Two men A and B have a choice to buy ₹ 100 shares. A buys shares at ₹ 120 per share and 5% dividend. B buys shares at ₹ 150 per share and 8% dividend. Which of the two men A and B gets the better return, if the nominal value of both the shares is ₹ 100?

1. A

2. B

3. both get equal returns

4. cannot say

Assertion (A) : The numbers 8, 10, 12, x and 15 are in ascending order of their values. If the mean of their observations is equal to their median, the value of x is 15.

Reason (R) : If the number of observations is n, their mean = $\dfrac{\text{Sum of observations}}{n}$ and median (if n is odd) = value of the $\Big(\dfrac{n + 1}{2}\Big)^{\text{th}}$ observation

1. A is true, R is true

2. A is true, R is false

3. A is false, R is true

4. A is false, R is false

Asit saves ₹ 50 daily and deposits ₹ 1,500 every month in a recurring deposit account for $2\dfrac{1}{2}$ years at r% per annum. If he gets ₹ 50,812.50 on maturity, find the value of r.

(i) Find angle A, if

2 sin² A - $\sqrt{3}$ sin A = 0 and 0 < ∠A < 90°

(ii) Find angle B, if

2 cos 2B - 1 = 0 and ∠B is an acute angle.

(iii) State the value of cot (A + B).