List of top Mathematics Questions

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
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 $ ?
$\int e^{x}\left(\cos x -\sin x\right)dx $ is equal to
If $y = \tan \: x $ then $ \frac{d^2 y}{dx^2} $ =
If $\vec{a}$ and $\vec{b}$ are two vectors of magnitude $2$, each inclined at an angle $60^\circ$, then angle between $\vec{a}$ and $\vec{a} +\vec{b}$ is
If $\sin(120 - A)= \sin(120 - B)$ and $0< A, B < \pi $ then all values of $A, B$ are given by.
Given that $P(A) = 0.1, P(B | A) = 0.6$ and $ P(B |A^c ) = 0.3$ what is $P(A | B)$ ?
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