List of top Mathematics Questions asked in MET

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

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

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 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

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

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

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

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

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

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

The area of the quadrilateral formed by the tangents at the end point of latus rectum to the ellipse \( \frac{x^2}{9} + \frac{y^2}{5} = 1 \) is

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

\( \lim_{x \to 0} \frac{e^{\sin x} - 1}{x} \) is equal to

If $p$ and $q$ are two statements, then $(p \land q) \lor (q \leftrightarrow p)$ is

The value of the determinant \[ \begin{vmatrix} (a^x + a^{-x})^2 & (a^x - a^{-x})^2 & 1 (b^x + b^{-x})^2 & (b^x - b^{-x})^2 & 1 (c^x + c^{-x})^2 & (c^x - c^{-x})^2 & 1 \end{vmatrix} \] is

If $a, b, c$ are cube roots of unity, then \[ \begin{vmatrix} e^a & e^{2a} & e^{3a}-1 e^b & e^{2b} & e^{3b}-1 e^c & e^{2c} & e^{3c}-1 \end{vmatrix} \] is equal to

If \( f \circ g = |\sin x| \) and \( g \circ f = \sin^2 \sqrt{x} \), then \( f(x) \) and \( g(x) \) are

Let \( f : \mathbb{R} \to \mathbb{R} \) be defined by \( f(x) = \frac{x}{\sqrt{1+x^2}} \), then \( (f \circ f)(x) \) is

If \( f(x) = \frac{a^x + a^{-x}}{2} \) and \( f(x+y) + f(x-y) = k f(x)f(y) \), then \( k \) is equal to

If \( \tan^{-1}\left(\frac{a}{x}\right) + \tan^{-1}\left(\frac{b}{x}\right) = \frac{\pi}{2} \), then \( x \) is equal to