List of top Mathematics Questions

Let $f$ be a non-negative function defined on the interval [0,1].if $\int_0^x \sqrt{1-(f'(t))^2}dt = \int_0^x f(t) dt , 0 \le x \le 1$ and $f (0) = 0$, then

In a $\triangle$ ABC w ith fixed base BC, the vertex A moves such that cos B + cos C = 4 $ sin^2 \frac{A}{2}$. If a, b and c denote th e lengths of th e sides of th e triangle opposite to the angles A, B and C respectively, then

A line with positive direction cosines passes through the point $P (2, -1, 2)$ and makes equal angles with the coordinate axes. The line meets the plane $2x + y+ z = 9$ at point $Q$. The length of the line segment $PQ$ equals

In a $\triangle$ ABC w ith fixed base BC, the vertex A moves such that cos B + cos C = 4 $ sin^2 \frac{A}{2}$. If a, b and c denote th e lengths of th e sides of th e triangle opposite to the angles A, B and C respectively, 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 $\alpha$ =

The directrix of the parabola y$^2$ + 4x + 3 = 0 is

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

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

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

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

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

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

The value of $\int^{^a}_{0}\sqrt{\frac{a-x}{x}}dx$ is

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

If $2x + 3y + 12 = 0$ and $x - y + 4 \lambda = 0$ are conjugate with respect to the parabola $y^2 = 8x$, then $\lambda$ is equal to

If $f: R \rightarrow R$ is defined by $f(x)=[x-3]+|x-4|$ for $x \in R$, then $\displaystyle\lim _{x \rightarrow 3} f(x)$ is equal to

If $f : R \rightarrow R$ is defined by $f(x) = \begin{cases} \frac{\cos \ 3x - \cos \ x}{x^2} &, \text{for } x \neq 0 \\ \lambda &, \text{for } x = \end{cases}$ and if $f$ is continuous at $x = 0,$ then $\lambda$ is equal to

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 $E$)