List of top Mathematics Questions

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

The shortest distance between the skew lines $\bar{r}=(i+2\bar{j}+3\bar{k})+t(i+3\bar{j}+2\bar{k}) $ and $\bar{r}=(4i+5\bar{j}+6\bar{k})+t(2i+3\bar{j}+\bar{k})$ is

If a line $l$ passes through $(k, 2 k),(3 k, 3 k)$ and $(3,1), k \neq 0$, then the distance from the origin to the line $l$ is

Set $ A $ and $ B $ have $ 3 $ and $ 6 $ elements respectively. What can be the minimum number of elements in $ A \cup B $ ?

If tan $ \theta$ + tan $4\theta$ + tan $7\theta$ = tan $\theta$ tan $4\theta$ tan $7\theta,$ then the general solution is

Let $S=\frac{2}{1} ^{n}C_{0}+\frac{2^{2}}{2} ^{n}C_{1}+\frac{2^{3}}{3} ^{n}C_{2}+ ...... +\frac{2^{n+1}}{n+1} ^{n}C_{n}$. Then $S$ equals

If the integers $m$ and $n$ are chosen at random from $1$ to $100$ , then the probability that a number of the form $7^{n}+7^{m}$ is divisible by $5$ , equals to

The area enclosed by the curves $y = sin\, x + cos \,x$ and $y\, =\, | cos\, x - sin\, x |$ over the interval $ \Bigg [0 , \frac{\pi}{2} \Bigg] $ is

For $x \in(0, \pi)$, the equation $\sin x+2 \sin 2 x-\sin 3 x=3$ has

Let $ V_r $ denote the sum of the first $ r $ terms of an arithmetic progression $ (AP) $ whose first term is $ r $ and the common difference is $ (2r - 1) $ . The sum $ V_1 + V_2 + ..... + V_n $ is

Let $ f(x) $ be differentiable on the interval $ (0, \infty) $ such that $ f(1) = 1 $ and $ lim_{t \rightarrow x} \frac {t^2f(x)-x^2f(t)}{t-x} =1 $ for each $ x>0 $ . Then, $ f(x) $ is

Let $ f $ be the function $ [-\pi, \pi] $ given by $ f(0) = 9 \,and\,f(x) \,=\, f(x) = sin (\frac {9x}{2})/sin(\frac {x}{2}) $ for $ x \neq 0 $ . The value of $ \frac{2}{\pi} \int^{\pi}_{-\pi} $ $ f(x) dx $ is