that the sum of the digits is 8, is

In a triangle, the lengths of two larger sides are 10 cm and 9 cm. If the angles are in AP, then the third side is

\( S = \{1,2,3,\dots,20\} \) is to be partitioned into four sets \( A, B, C, D \) of equal size. The number of ways is

If \( \tan \frac{\alpha}{2} \) and \( \tan \frac{\beta}{2} \) are the roots of \( 8x^2 - 26x + 15 = 0 \), then \( \cos(\alpha + \beta) \) is

If \( a\cos^3\alpha + 3a\cos\alpha\sin^2\alpha = m \) and \( a\sin^3\alpha + 3a\cos^2\alpha\sin\alpha = n \), then \( (m+n)^{2/3} + (m-n)^{2/3} \) is equal to

10 different toys are to be distributed among 10 children such that exactly two children do not get any toy. Total number of ways is

Middle term in the expansion of $\left(x^2 + \frac{1}{x^2} + 2\right)^n$ is

The common tangent of the parabolas $y^2 = 4x$ and $x^2 = -8y$ is

A circle of radius 2 is touching both the axes and a circle with centre (6, 5). The distance between their centres is

The variance of first $n$ natural numbers is

If \( a = \cos \frac{2\pi}{7} + i \sin \frac{2\pi}{7} \), then the quadratic equation whose roots are \( \alpha = a + a^2 + a^4 \) and \( \beta = a^3 + a^5 + a^6 \) is

If \( 1, \omega, \omega^2, \ldots, \omega^{n-1} \) are \( n \)th roots of unity, then the value of \( (9-\omega)(9-\omega^2)\cdots(9-\omega^{n-1}) \) is

Which of the following is the strongest base?

Which of the following best define the term hyperconjugation?

The complex [Fe(H\(_2\)O)\(_5\)NO]\(^{2+}\) is formed in the ring test for nitrate ion. This complex is formed by charge transfer in which

Which pair is different from the others?

Valence electrons in the element A are 3 and that in element B are 6. Most probable compound formed from A and B is