Class 12th

Let a, b and c be distinct positive numbers. If the vectors ai + aj + ck, i + k and ci + cj + bk are co-planar, then c is equal to:

CO₂ gas adsorbs on charcoal following Freundlich adsorption isotherm. For a given amount of charcoal, the mass of CO₂ adsorbed becomes 64 times when the pressure of CO₂ is doubled. The value of n in the Freundlich isotherm equation is _______ * 10⁻². (Round off to the Nearest integer)

Sodium stearate CH?(CH?)?COO?Na? is an anionic surfactant which forms micelles in oil. Choose the correct statement for it from the following:

The number of distinct real roots of the determinant |sin x, cos x, cos x; cos x, sin x, cos x; cos x, cos x, sin x| = 0 in the interval -π/4 ≤ x ≤ π/4 is:

1.46 g of a biopolymer dissolved in a 100 mL water at 300 K exerted an osmotic pressure of 2.42 * 10⁻³ bar. The molar mass of the biopolymer is _______ * 10⁴ g mol⁻¹. (Round off to the Nearest integer) [Use: R = 0.083 L bar mol⁻¹ K⁻¹]

If [x] be the greatest integer less than or equal to x, then ∑₁₀₀ₙ₌₈ [(-1)ⁿ n]/2 is equal to:

An organic compound is subjected to chlorination to get compound A using 5.0 g of chlorine. When 0.5 g of compound A is reacted with AgNO₃ [Carius Method], the percentage of chlorine in compound A is _______ when it forms 0.3849 g of AgCl (Round off to the Nearest integer) (Atomic masses of Ag and Cl are 107.87 and 35.5 respectively)

In gaseous triethyl amine the "-C-N-C-" bond angle is _______ degree.

The number of geometrical isomers possible in triamminetrinitrocobalt(III) is X and in trioxalatochromate(III) is Y. Then the value of X + Y is _______.

The conductivity of a weak acid HA of concentration 0.001 mol L⁻¹ is 2.0 * 10⁻⁵ S cm⁻¹. If Λ⁰ₘ(HA) = 190S cm²mol⁻¹, the ionization constant (Kₐ) of HA is equal to _______ * 10⁻⁶ (Round off to the nearest integer)