List of top Mathematics Questions asked in MET

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

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

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

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

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 ________.

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 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

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

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

Let \( f(x) = x^{2} + ax + b \), where \( a, b \in \mathbb{R} \). If \( f(x)=0 \) has all its roots imaginary, then the roots of \( f(x) + f'(x) + f''(x) = 0 \) are

If \( \alpha, \beta, \gamma \) are the roots of \( x^{3} + 4x + 1 = 0 \), then the equation whose roots are \[ \frac{\alpha^{2}}{\beta+\gamma}, \quad \frac{\beta^{2}}{\gamma+\alpha}, \quad \frac{\gamma^{2}}{\alpha+\beta} \] is

If \( f(x) = 2x^{4} - 13x^{2} + ax + b \) is divisible by \( x^{2} - 3x + 2 \), then \( (a, b) \) is equal to

If one of the roots of \( \begin{vmatrix} 3 & 5 & x \\ 7 & x & 7 \\ x & 5 & 3 \end{vmatrix} = 0 \), then the other roots are

If \( x, y, z \) are all positive and are the \( p \)th, \( q \)th and \( r \)th terms of a geometric progression respectively, then the value of the determinant \( \begin{vmatrix} \log x & p & 1 \\ \log y & q & 1 \\ \log z & r & 1 \end{vmatrix} \) equals

If \( \begin{bmatrix} 1 & -1 & x \\ 1 & x & 1 \\ x & -1 & 1 \end{bmatrix} \) has no inverse, then the real value of \( x \) is

If \( \alpha \) and \( \beta \) are the roots of \( x^{2} - 2x + 4 = 0 \), then the value of \( \alpha^{6} + \beta^{6} \) is

If \( n \) is an integer which leaves remainder one when divided by three, then \( (1+\sqrt{3}i)^{n} + (1-\sqrt{3}i)^{n} \) equals

The period of \( \sin(4x + \cos^{4} x) \) is

\( \frac{\cos x}{\cos(x - 2y)} = \lambda \Rightarrow \tan(x - y)\tan y \) is equal to