List of top Mathematics Questions

The area of the parallelogram whose adjacent sides are $\hat{i}+ \hat {k} $ and $2\hat {i}+\hat {j}+\hat {k}$ is

Area of the region bounded by two parabolas $y\, =\, x^2$ and $x \,= \, y^2 $ is

If $a, b$ and $c$ are in A.P., then the value of $\begin{vmatrix} {x+2}&{x+3} &{x+a}\\ {x+4}&{x+5}& {x+b} \\ {x+6}&{x+7} &{x+c}\\ \end{vmatrix}$ is

How many $5$ digit telephone numbers can be constructed using the digits $0$ to $9$, if each number starts with $67$ and no digit appears more than once ?

The order and degree of the differential equation $y=x\frac{dy}{dx}+\frac{2}{\frac{dy}{dx}}$ is

The value of $\sin (2\, \sin^{-1}\, 0.8)$ is equal to

The value of the integral $\int_\limits{-\pi/4}^{\pi/4} \log (\sec \theta-\tan \theta) d \theta$ is

A stone is dropped into a quiet lake and waves move in circles at the speed of $5\, cm/sec$. At that instant, when the radius of circular wave is $8 \,cm$, how fast is the enclosed area increasing ?

The standard deviation of $9, 16, 23, 30, 37, 44, 51$ is

If $A$ is $3 \times 4$ matrix and $B$ is a matrix such that $A'B$ and $BA'$ are both defined. Then $B$ is of the type

The angle between two diagonals of a cube is

In a triangle $ABC, a[b \,cos \,C - c\, cos\, B]$ =

The symmetric part of the matrix $A =\begin{bmatrix} {1}&{2} &{4}\\ {6}&{8}& {2} \\ {2}&{-2}&{7}\\ \end{bmatrix} $ is

Let $S$ denote the sum of the infinite series $1+\frac{8}{2!}+\frac{21}{3!}+\frac{40}{4!}+\frac{65}{5!} ....... $. Then

The condition for the lines $l x+m y+n=0$ and $l_{1} x+m_{1} y+n_{1}=0$ to be conjugate with respect to the circle $x^{2}+y^{2}=r^{2}$, is

The slopes of the focal chords of the parabola $y^{2}=32 x$, which are tangents to the circle $x^{2}+y^{2}=4$, are

The point at which the circles $x^{2}+y^{2}-4 x-4 y+7=0 $ and $x^{2}+y^{2}-12 x -10 y+45=0$ touch each other, is

Coefficient of $ x^{11}$ in the expansion of $(1 + x^2)^4 (1 + x^3)^7 (1 + x^4)^{12} $

If $ x, y $ and $ z $ are all different and $ \begin{vmatrix}x&x^{2}&1+x^{3}\\ y&y^{2}&1+y^{3}\\ z&z^{2}&1+z^{3}\end{vmatrix}=0 $ then

Let the straight line $ x = b $ divide the area enclosed by $ y = (1 - x)^2 $ , $ y = 0 $ and $ x = 0 $ into two parts $ R_1(0 \le x \le b) $ and $ R_2(b \le x \le 1) $ such that $ R_1-R_2 = \frac {1}{4}. $ Then, $b$ equals

If \(\alpha, \beta\) are the roots of the quadratic equation \(x^2 + px + q = 0\), then the values of \(\alpha^{3}, \beta^{3}\) and \(\alpha^{4}+\alpha^{2}\beta^{3}+\beta^{4}\) are respectively

If $ \alpha,\beta $ are the roots of the equation $ ax^2+bx+c = 0 $ and $ S_n = \alpha^n + \beta^n, $ then a $ S_{n+1} + bS_{n} + cS_{n-1} $ is equal to

Let, $\vec {a} = - \hat {i} - \hat {k}, \vec {b} = - \hat {i} +\hat {j} $ and $\vec {c} = \hat {i}+2\hat {j}+3\hat {k} $ be three given vectors. If $\vec {r} $ is a vector such that $ \vec {r} \times \vec {b} = \vec {c} \times \vec{b} $ and $\vec {r} \cdot \vec{a} = 0 $ , then the value of $\vec {r} \cdot \vec {b} $ is

If $ \int_{0}^{\frac{\pi}{3}}\frac{cos x}{3 + 4 sin x}dx = k\, log \left(\frac{3+2\sqrt{3}}{3}\right) $ then $k$ is