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

Solution : $\frac{\cos^2 15^{\circ}-\sin^2 15^{\circ}}{\cos^2 145^{\circ}+\sin^2 145^{\circ}}$
= $\frac{\cos^2 15^{\circ}-\sin^2 15^{\circ}}{1}$
= $\cos (2×15)^{\circ}$ (Since $\cos^2A-\sin^2A=\cos2A$)
= $\cos 30^{\circ}$ 
= $\frac{\sqrt 3}2$
Hence, the correct answer is $\frac{\sqrt 3}2$.

Correct Answer: LTR

Solution : Given
EFH : BJI :: OPQ : ?

Subtract 3 from the place value of the first letter and add 4 and 1 to the place value of the second and third letters respectively of EFH to obtain the required code –
E – 3

Correct Answer: 60° and 30°

Solution : Given, $\cos (A-B)=\frac{\sqrt{3}}{2}$ and $\cos (A+B)=0$
Since $A$ and $B$ are acute positive angles,
$\cos (A-B)=\frac{\sqrt{3}}{2}$
⇒ $(A-B) = \cos^{-1} \frac{\sqrt{3}}{2}$
⇒ $(A-B) = 30°$ ------------------ (1)
$\cos (A+B)=0$
⇒ $(A+B) = \cos^{-1} 0$
⇒ $(A+B) = 90°$ --------------------- (2)
Solving (1) and

Correct Answer: Reef

Solution : Given:
Reef, Ready, Rainbow, Rain

Step 1: Compare the first letter of each word. Since all the words start with the same letter R, then move on to the next letter.
Step 2: The second letter of the words is either a or e

Correct Answer: 6.2% p.a.

Solution : Given: Principal = Rs. 21850
Simple interest = Amount – Principal = Rs. 28623.50 – 21850 = 6773.5
Time = 5 years
Rate = to find
Simple interest = $\frac{\text{Principal × Rate × Time}}{100}$
⇒ $6773.5=\frac{21850 × \text{Rate} × 5}{100}$
⇒ Rate = $\frac{6773.5\times100}{21850

Correct Answer: (2)

Solution : The sentence can be improved using the second option "credulous".

The word "credulous" means "ready to believe too easily". In this sentence, it is used to describe Manoj's tendency to believe everything he is told, even if it is not true.

The meanings of the

Correct Answer: 2

Solution : $17 ÷ 34 + 2 × 12 ÷ 6 - 5 × 3 ÷ 6$
$=\frac{1}{2} + 2 × 2 - 5 × \frac{1}{2}$
$=\frac{1}{2} + 4 - \frac{5}{2}$
$=\frac{9}{2} - \frac{5}{2}$
$=\frac{4}{2}$
$= 2$
Hence, the correct answer is 2.

Correct Answer: $\frac{2n+5}{2}$

Solution : Average of 5 consecutive integers starting with 'm' = n
Let m, m + 1, m + 2, m + 3, m + 4 be the 5 consecutive integers.
Average of 5 consecutive integers = middle term
$n$ = m + 2---------------------------------(i)
Then 6 consecutive

Correct Answer: Many lessons have been learned by her in this camp.

Solution : The third option is the correct choice.

Passive voice is the voice in which the object experiences an action rather than the person who performs the action. Hence, the object in the active sentence becomes the

Correct Answer: 4365

Solution : Divisibility rule of 15: The number should be divisible by both 3 and 5.
Divisibility rule of 3: The sum of the digits in a number is a multiple of 3.
Divisibility rule of 5: The unit place digit must be 5 or 0.
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