List of top Mathematics Questions

If a₁, a₂,….a_n are in G.P. then
\(\begin{vmatrix} \log a_n & \log a_{n+1} & \log a_{n+2} \\ \log a_{n+3} & \log a_{n+4} & \log a_{n+5} \\ \log a_{n+6} & \log a_{n+7} & \log a_{n+8} \end{vmatrix}\) is

The inverse of the matrix \(\begin{bmatrix} 2 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 4 \end{bmatrix}\) is

The area of region bounded by the lines y = mx, x = 1 and x = 2 and the x-axis is 7.5 sq. units, then m is

If A is 3 × 4 matrix and B is a matrix such that A'B and B'A are both defined, then the order of B is

If the matrix \(\begin{bmatrix} 2 & 3 \\ 5 & -1 \end{bmatrix}\)= A + B, where A is symmetric and B is skew-symmetric then B =

Inverse of a diagonal non-singular matrix is

The sum value of the series $ \frac{3}{4} +\frac{5}{36} +\frac{7}{144} +\frac{9}{400} + ...\infty $ is

$2^{1/4}. 2^{2/8}. 2^{3/16}. 2^{4/32}......\infty$ is equal to-

$\Delta \, ABC$ has vertices at $A = (2, 3,5), B = (-1,3, 2)$ and $C = (\lambda , 5, \mu )$. If the median through A is equally inclined to the axes, then the values of $\lambda$ and $\mu$ respectively are

Let $F(x) = e^x, G(x) = e^{-x}$ and $H(x) = G(F(x))$, where $x$ is a real variable. Then $\frac{dH}{dx}$ at $x = 0$ is

Let \( a, b, c \) be distinct real numbers such that
\[\Delta = \begin{vmatrix}2014 & 2015 & 2013 + a^{-1} \\2015 & 2016 & 2013 + b^{-1} \\2016 & 2017 & 2013 + c^{-1}\end{vmatrix} = 0\]
Then:

Solution of the differential equation\( \frac{dy}{dx}=y^2\) with the condition y(1)=1 is

The points (a, 2), (0, b), (1, 1) are collinear. Then

The area bounded by the curve \(y=x^3, y=0, x=1\) is

The value of \(\int_{-\frac{\pi}{4}}^{\frac{\pi}{4}} (x^2 \sin x + x^3) \, dx\) is:

The sum of the perpendicular distances from the origin to the planes 12x-3y+4z+26=0 and 2x-4y+4z+18=0 is

If \(^nc_7=^nc_4\), then the value of n is

Three cubes of side 2 cm are glued surface to surface horizontally such that it produces a cuboid. What is the surface area of the cuboid?

\( m \) men and \( w \) women are to be seated in a row so that all women sit together. The number of ways in which they can be seated is:

Value of the determinant \[\begin{vmatrix}1 & w & w^2 \\w & w^2 & 1 \\w^2 & 1 & w\end{vmatrix}\] where \( w \) is the cube root of unity is:

If \( A = \begin{bmatrix} -\frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ -\frac{1}{\sqrt{2}} & -\frac{1}{\sqrt{2}} & 0 \\ 0 & 0 & 1 \end{bmatrix} \), then \( A^{-1} \) is:

The value of \(\lambda\) for which the straight line (2x+3y+4)+\(\lambda\)(6x-y+12)=0 is parallel to y-axis is 

A point moves so that the sum of the squares of its distances from the six faces of a cube given by \( x = \pm 1 \), \( y = \pm 1 \), \( z = \pm 1 \) is 10 units. The locus of the point is:

The system of linear equations -2x+y+2=a, x-2y+z=b, x+y-2z=c have infinitely many solutions if

If \( a, b, c \) are non-zero, then the number of solutions of \[\frac{2x^2}{a^2} - \frac{y^2}{b^2} - \frac{z^2}{c^2} = 0,\]\[-\frac{x^2}{a^2} + \frac{2y^2}{b^2} - \frac{z^2}{c^2} = 0\]is: