List of top Mathematics Questions asked in MET

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 \[ \Delta_r = \begin{vmatrix} 1 & n & n \\ 2r & n^2+n+1 & n^2+n \\ 2r-1 & n^2 & n^2+n+1 \end{vmatrix} \] and \( \sum_{r=1}^{n} \Delta_r = 56 \), then \( n \) 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 $p$ and $q$ are two statements, then $(p \land q) \lor (q \leftrightarrow p)$ 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 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
$AB$ 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 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
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
The distance of the point (3, 5) from $2x + 3y -14 = 0$ measured parallel to $x - 2y = 1$ 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
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
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
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
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
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 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