List of practice Questions

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

If A is an orthogonal matrix, then determinant 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

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 $a>1$ 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

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

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

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

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

Ammonia is dried over ________.

Collin's reagent is used to convert ________.

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

Inductive effect involves ________.

The solubility of AgCl in 0.2 M NaCl solution is ($Kₛp$ of $AgCl = 1.20 × 10^-10$).

Lipids are ________.

The enzyme pepsin hydrolyses ________.

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

In a homonuclear molecule which of the following set of orbitals is degenerate?

The pH of a neutral water sample is 6.5. Then the temperature of water ________.