List of top Mathematics Questions

A circle makes intercepts \(2\sqrt7\) and \(2\sqrt{12}\) on axes and diameter lies on \(3x+2y=0\). Find a point on circle.

For circle \(x^2+y^2+12x-4y-9=0\), line \(x+2y-3=0\) represents

If the image of the point (2,6) in the line \(x-3y+10=0\) is (h,k), then \(2h-k=\)

Point \((a,2a)\), \(a>0\), lies in region between lines \(3x-y-3=0\) and \(6x-y-6=0\). Then \(a\in\)

If an acute angle \(\theta\) is used to rotate axes to remove the \(xy\)-term from \[ 4x^{2}+3xy+y^{2}+1=0, \] then \((1+\tan\theta)^2=\)

If sum of reciprocals of intercepts of a line equals A.M. of \(\frac{2}{3}\) and \(\frac{4}{5}\), then point of concurrence is

Let P be a variable point such that it forms a triangle of area 14 square units with two fixed points \((-3,4)\) and \((4,-3)\). Then the locus of P represents a pair of parallel lines. The distance between these two parallel lines is

Bag A: 4W,3R,2B; Bag B: 2W,4R,3B. One bag chosen randomly, two balls drawn. Probability of one white and one black is

If 2 coins are tossed and 2 dice are thrown, probability of getting at least 1 head and sum at least 9 is

If \(P(X=k)=c\left(\frac{2}{7}\right)^k,\ k=0,1,2,\dots\), then \(P(X=2)=\)

If \(X\sim B(n,\frac12)\), minimum \(n\) such that \[ P(X\ge2)\ge0.6 \] is

A card is drawn from 52 cards. If A = diamond, B = ace, probability that exactly one occurs is

Let \[ \vec a=i+2j+2k,\quad \vec b=2i-j+2k,\quad \vec c=2i+j+2k \] If \(\vec d\times \vec a=\vec b\times \vec a\) and \(\vec d\cdot \vec c=8\), then for \(\vec r=2i+2j+k\), find \(\vec d\cdot \vec r\)

Let \(\vec a=i+j+k\), \(\vec b=i-j+k\). If \(\vec c \perp \vec a\), \(\vec d \parallel \vec a\), and \(\vec b=\vec c+\vec d\), then \((\vec c\times \vec d)^2=\)

The variance for the following discrete frequency distribution is

If \[ \vec a=i+2j-2k,\quad \vec b=6i-3j+2k, \] and \(\vec c\perp \vec a\), \(\vec c\times \vec b=i-2j-6k\), then angle between \(\vec b\) and \(\vec c\) is

Let \(O\) be the origin and \(\vec r\) be the position vector of a point \(P\). If \(\overline{OP}\) makes angles \(\frac{\pi}{3}\) and \(\frac{\pi}{6}\) with \(\overline{i}\) and \(\overline{j}\) respectively, then a vector along \(\overline{OP}\) with magnitude 2 is

In triangle ABC, \[ (r_1-r)\cos\frac{B-C}{2} = ? \]

If \(\sinh x=\frac{12}{5}\), then \[ \cosh2x-\sinh2x= \]

Given position vectors of A, B, C, D are coplanar, find \(y-x\) for intersection of AB and CD.

If sides of a triangle are \(6\) and \(3+3\sqrt3\) with included angle \(60^\circ\), then circumradius is

If \(x\in\left(0,\frac{1}{\sqrt2}\right)\), then \[ \cot\left[\cos^{-1}\{\tan(\sin^{-1}x)\}\right]= \]

\[ \sin9^\circ\sin18^\circ\sin36^\circ\sin54^\circ\sin72^\circ\sin81^\circ \]

If \(x=\tan A, y=\tan B, z=\tan C\) and \[ xy+yz+zx=1, \] then evaluate \[ \frac{(1-x^2)(1-y^2)(1-z^2)}{(1+x^2)(1+y^2)(1+z^2)} \]

Number of solutions of the equation \[ \sin\theta+\sin3\theta+\sin5\theta=0 \] in \([-\pi,\pi]\) is