List of top Questions asked in MET

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

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

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

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

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

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

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 ________.

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

The term independent of \( x \) in the expansion of \( \left[ \sqrt{\frac{x}{3}} + \sqrt{\frac{3}{2}} x^2 \right]^{10} \) 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 ________.

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 ________.

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 domain of the function \( f(x) = \frac{\sqrt{9 - x^2}}{\sin^{-1}(3 - x)} \) is ________.

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

Collin's reagent is used to convert ________.

\( C_6H_6 \xrightarrow{350 \, K, \, H_2SO_4} A \xrightarrow{\text{Alkali Fusion}} B \xrightarrow{\text{Br}_2/\text{H}_2O} C \). In the above sequence, C is ________.

Ammonia is dried over ________.

At $25^\circC$ the highest osmotic pressure is exhibited by 0.1 M solution of ________.

Oxalic acid when heated with conc. $H₂SO₄$ gives ________.

Carbon cannot be used in the reduction of $Al₂O₃$ because ________.

The enzyme pepsin hydrolyses ________.