List of top Mathematics Questions

The values of $x$ for which $ -11\le 4x-3\le 13 $ is

A bag contains $50$ tickets numbered $1, 2, 3, ...,50$ of which five are drawn at random and arranged in ascending order of magnitude $ ({{x}_{1}}

Distance between two parallel planes $2x+ y + 2z = 8$ and $4x + 2y + 4z + 5 = 0$ is

The expression$\frac{tan\, A}{1-cot\, A}+\frac{cot\, A}{1-tan \, A}$ can be written as

Let $x \in \left(0,1\right).$ The set of all x such that $sin^{-1} x >\, cos^{-1} x, $ is the interval:

A man covers a certain distance on a toy train. If the train moved 4 km/h faster, it would take 30 min less. If it moved 2 km/h slower, itwould have taken 20 min more. What is the distance covered?

The $x$-coordinate of the incentre of the triangle that has the coordinates of mid-points of its sides as $(0, 1), (1, 1)$ and $(1,0)$ is

The maximum area of a right angled triangle with hypotenuse $h$ is :

If the line $2x - 3y = k$ touches the parabola $y^2 = 6x$, then find the value of $k$.

If the ages of P and R are added to twice the age of Q, the total becomes 59. If the ages of Q and R are added to thrice the age of P, the total becomes 68 and if the age of P is added to thrice the age of Q and thrice the age of R, the total becomes 108. What is the age of P?

If $ \sin B=3\sin (2A+B), $ then $ 2\tan A+\tan (A+B) $ =

$S$ and $T$ are the foci of an ellipse and $B$ is an end of the minor axis. If $STB$ is an equilateral triangle, then the eccentricity of the ellipse is

A box contains two white balls, three black balls and four red balls. In how many ways can three balls be drawn from the box if at least one black ball is to be included in the draw?

If $4a^2 + b^2 + 2c^2 + 4ab - 6ac - 3bc = 0$, the family of lines $ax + by + c = 0$ is concurrent at one or the other of the two points-

Let $R$ be the relation on the set $R$ of all real numbers, defined by $aRb$ If $|a - b| \le 1$. Then, $R$ is

The value of the integral $\int\limits ^{1/2}_{-1/2}\left[\left(\frac{x+1}{x-1}\right)^{^2}+\left(\frac{x+1}{x-1}\right)^{^2}-2\right]^{^{1/2}}\:\:dx$ is

The line $2x+\sqrt{6y}=2$ is a tangent to the curve $x^{2}-2y^{2}=4$. The point of contact is

The number of integral values of $K$, for which the equation $7\, \cos \,x + 5\, \sin\, x = 2K + 1$ has a solution, is

The sum of the series $ \displaystyle\sum_{r = 0}^{n}\left(-1\right)^{r}\, ^{n}C_{r}\left(\frac{1}{2^{r}}+\frac{3^{r}}{2^{2r}}+\frac{7^{r}}{2^{3r}}+\frac{15^{r}}{2^{4r}}+...m \text{terms}\right)$ is

If a tangent having slope of $-\frac{4}{3}$ to the ellipse $\frac{x^{2}}{18}+\frac{y^{2}}{34}=1$ intersects the major and minor axes in points $A$ and $B$ respectively, then the area of $\Delta OAB$ is equal to (O is the centre of the ellipse)

The line joining two points $A(2,0), B(3,1)$ is rotated about $A$ in anti-clockwise direction through an angle of $15^{\circ}$. The equation of the line in the now position,is

The angle of intersection of the circles $x^{2}+y^{2}-x+y-8=0$ and $x^{2}+y^{2}+2 x+2 y-11=0$ is

The value of $2 \,tan^{-1} (cosec \,tan^{-1} x - tan \,cot^{-1} x))$ is

The vector $b = 3j + 4k$ is to be written as the sum of a vector $b_1$ parallel to $a = i +j$ and a vector $b_2$ perpendicular to $a$. Then $b_1$ is equal to

If the points ($x_1$, $y_1$), ($x_2$, $y_2$) and ($x_3$, $y_3$) are collinear, then the rank of the matrix $\begin{bmatrix}x_{_1}&y_{_1}&1\\ x_{_2}&y_{_2}&1\\ x_{_3}&y_{_3}&1\end{bmatrix}$will always be less than