Class 11th

Let f(x) = $min\left\{\left[x-1\right],\left[x-2\right],....,\left[x-10\right]\right\}$  where [t] denotes the greatest integer $\le$  t. Then ${\displaystyle \underset{0}{\overset{10}{\int }}f\left(x\right)dx+{\displaystyle \underset{0}{\overset{10}{\int }}{\left(f\left(x\right)\right)}^{2}dx+{\displaystyle \underset{0}{\overset{10}{\int }}\left|f\left(x\right)\right|dx}}}$  is equal to……….

  $\frac{2^3-1^3}{1*7}+\frac{4^3-3+2^3-1^3}{2*11}+\frac{6^3-5^3+4^3+2^3-1^3}{3*15}+.......+$

$\frac{30^3-29^3+28^3-27^3+....+2^3-1^3}{15*63}isequalto.............$

Let for the 9^th term in the binomial expansion of ${\left(3+6x\right)}^n$ , in the increasing powers of 6x, to be the greatest for x $=\frac{3}{2}$ , the least value of n is n₀. If k is the ratio of the coefficient of x⁶ to the coefficient of x³, then k + n₀ is equal to:

The number of functions f, from the set A = $\left\{x\in N:x^2-10x+9\le 0\right\}$  to the set B = $\left\{n^2:n\in N\right\}$  such that f(x) $\le$ (x – 3)² + 1, for every x $\in$  A, is…………

Consider, PF₅, BrF₅, PCl₃, SF₆, ${\left[IC{l}_4\right]}^{-}$ , CIF₃ and IF₅.

Amongst the above molecule(s) / ion(s), the number of molecule(s) / ion(s) having sp³d² hybridisation is_____________.

'x' g of molecular oxygen(O₂) is mixed with 200g of neon (Ne). The total pressure of the non-reactive mixture of O₂ and Ne in the cylinder is 25 bar. The partial pressure of Ne is 20 bar at the same temperature and volume. The value of 'x' is_________.

The number of molecule(s) or ion(s) from the following having non-polar structure is _________.

$N{O}_3^{-},H_{2}O,B{F}_3,PC{l}_3,Xe{F}_4,S{F}_4,Xe{O}_3,P{H}_4^{+},S{O}_3,{\left[Al{\left(OH\right)}_4\right]}^{-}$

A gas (Molar mass = 280 g mol^-1) was burnt in excess O₂ in a constant volume calorimeter and during combustion the temperature of calorimeter increased from 298.0 K to 298.45K. If the heat capacity of calorimeter is 2.5 kJ K^-1 and enthalpy of combustion of gas is 9 kJ mol^-1 the amount of gas burnt is _____________g. (Nearest Integer)

For a real at 25°C temperature and high pressure (99 bar) the value of compressibility factor is 2, so the value of Vander Waal's constant 'b' should be__________* 10^-2 L mol^-1. (Nearest Integer)       

(Given R = 0.083 L bar K^-1 mol^-1)

The normality of H₂SO₄ in the solution obtained on mixing 100 mL of 0.1 M H₂SO₄ with 50 mL of 0.1 M NaOH is__________* 10^-1N. (Nearest Integer)