Correct Answer: 1

Solution : Given:
$\frac{1}{2}, \frac{3}{4}, ?, \frac{5}{4}$

In the given series, add $\frac{1}{4}$ to the previous number to get the next number.
$\frac{1}{2}$ + $\frac{1}{4}$ = $\frac{3}{4}$; $\frac{3}{4}$ + $\frac{1}{4}$ = $\frac{4}{4}$ = 1; 1 + $\frac{1}{4}$ = $\frac{5}{4}$

So, 1 is the missing number of the

Correct Answer: 1

Solution : $ax+by=1$ ---------------------------------------(1)
$bx+ay=\frac{2ab}{a^{2}+b^{2}}$ -----------------------------------(2)
On dividing equation (1) by (2), we get,
⇒ $\frac{ax+by}{bx+ay}=\frac{a^{2}+b^{2}}{2ab}$
⇒ $2a^{2}xb+2ab^{2}y=a^{2}bx+b^{3}x+a^{3}y+ab^{2}y$
⇒ $a^{2}xb+ab^{2}y=b^{3}x+a^{3}y$
⇒ $a^{2}xb-b^{3}x=a^{3}y-ab^{2}y$
⇒ $x(a^{2}b-b^{3})=y(a^{3}-ab^{2})$
⇒ $\frac{x}{y}=\frac{(a^{3}-ab^{2})}{(a^{2}b-b^{3})}$
⇒ $\frac{x}{y}=\frac{a(a^{2}-b^{2})}{b(a^{2}-b^{2})}$
⇒ $\frac{x}{y}=\frac{a}{b}$ ---------------------------------(3)
Putting the value of $(x,y)$ from equation (3) in equation (1), we get,
⇒ $y=\frac{b}{a^{2}+b^{2}}$
⇒

Correct Answer: 25 years

Solution : Given: Rate is 8%
Let the Principle be P.
It amounts to 3 times of itself.
Simple interest = 3P – P = 2P
We know, Simple interest $= \frac{\text{Principal × Rate × Time}}{100}$
⇒ $2P =\frac{P×8×\text{Time}}{100}$
⇒ Time = 25 years
Hence, the

Correct Answer: Tamil Nadu

Solution : The correct option is - Tamil Nadu

Most of the yearly rainfall in Tamil Nadu is accounted by the northeast monsoon. The northeast monsoon, commonly known as the winter monsoon, approaches India from that direction. The wind blows from land to sea during this

Correct Answer: $4 \frac{8}{13}$

Solution : P, Q and R can complete a task in 10 days, 15 days and 20 days, respectively.
P's work in 1 day = $\frac{1}{10}$
Q's work in 1 day = $\frac{1}{15}$
R's work in 1 day = $\frac{1}{20}$
Work done by P, Q, and

Correct Answer: 1

Solution : $\tan 5^{\circ} \tan 25^{\circ} \tan 45^{\circ} \tan 65^{\circ} \tan 85^{\circ}$
$=\tan 5^{\circ} \tan (90^{\circ} - 5^{\circ})\tan 25^{\circ} \tan (90^{\circ} - 25^{\circ}) \tan 45^{\circ}$
$=\tan 5^{\circ} \cot 5^{\circ}\tan 25^{\circ} \cot 25^{\circ} \times 1$
$=1 \times 1\times 1$
$= 1$
Hence, the correct answer is 1.

Correct Answer: will have reached the hotel

Solution : The right choice is the third option.

The original sentence, "I have reached the hotel, by the time you call me" uses the present perfect tense (have reached) in a way that doesn't align well with the time frame indicated

Correct Answer: LUFFLLI

Solution : Given:
ANIMISM is written as INAMMSI and EAGERLY is written as GAEEYLR.

Here, the position of the letters before and after the middle letter of the given words gets reversed as shown below –
ANIMISM is written as INAMMSI→

EAGERLY is written as GAEEYLR→

Similarly,

Correct Answer: wrote a letter

Solution : The second option is the correct choice.

The original sentence discusses an action that occurred in the past. So, the correct past tense should be used. "Wrote a letter" is the appropriate past tense form, making the sentence grammatically correct.

Therefore, the

Correct Answer: She was distributing the cards to her friends.

Solution : The correct choice is the first option.

Active voice emphasises the doer of the action, while passive voice emphasises the receiver. To convert passive to active, we make the subject perform the action and rephrase the verb.

The