List of top Mathematics Questions

The value of $f(0)$ so that $\frac{\left(-e^{x} +2^{x}\right)}{x}$may be continuous at $x = 0$ is

The length of the parabola y$^2$ = 12x cut off by the latus-rectum is

Let [ ] denote the greatest integer function and f (x) = [tan$^2$ x]. Then

The shortest distance between the straight lines through the points $A_1 = (6, 2, 2)$ and $A_2 = (-4, 0, -1)$, in the directions of $(1, -2, 2)$ and $(3, -2, -2)$ is

$\begin{bmatrix}0&a\\ b&0\end{bmatrix}^{^4}=I$, then

The vector equation of the line passing through the points $ (3,2,1) $ and $ (-2,1,3) $ is

The distance between the parallel lines $ y=x+a,\,\,y=x+b $ is

If the circles $x ^2 + y ^2 =9$ and $x^2 + y^ 2 + 2\alpha x + 2y +1 = 0$ touch each other internally, then $\alpha$ =

A point P moves so that the sum of its distances from $ (-ae,\,0) $ and $ (ae,\,0) $ is $ 2a $ . Then the locus of P is

If $ {{C}_{0}},{{C}_{1}},{{C}_{2}},.....{{C}_{n}} $ denotes the binomial coefficients in the expansion of $ {{(1+x)}^{n}}, $ then $ {{C}_{0}}+\frac{{{C}_{1}}}{2}+\frac{{{C}_{2}}}{3}+....+\frac{{{C}_{n}}}{n+1} $ is equal to

Solution of the differential equation $xdy - ydx - \sqrt{x^{2}+y^{2}}dx = 0$ is

If $\left|\frac{z-25}{z-1}\right|=5$ , the value of |z|

Probability of getting positive integral roots of the equation x$^2$ - n = 0 for the integer n, 1 $\le$ n $\le$ 40 is

The center and radius of the sphere $x^2 + y^2 + z^2 + 3x - 4z + 1 = 0$ are

The simplified expression of sin ($tan^{-1} x$), for any real number $x$ is given by

If $f(2) = 4$ and $f'(2) = 1$, then $\displaystyle\lim_{x \to 2} \frac{xf (2) - 2 f (x) }{x -2}$ is equal to

If $A$ and $B$ are independent events of a random experiment such that $P(A \cap B) = \frac{1}{6} $ and $P(A \cap B) = \frac{1}{3}$, then $P(A)$ is equal to (Here, $E$ is the complement of the event $E$)

If the lines $2x - 3y = 5$ and $3x - 4y = 7$ are two diameters of a circle of radius $7$, then the equation of the circle is

In $\triangle A B C$ the mid points of the sides $A B, B C$ and $C A$ are respectively $(1,0,0),(0$, $m , 0)$ and $(0,0, n )$. Then, $\frac{A B^{2}+B C^{2}+C A^{2}}{l^{2}+m^{2}+n^{2}}$ is equal to

A pair of perpendicular straight lines passes through the origin and also through the point of intersection of the curve $x^2 + y^2 = 4$ with $x + y = a$. The set containing the value of '$a$' is

If the selling price of a product is increased by Rs 162, then the business would make a profit of 17% instead of a loss of 19%. What is the cost price of the product?

A class consists of 100 students; 25 of them are girls and 75 boys; 20 of them are rich and the remaining poor; 40 of them are fair-complexioned. The probability of selecting a fair- complexioned rich girl is

A box contains 5 brown and 4 white socks. A man takes out two socks. The probability that they are of the same colour is

India plays two matches each with West Indies and Australia. In any match the probabilities of India getting points 0, 1 and 2 are 0.45, 0.05 and 0.50 respectively. Assuming that the outcomes are independent, the probability of India getting at least 7 points is

Out of 13 applications for a job, there are 5 women and 8 men. It is desired to select 2 persons for the job. The probability that at least one of the selected persons will be a woman is