Ncert Solutions Maths class 11th

17. The sample space of the experiment is

S = {1, 2, 3, 4, 5, 6} and E = {4}

F = {2, 4, 6}

So, E∩ F = {4} ∩ {2, 4, 6} = {4} ≠

Therefore E and F are not mutually exclusive.

16. When a die is drawn we can have 1, 2, 3, 4, 5 and 6. So, sample space of throwing dice until a six comes up is

S = { (6, (1, 6), (2, 6), (3, 6), (4, 6), (5, 6), (1, 6), (1, 2, 6), (1, 3, 6), (1, 4, 6), (1, 5, 6), (1, 6)……., (1, 5, 6), (1, 6)……… (1, 5, 6)………}

Hence, the sample space is indefinite.

15. The possible outcome when a coin is tossed is a head or a tail. When a dice is thrown we can have the possible outcomes 1, 2, 3, 4, 5 and 6. Let R1, R2 be the two red balls and B1, B2, B3 be the two black balls. So, the desired sample space is

S = { (T, R1), (T, R2), (T, B1), (T, B2), (T, B3), (H, 1), (H, 2), (H, 3), (H, 4), (H, 5), (H, 6)}

14. The possible outcome when a coin is tossed is a head or a tail. When a die is thrown we can have the possible outcome 1, 2, 3, 4, 5 and 6. So, the desired sample space is

S = { (2, H), (2, T), (4, H), (4, T), (6, H), (6, T), (1, H, H), (1, H, T), (1, T, H), (1, T, T), (3, H, H), (3, H, T), (3, T, H), (3, T, T), (5, H, H), (5, H, T), (5, T, H), (5, T, T)}

13. The possible numbers to be chosen are 1, 2, 3 and 4. The sample space of drawing two slips one after another without replacement is

S = { (1, 2), (1, 3), (1, 4), (2, 1), (2, 3), (2, 4), (3, 1), (3, 2), (3, 4), (4, 1), (4, 2), (4, 3)}

12. When a coin is thrown we have the possible outcome of a head or a tail. And when a dice is thrown we have the possible outcomes 1, 2, 3, 4, 5 and 6. So, the desired sample space is

S = {T, (H, 1), (H, 2, 1), (H, 2, 2), (H, 2, 3), (H, 2, 4), (H, 2, 5), (H, 2, 6), (H, 3), (H, 4, 1), (H, 4, 2), (H, 4, 3), (H, 4, 4), (H, 4, 5), (H, 4, 6), (H, 5), (H, 6, 1), (H, 6, 2), (H, 6, 3), (H, 6, 4), (H, 6, 5), (H, 6, 6)}

38. For $\frac{-2}{7}$ ,  $x$ ,  $\frac{-7}{2}$ to be in G.P. we have the condition,

$\Rightarrow$ $\frac{x}{-2/7}=\frac{-7/2}{x}$

$\Rightarrow$ $x^2=\left(\frac{-7}{2}\right)*\left(\frac{-2}{7}\right)$

$\Rightarrow$ $x^2=1$

$\Rightarrow$ $x=+1$

36. Given, a = 3

Let r be the common ratio of the G.P.

Then, a₄ = (a₂)²

$\Rightarrow$ar^4-1 =   (ar^2-1)²

$\Rightarrow$ ar³=  (ar)²

$\Rightarrow$ ar³=  a²r²

$\Rightarrow$ $\frac{r^3}{r^2}=\frac{a^2}{2}$

$\Rightarrow$ r = a = 3

$\therefore$ a₇ = ar^7-1  = ar⁶= (-3) (-3)⁶  = (-3)⁷ = -2187.