List of top Mathematics Questions

Let $d_1$ and $d_2$ be the lengths of the perpendiculars drawn from any point of the line $7x - 9y + 10 = 0$ upon the lines $3x + 4y = 5$ and $12x + 5y = 7$ respectively. Then

The point $P \,(3, 6)$ is first reflected on the line $y = x$ and then the image point $Q$ is again reflected on the line $y = - x$ to get the image point $Q'$. Then the circumcentre of the $\Delta PQQ'$ is

If $\left( \frac{1 + i}{1 - i} \right)^m =1$, then the least positive integral value of $m$ is

Equation of line passing through the point $(1,2)$ and perpendicular to the line $y = 3x -1$ is

If $|x -1| \leq 1$, then

For real $x$, the greatest value of $\frac{x^{2}+2x+4}{2x^{2}+4x+9}$ is

If $A$ is a square matrix of order $3 \times 3$, then $|KA|$ is equal to

If $A$ and $B$ are finite sets and , ${A \subset B}$ then

The derivative of $\cos^{-1} (2x^2 - 1)$ w.r.t $\cos^{-1} x$ is

If $\, {{^n C}_{12}}$ =$\, {{^n C}_8}$ then $n$ is equal to

If $tan^{-1} \,x + tan^{-1} \,y = \frac{4\pi}{5}$, then $cot^{-1}\, x + cot^{-1} \,y$ is equal to

Given the system of straight lines a $(2x + y - 3) + b(3x + 2y - 5) = 0$, the line of the system situated farthest from the point $(4, -3)$ has the equation

An urn contains five balls. Two balls are drawn and found to be white. The probability that all the balls are white is

The point on the curve $y^2 = x$ where the tangent makes an angle of $\pi /4$ with X-axis is

The eccentricity of the ellipse $\frac{x^2}{36} + \frac{y^2}{16} = 1$ is

Let $f(x) = x^{13} + x^{11} + x^9 + x^7 + x^5 + x^3 + x + 19$. Then $f(x) = 0$ has

Let $A(2, -3)$ and $B (-2, 1)$ be two angular points of $\Delta ABC$. If the centroid of the triangle moves on the line $2x + 3y = 1$, then the locus of the angular point $C$ is given by

The locus of the mid-points of the chords of the circle $x^2 + y^2 + 2x - 2y - 2 = 0$ which make an angle of $90�$ at the centre is

Transforming to parallel axes through a point $(p, q)$, the equation $2x^2 + 3xy + 4y^2 + x + 18y + 25 = 0$ becomes $2x^2 + 3xy + 4y^2 = 1$. Then

Let $\vec{a}, \vec{b}$ & $\vec{c}$ be non-coplanar unit vectors equally inclined to one another at an acute angle $\theta$. Then $| [ \vec{a} \; \vec{b} \; \vec{c}] |$ in terms of $\theta$ is equal to

The value of $cos^2 \, 45^{\circ} - sin^2 \, 15^{\circ}$ is

If $x$ is real number, then $\frac{x}{x^{2}-5 x+9}$ must lie between

IF $f\left(z\right) = \frac{7-z}{1-z^{2}} $ , where $z = 1 + 2i$, then $|f(z)|$ is equal to :

Let $S=\{1,2,3, \ldots \ldots, 9\}$. For $k=1,2, \ldots \ldots, 5$, let $N_{k}$ be the number of subsets of $S$, each containing five elements out of which exactly $k$ are odd. Then $N_{1}+N_{2}+N_{3}+N_{4}+N_{5}=$

The length of the semi-latus rectum of an ellipse is one thrid of its major axis, its eccentricity would be