Class 12th

Let $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1(ab)$ be given ellipse, length of whose latus rectum is 10 . If its eccentricity is the maximum value of the function, $?\left(t\right)=\frac{5}{12}+t-t^2$ , then $a^2+b^2$ is equal to:

Among the following the number of state variable is____________.

Internal energy (U)

Volume (V)

Heat (q)

Enthalpy (H)

For a reaction, given below is the graph of ink vs $\frac{1}{T}.$  The activation energy for the reaction is equal to_____________ cal mol^-1 (Nearest integer)

(Given: R = 2 cal K^-1 mol^-1)

Let $f$ be a twice differentiable function on $\left(\mathrm{1,6}\right)$ . If $f\left(2\right)=8,f^{\mathrm{\text{'}}}\left(2\right)=5,f^{\mathrm{\text{'}}}\left(x\right)\ge 1$ and $f$ " $\left(x\right)\ge 4$ , for all $x\in \left(\mathrm{1,6}\right)$ , then:

On reaction with stronger oxidizing agent like KlO₄,hydrogen peroxide oxidizes with the evolution of O₂. The oxidation number of I in KlO₄, changes to__________.

A sample of 0.125g of an organic compound when analyzed by Duma's method yields 22.78 mL of nitrogen gas collected over KOH solution at 280 K and 759 mm Hg. The percentage of nitrogen in the given organic compound is__________. (Nearest integer)

[Given: (a) The vapour pressure of water of 280K is 14.2mm Hg

(b) R = 0.082 L atm K^-1 mol^-1]

Let $f\left(x\right)=|x-2|$ and $g\left(x\right)=f\left(f\right(x\left)\right),x\in \left[\mathrm{0,4}\right]$ . Then ${\int }_0^3?\left(g\right(x)-f(x\left)\right)dx$ is equal to:

At 600K, 2 mol of NO are mixed with 1 mol of O₂.

2NO_(g) + O₂(g) $\rightleftarrows$  2NO₂(g)

The reaction occurring as above comes to equilibrium under a total pressure of 1 atm. Analysis of the system shows that 0.6 mol of oxygen are present at equilibrium. The equilibrium constant for the reaction is__________. (Nearest integer)

Let $\alpha$ and $\beta$ be roots of $x^2-3x+p=0$ and $\gamma$ and $\delta$ be the roots of $x^2-6x+q=0$ . If $\alpha ,\beta$ , $\gamma ,\delta$ , form a geometric progression. Then ratio $(2q+p):(2q-p)$ is:

A gaseous mixture of two substances A and B, under a total pressure of 0.8 atm is in equilibrium with an ideal solution. The mole fraction of substance A is 0.5 in the vapour phase and 0.2 in the liquid phase. The vapour pressure of pure liquid A is_________atm. (Nearest integer)