List of top Mathematics Questions

If $\frac{d}{dx} \left\{f\left(x\right)\right\} = g\left(x\right)$, then $\int\limits^{b}_{a}$ $f (x)g(x)dx$ is equal to

If $I_{1} = \int\limits^{3\pi}_{0}f\left(\cos^{2}\,x\right)dx$ and $I_{2} = \int\limits^{\pi}_{0} f\left(\cos^{2}\,x\right)dx$, then

The equation of one of the curves whose slope at any point is equal to $y + 2x$ is

The value(s ) of $ \int^1_0 \frac { x^4 ( 1 - x )^4 }{ ( 1 + x^2 ) } \, dx $ is are

The interior angles of a polygon are in arithmetic progression. The smallest angle is $ 120 $ and the common difference is $ 5 $ . The number of sides of the polygon is

$ \int e^{x}\left(cosec^{-1}x+\frac{-1}{x\sqrt{x^{2}-1}}\right) \, dx$ is equal to

In a $G.P.$ $ t_2 + t_5 = 216 $ and $ t_4 : t_6 $ = $ 1 : 4 $ and all terms are integers, then its first term is

In a certain progression three consecutive terms are $ 30, 24, 20 $ . The next term of the progression is

Let $\omega$ be a complex cube root of unity with $\omega \, \ne$ 1. A fair die is thrown three times. If r$_1$, r$_2$ and r$_3$ are the numbers obtained on the die, then the probability that $\omega ^{r_1} +\omega ^{r_2} +\omega ^{r_3}=0 , $ is

If the distance of the point $P (1, - 2,1)$ from the plane $x + 2y - 2z = a$, where $a > 0$, is $5$, then the foot of the perpendicular form $ P$ to the plane is

Equation of the plane containing the straight line $\frac{x}{2}=\frac{y}{3}= \frac{z}{4}$ and perpendicular to the plane containing the staight lines $\frac{x}{2}=\frac{y}{4}= \frac{z}{2}$ and $\frac{x}{4}=\frac{y}{2}= \frac{z}{3}$ is

If the angles $A, B$ and $C$ of a triangle are in an arithmetic progression and if $a, b$ and $c$ denote the lengths of the sides opposite to $A, B$ and $C$ respectively, then the value of the expression $ \frac{a}{c} sin \, 2 C + \frac{c}{a} sin \, 2 A $ is

For the function $ f(x) = \frac {4}{3} x^3-8x^2+16x+5, $ $ x = 2\,is \,a\,point\, of $

Bag $I$ contains $3$ red and $4$ black balls, while another bag $II$ contains $5$ red and $6$ black balls. One ball is drawn at random from one of the bags and it is found to be black. The probability that it was drawn from bag $II$ is

Let $A = \{ 0,1,2 \}$, $B =\{ 4,2,0 \}$ and $ f,g $ : $ A \rightarrow B $ be the functions defined by $ f(x) = x^2-x $ and $ g(x) = 2|x-\frac{1}{2}|-1 $ Then,

Let $f = \{ (1,1),(2,4),(0,- 2),(-1,- 5) \}$ be a linear function from $ Z $ into $ Z $ . Then, $ f (x) $ is

If $ A $ is a square matrix such that $ A^2 $ = $ A $ , then $ (I-A)^3+A $ is equal to

The ratio in which the line segment joining the points $(4, 8, 10)$ and $(6, 10, - 8)$ is divided by xy-plane is

The value of $\lambda$ for which the lines $\frac{1-x}{3}=\frac{y-2}{2\lambda}=\frac{z-3}{2}$ and $ \frac{x-1}{3\lambda}=\frac{y-1}{1}=\frac{6-z}{7}$

The co-ordinates of a point on the line $\frac{x-1}{2}=\frac{y+1}{-3}=z$ at a distance $4\sqrt{14}$ from the point $(1, - 1, 0)$ are

A fair coin is tossed $ n $ number of times. If the probability of having at least one head is more than 90%, then $ n $ is greater than or equal to

The value of $ \lambda $ for which the lines $ \frac{1-x}{3} = \frac{y-2}{2\lambda}=\frac {z-3}{2} = \frac{x-1}{3\lambda} =\frac{y-1}{1} =\frac {6-z}{7} $ are perpendicular to each other is

$P$ is the point of contact of the tangent from the origin to the curve $y = log_ex$ The length of the perpendicular drawn from the origin to the normal at $P$ is ______

If $ (3+i)\,(z+\bar{z})-(2+i)(z-\bar{z})+14i\,=0, $ then $ z\bar{z} $ is equal to

If $\frac{sin^4 x}{2}+\frac{cos^4 x}{3}=\frac{1}{5}$ then