Correct Answer: $2 \sin \theta$

Solution : $\frac{\cos ^4 \theta-\sin ^4 \theta+2 \sin ^2 \theta+3}{(\operatorname{cosec} \theta+\cot \theta+1)(\operatorname{cosec} \theta-\cot \theta+1)-2}, 0^{\circ}<\theta<90^{\circ}$
$=\frac{(cos^2\theta)^2-(\sin^2\theta)^2+2 \sin ^2 \theta+3}{(\operatorname{cosec} \theta+1+\cot \theta)(\operatorname{cosec} \theta+1-\cot \theta)-2}$
$=\frac{(cos^2+\sin^2\theta)(cos^2-\sin^2\theta)+2 \sin ^2 \theta+3}{[(\operatorname{cosec} \theta+1)^2-\cot^2 \theta]-2}$
$=\frac{cos^2+\sin^2\theta +3}{[\operatorname{cosec^2} \theta+1+2\operatorname{cosec \theta}-\cot^2 \theta]-2}$
$=\frac{4}{2+2\operatorname{cosec} \theta-2}$
$=\frac{4}{2\operatorname{cosec} \theta}$
$=2 \sin \theta$
Hence, the correct answer

Correct Answer: PR

Solution : Let's check the options –
First option: CD; C + 1 = D
Second option: PR; P + 2 = R
Third option: ST; S + 1 = T
Fourth option: WX; W + 1 = X

So, the second option is different from the

Correct Answer: 225%

Solution : Number of salesmen in J = 45
Number of salesmen in K = 20
Percent = $\frac{45}{20}\times 100 = 225$%
Hence, the correct answer is 225%.

Correct Answer: 2010

Solution : First term, $a$ = 91
Last term, $l$ = 110
Number of terms, $n$ = 20
The sum of n terms of series = $\frac{n}{2}(a+l)$
The sum of 20 terms of series = $\frac{20}{2}(91+110)=10(91+110)=2010$
Hence, the correct answer is 2010.

Correct Answer: 45

Solution : Let his average before the 21^st match be $x$.
New average after 21^st match = $(x + 2)$
Total runs before the 21^st match = $20x$
Runs scored in the 21^st match = 87
⇒ $x + 2$ = $\frac{87 +

Correct Answer: MS

Solution : Given:

AG : IO :: EK : ?

A + 8 = I ; G + 8 = O; 

Similarly, E + 8 = L ; K + 8 = R

Therefore, LR is the related word.

Hence, the first option is correct.

Correct Answer: $2 \sqrt{6}$

Solution : We know that LCM × HCF = Product of two numbers
Now Mean proportion = $\sqrt{\text{Product of two numbers}}$
Given:
LCM = 12
HCF = 2
$\therefore$ Product of two numbers $= 12 \times 2 = 24$
Mean proportion $=\sqrt{24} = \sqrt{4\times 6}=2\sqrt{6}$
Hence

Correct Answer: 16 - 24

Solution : Let's check the options —

First option: 13 - 21; Both 13 and 21 are odd numbers.

Second option: 19 - 27; Both 19 and 27 are odd numbers.

Third option: 15 - 23; Both 15 and 23 are odd numbers. 

Fourth option: 

Correct Answer: Joseph Aspdin

Solution : The correct answer Joseph Aspdin

Joseph Aspdin was born in England in 1779. He is credited for the invention of cement and got the patent for portland cement. He was an English businessman, inventor and stonemason. While experimenting he found that when clay and

Correct Answer: broaden

Solution : The correct choice is the second option.

Explanation:

Constrict means to make narrower or tighten, which is the opposite of what is intended.

Localise means to confine to a particular place, which is not the intended meaning.

Contract means to make smaller or shrink, which