List of top Mathematics Questions

For ellipse \(9x^2+25y^2=225\), focal chord \(L_1\) makes equal intercepts on axes. Intersection with tangent at end of latus rectum lies in

Common tangent to circle \(x^2+y^2=4\) and parabola \(y^2=8\sqrt2 x\) is \(y=mx+c\). Then \(\sqrt{m+c^2}=\)

If \((h,k)\) is the centre of a circle cutting three circles orthogonally, then \(\frac{3}{h}+\frac{1}{k}=\)

Line \(x+y+k=0\) touches hyperbola \(x^2-5y^2=5\). Point of contact is

If line \(2y-3=0\) bisects angle between \(x+2y-k=0\) and \(x-2y+k=0\), then a point on the bisector of other angle is

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

Tangent to circle \(x^2+y^2-4x-8y-5=0\) equally inclined to axes is \(x+by+c=0\), \(b0\). Find \(2b+c\).

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

If \((h,k)\) is external centre of similitude of circles \[ x^2+y^2-6x-10y+9=0 \] and \[ x^2+y^2+6x+6y+2=0, \] then \(k-h=\)

If \(\theta\) is the angle between the circles \[ x^{2}+y^{2}+2x-4y-4=0,\quad x^{2}+y^{2}-4x-6y-3=0 \] then \(\cos\theta=\)

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

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

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 \((1+\tan\theta)^2=\)

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

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

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

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

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 \[ \vec a=i+2j+2k,\quad \vec b=2i-j+2k,\quad \vec c=2i+j+2k \] 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 \(O\) 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