List of top Mathematics Questions

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

If three-digit numbers $ A28, 3B9 $ and $ 62C $ , where $ A, B $ and $ C $ are integers between $ 0 $ and $ 9 $ , are divisible by a fixed integer $ k $ , then the determinant $ \begin{vmatrix}A&3&6\\ 8&9&C\\ 2&B&2\end{vmatrix} $ is

If $ A = \begin{bmatrix}2&3\\ 5&-2\end{bmatrix} $ be such that $ A^{-1} = kA, $ then $ k $ is equal to

The existence of the unique solution of the system of equations $ x + y + z = \beta $ $ 5x - y + az = 10 $ $ 2x + 3y - z = 6 $ depends on

If a normal chord at a point $t$ on the parabola $y^{2}=4 \,a \,x$ subtends a right angle at the vertex, then $t$ equals to

The solution of $\left(x+y\right)^{2} \left(x \frac{dy}{dx}+y\right)=xy \left(1 +\frac{dy}{dx}\right) $ is

The length of the common chord of the two circles $x^{2}+y^{2}-4 y=0 $ and $x^{2}+y^{2}-8 x - 4 y+11=0$, is

A circle with centre at $(2,4)$ is such that the line $x+y+2=0$ cuts a chord of length $6$ . The radius of the circle is

The locus of the centre of the circle, which cuts the circle $x^{2}+y^{2}-20 x+4=0$ orthogonally and touches the line $x=2$, is

The area (in s units) of the triangle formed by the lines $x^{2}-3 x y+y^{2}=0$ and $x+y+1=0$, is