List of top Mathematics Questions

Let $PQR$ be a triangle Let $\vec{a} = \overrightarrow{QR}, \, \vec{ b} = \overrightarrow{RP} and \vec{c} = \overrightarrow{PQ}$. If $\left|\vec{a}\right| = 12, \left|\vec{b}\right| = 4\sqrt{3}$ and $\vec{b}. \vec{c} = 24$, then which of the following is (are) true ?

The area (in sq units) of the quadrilateral formed by the tangents at the end points of the latusrectum recta to the ellipse $\frac{x^2}{9} +\frac{y^2}{ 5}=1 is $

The equation of the curve satisfying the differential equation $ y(x+y^3)dx = x(y^3- x)dy $ and passing through the point $ (1, 1) $ is

The complex number $ z = x + iy $ satisfy the equation $ |\frac {z-5i}{z+5i}| = 1 $ lies on

For all real $ x, 4^{sin^2x}+ 4cos^{2x} $ is

Given that $ \int_{0}^{\infty}\frac{x^{2}}{\left(x^{2}+a^{2}\right)\left(x^{2}+b^{2}\right)\left(x^{2}+c^{2}\right)} $ dx = $ \frac{\pi}{2\left(a+b\right)\left(b+c\right)\left(c+a\right)'} $ then $ \int_{0}^{\infty}\frac{dx}{\left(x^{2}+4\right)\left(x^{2}+9\right)} $ is

The length of the perpendicular drawn from $(1,2,3)$ to the line $ \frac{x-6}{3} = \frac {y-7}{2} = \frac {z-7}{-2} $ is

$ lim_{n\rightarrow \infty} \frac {(n!)^{1/n}}{n} $ equals

The equation $ \sqrt{\left(x-2\right)^{2}+y^{2}}+\sqrt{\left(x+2\right)^{2}+y^{2}}=4 $ represents

If $ C_o, C_1,C_2,....C_{15} $ are the binomial coefficients in the expansion of $ (1+x)^{15} $ then $ \frac {C_1}{C_o} +\frac {2C_2}{C_1}+\frac {3C_3}{C_2} +....+\frac {15C_{15}}{C_{14}} $ is equal to

Consider the family of all circles whose centers lie on the straight line $y = x$. If this family of circles is represented by the differential equation $Py" + Qy' + 1 = 0$, where $P$, $Q$ are functions of $x, y$ and $y'$ (here $y' = \frac{dy}{dx}, \,y'' = \frac{d^{2}y}{dx^{2}}$), then which of the following statements is (are) true ?

The shortest distance between the lines $ \frac{x}{-1}=\frac{y}{1}=\frac{z}{1} $ and $ \frac{x-3}{0}=\frac{y+3}{1}=\frac{z-3}{-1} $ is

A fair die is rolled. Consider the events A = { $ 1, 3, 5 $ }, B = { $ 2, 3 $ } and C = { $ 2, 3, 4, 5 $ }. Then, the conditional probability $ P (A \cup B / C) $ is

If the eccentricity of the hyperbola $\frac {x^2}{a^2}-\frac {y^2}{b^2}=1$ is $\frac {5}{4}$ and $2x + 3y -6 = 0$ is a focal chord of the hyperbola, then the length of transverse axis is equal to

If $A$ is a matrix of order $3$, such that $A (adj A) = 10\, I$, then $|adj A| $ =

If $ y=x{{e}^{2y}}, $ then find $\frac{ dy}{dx} $ .

The integral $\int^{^{\frac{1}{2}}}_{_0} \frac{ln \left(1+2x\right)}{1+4x^{2}}dx,$ equals :

The coefficient of $x^{1012}$ in the expansion of $(1 + x^n + x^{253})^{10}$, (where n $\le$ 22 is any positive integer), is :-

The angle between the lines whose direction cosines satisfy the equations $l + m + n = 0 $ and $ l^2= m^2 + n^2 $is

Given an $A.P$. whose terms are all positive integers. The sum of its first nine terms is greater than $200$ and less than $220$. If the second term in it is $12$, then its $4^{th}$ term is :

The minimum area of a triangle formed by any tangent to the ellipse $\frac{x^{2}}{16}+\frac{y^{2}}{81}=1$ and the co-ordinate axes is :

The variance of first $50$ even natural numbers is

An eight digit number divisible by 9 is to be formed using digits from 0 to 9 without repeating the digits. The number of ways in which this can be done is :

The solution of $\frac{dy}{dx} = \frac{x^{2} + y^{2} + 1}{2xy}$, satisfying $ y\left(1\right) = 0$ is given by

An arch of a bridge is semi-elliptical with major axis horizontal. If the length the base is $9$ meter and the highest part of the bridge is $3$ meter from the horizontal; the best approximation of the height of the arch. $2$ meter from the centre of the base is