List of top Mathematics Questions

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

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

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

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

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

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

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

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 ________.

Out of 18 points in a plane no three are in the same straight line except five points which are collinear. The number of straight lines that can be formed joining them is ________.

Nishi has 5 coins each of different denomination. The number of different sums of money she can form is ________.

The numbers $aₙ$ are defined by $a₀=1$ and $aₙ+1=3n²+n+aₙ$ for $n ≥ 0$. Then, $aₙ$ is equal to ________.

The range of the function $f(x)=\logₑ(3x²-4x+5)$ is ________.

If $I_{m}=\int\limits_{1}^{e}(\ln x)^{m} d x$, where $m \in N$, then $I_{10}+10 I_{9}$ is equal to -

The area of the region bounded by the curve $y=x |x|, x$-axis and the ordinates $x=1, x=$ $-1$ is given by:

The digit in the unit place of $2009! + 3^{7886}$ is