It's a Question of your Career!

Correct Answer: $\frac{\sqrt{5}}{3}$

Solution : Given that $\operatorname{cosec B} = \frac{3}{2}$.
$\mathrm{\sin B = \frac{2}{3}}$
$⇒\mathrm{\cos B = \sqrt{1 - \sin^2 B} = \sqrt{1 - \left(\frac{2}{3}\right)^2} = \sqrt{1 - \frac{4}{9}} = \sqrt{\frac{5}{9}} = \frac{\sqrt{5}}{3}}$
$⇒\mathrm{\cot B = \frac{\cos B}{\sin B} = \frac{\frac{\sqrt{5}}{3}}{\frac{2}{3}} = \frac{\sqrt{5}}{2}}$
$\therefore \mathrm{\cot B \sin B =

Correct Answer: $\frac{2}{3}$

Solution : $\cos^{4}\theta-\sin^{4}\theta=\frac{2}{3}$
⇒ $(\cos^{2}\theta-\sin^{2}\theta)(\cos^{2}\theta+\sin^{2}\theta) = \frac{2}{3}$
We know that, $\cos^{2}\theta+\sin^{2}\theta= 1$
⇒ $(\cos^{2}\theta-\sin^{2}\theta)=\frac{2}{3}$
Putting the value of $\cos^{2}\theta = 1-\sin^{2}\theta$
⇒ $(1-\sin^{2}\theta-\sin^{2}\theta)=\frac{2}{3}$
$\therefore(1-2\sin^{2}\theta)=\frac{2}{3}$
Hence, the correct answer is $\frac{2}{3}$.

Correct Answer: 80

Solution : In a column, add the first two numbers and then multiply the resultant number by the third number to get the fourth number.

In the second column→(4 + 5) × 6 = 9 × 6 = 54
In the third column→(2 + 1) × 3

Correct Answer: 60

Solution : Factors of 10 = 2 × 5
Factors of 12 = 2 × 2 × 3
Factors of 15 = 3 × 5
LCM of 10, 12, and 15 = 2 × 2 × 3 × 5 = 60
Hence, the correct answer is 60.

Correct Answer: $\frac{31}{20}$

Solution :
Using the Pythagoras theorem we get, 
$AC^2=BC^2-AB^2$
⇒ $AC=\sqrt{5^2-4^2}$
⇒ $AC=3$ cm
Now, $\cos B=\frac{4}{5}$ and $\cot C=\frac{3}{4}$
So, $\cos B + \cot C=\frac{4}{5}+\frac{3}{4}=\frac{31}{20}$
Hence, the correct answer is $\frac{31}{20}$.

Correct Answer: 2

Solution : Given, $x+\frac{1}{x}=2$
⇒ $x^2 + 1 = 2x$
⇒ $x^2-2x+1 = 0$
⇒ $(x-1)^2 = 0$
⇒ $x-1 = 0$
⇒ $x=1$
$\therefore x^{57}+\frac{1}{x^{57}}=1^{57}+\frac{1}{1^{57}} = 2$
Hence, the correct answer is 2.

Correct Answer: Rs. 9.80

Solution : The price of the sewing machine = Rs. 700
Single discount of 30% and 6% = $30+6-\frac{30\times 6}{100} = 36-1.8 =34.2\%$
Single discount of 20% and 16% = $20+16-\frac{20\times 16}{100} = 36-3.2 =32.8\%$
Difference of discount percentage = $34.2 -32.8 =1.4\%$
$\therefore$ The difference

Correct Answer: COQWNCGF

Solution : Given: 
CIVILIAN : AGREFCSF :: DOCTRINE : BMYPLCFW :: EQUATION : ?

In each pair, the first two letters of each word have a difference of 2; the third and fourth letters have a difference of 4; the fifth and sixth letters have a difference

Correct Answer: keep

Solution : The correct choice is the fourth option.

In this sentence, the word keep would be used to express the unintentional action of causing a group of people to wait. It implies the continuation of a situation—in this case, causing others to wait.

The meanings

Correct Answer: (22, 35, 48)

Solution : Given:
(15, 28, 41); (19, 32, 45)

⇒(15, 28, 41)→15 + 41 = 56; 56 ÷ 2 = 28
⇒(19, 32, 45)→19 + 45 = 64; 64 ÷ 2 = 32

Let's check the options –
First option: (16, 28, 43)→16 + 43