List of top Mathematics Questions

The reflection of the point (2, 1, 3) in the plane $3x-2y-z=9$ is

The tangent and normal to a rectangular hyperbola $xy=c²$ at a point cut off intercepts $a₁, a₂$ on one axis and $b₁, b₂$ on the other, then $a₁a₂ + b₁b₂$ is equal to

If $(mᵢ, 1/mᵢ)$ are four distinct points on a circle, then

If the equation $lx²+2mxy+ny²=0$ represents a pair of conjugate diameters of the hyperbola $x²/a² - y²/b² = 1$, then

If $e$ is the eccentricity of the hyperbola $x²/a² - y²/b² = 1$ and $θ$ is the angle between the asymptotes, then $\cos(θ/2)$ is equal to

If the normal to the parabola $y²=4ax$ at the point $(at², 2at)$ cuts the parabola again at $(aT², 2aT)$, then

The number of real tangents that can be drawn to the ellipse $3x²+5y²=32$ passing through (3, 5) is

The equation of the circle passing through (1, 0) and (0, 1) and having the smallest possible radius is

The length of the common chord of the two circles $(x-a)²+(y-b)²=c²$ and $(x-b)²+(y-a)²=c²$ is

Consider four circles $(x ± 1)² + (y ± 1)² = 1$, then the equation of smaller circle touching these four circles is

The equation $3x²+7xy+2y²+5x+5y+2=0$ represents

To the lines $ax²+2hxy+by²=0$ the lines $a²x²+2h(a+b)xy+b²y²=0,$ are

The locus of the point of intersection of tangents to the circle $x=a\cosθ, y=a\sinθ$ at the points whose parametric angles differ by $π/2$ is

The distance of the point (2, 3) from the line $2x-3y+9=0$ measured along a line $x-y+1=0$ is

The equation of the straight line which passes through the intersection of the lines $x-y-1=0$ and $2x-3y+1=0$ and is parallel to x-axis, is

If the axes be turned through an angle $\tan^-12$, what does the equation $4xy-3x²=a²$ become?

If the lines $a₁x+b₁y+c₁=0$, $a₁x+b₁y+c₂=0$, $a₂x+b₂y+d₁=0$ and $a₂x+b₂y+d₂=0$ are sides of a rhombus, then

If $t₁, t₂$ and $t₃$ are distinct, the points $(t₁, 2at₁+at₁³), (t₂, 2at₂+at₂³), (t₃, 2at₃+at₃³)$ are collinear if

For two events A and B, $P(A)=P(A/B)=1/4$ and $P(B/A)=1/2$. Then

The least number of times a fair coin must be tossed so that the probability of getting at least one head is at least 0.8 is

If x follows a binomial distribution with parameters $n=100$ and $p=1/3$, then $p(X=r)$ is maximum when r equals

$2 \tan^-1(\csc \tan^-1x - \tan \cot^-1x)$ is equal to

A and B are two points on one bank of a straight river and C, D are two other points on the other bank... AB=a, $\angle CAD=α, \angle DAB=β, \angle CBA=γ$, then CD is equal to

In a triangle, if $r₁ > r₂ > r₃$ then

The sum of all the solutions of the equation $\cos x · \cos(\frac\pi3+x) · \cos(\frac\pi3-x) = \frac14, x \in [0, 6π]$ is