List of top Questions asked in MET- 2010

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

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

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

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

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

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

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

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

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

Let a, b, c be real numbers with $a ≠ 0$ and let $α, β$ be the roots of the equation $ax²+bx+c=0$, then $a³x²+abcx+c³=0$ has roots

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

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

If A is an orthogonal matrix, then determinant of A is

For positive numbers x, y, z the numerical value of the determinant $$ is

The constant term in the expansion of $(1+x)ᵐ(1+\frac1x)ⁿ$ is ________.

The number of terms in the expansion of $(\sqrt5+\sqrt[4]11)¹24$ which are integers is equal to ________.

If $a>1$ roots of the equation $(1-a)x²+3ax-1=0$ are

The greatest coefficient in the expansion of $(1+x)²n$ is ________.

The number of values of the triplet (a, b, c) for which $a \cos 2x + b \sin² x + c = 0$ is satisfied by all real x, is

If $α, β, γ$ are such that $α+β+γ=2$, $α²+β²+γ²=6$, $α³+β³+γ³=8$, then $α⁴+β⁴+γ⁴$ is

There are P copies of n-different books. The number of different ways in which a non-empty selection can be made from them is ________.