List of practice Questions

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

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

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 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

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

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

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

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

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

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

In a triangle, if $r₁ > r₂ > r₃$ then

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

If $n₁, n₂$ are positive integers, then $(1+i)ⁿ₁+(1+i³)ⁿ₁+(1+i⁵)ⁿ₂+(1+i⁷)ⁿ₂$ is a real number if and only if

The equation $|z+i|-|z-i|=k$ represents a hyperbola, if

The period of function $f(x)=| \sin 4x | + | \cos 4x |$ is

The value of $\cos \frac2π15 · \cos \frac4\pi15 · \cos \frac8\pi15 · \cos \frac16\pi15$ is equal to

If a, b, c are three distinct positive real numbers, the number of real roots of $ax²+2b|x|-c=0$ is

If A is a skew-symmetric matrix, then trace of A is

If the matrix $A = $ has rank 3, then