Class 11th

Variance of a, b, c & a+2, b+2, c+2, are same.
Given: b = a + c (i)
d² = (1/3) (a² + b² + c²) - [ (a+b+c)/3]²
as a + c = b
d² = (1/3) (a² + b² + c²) - (2b/3)²
9d² = 3 (a² + b² + c²) - 4b²
⇒ b² = 3 (a² + c²) - 9d²

log? /? [ (|z|+11)/ (|z|-1)²] < 2
(|z|+11)/ (|z|-1)² > (1/2)²
(|z|+11)/ (|z|-1)² > 1/4
⇒ 4|z| + 44 > |z|² - 2|z| + 1
⇒ |z|² - 6|z| - 43 < 0

⇒ |z| - 7 ≤ 0
∴ |z|max = 7

The inequality is experience ( (|z|+3) (|z|-1) / (|z|+1) * log?2 ) ≥ log√? 16.
The right side is log? (1/2) 16 = log? (2? ¹) 2? = (4/-1)log?2 = -4. This seems incorrect.
Let's assume the base of the log on the right is √2. log√? 16 = log? (1/2) 2? = 2 * log?2? = 8.
The inequality becomes: 2^ (|z|+3) (|z|-1) / (|z|+1) ≥ 8 = 2³.
So, (|z|+3) (|z|-1) / (|z|+1) ≥ 3.
Let |z| = t. (t+3) (t-1) / (t+1) ≥ 3
t² + 2t - 3 ≥ 3t + 3
t² - t - 6 ≥ 0
(t-3) (t+2) ≥ 0
Since t = |z| ≥ 0, we must have t-3 ≥ 0.
So, t ≥ 3, which means |z| ≥ 3.
The minimum value of |z| is 3.

ΔG° = -9.478 kJ/mol
Using ΔG° = -2.303 RT log K_p
-9.478 * 10³ = -2.303 * 8.314 * 495 log K_p
1 = log K_p ⇒ K_p = 10
Here, for the given reaction A (g)? B (g), K_p = K_c
Initial A = 22 mmol
At equilibrium A = 22 - x mmol; B = x mmol
K_c = [B] / [A] = (x/V) / (22-x)/V) = x / (22-x) = 10
x = 10 (22-x) ⇒ x = 220 - 10x ⇒ 11x = 220 ⇒ x = 20
So, mmol of B at equilibrium are 20.

Moles of carbon in organic compound = Moles of carbon in CO?
n_c = 420 / 44 moles
Mass of carbon in organic compound = (420 / 44) * 12 = 114.54 g
Moles of hydrogen in compound = 2 * moles of H? O
n_H = 2 * (210 / 18) moles
Mass of hydrogen = 2 * (210 / 18) g = 23.33 g
% of H = (23.33 / 750) * 100 = 3.11%
The nearest integer is 3.

The balanced equation is:
2MnO? + 5C? O? ²? + 16H? → 2Mn²? + 10CO? + 8H? O
So, the value of c (coefficient for H? ) = 16.

H? O? can act as both an oxidizing & reducing agent in both acidic & basic medium. In the hydrogen economy, energy is stored & transmitted in the form of dihydrogen.

Bismuth (Bi) is a metal in group 15. Its hydride is BiH? , which is the strongest reducing agent due to its the lowest thermal stability.