Correct Answer: 10 cm

Solution :
Let O be the centre of the circle. OA = 13 cm and OM = 12 cm.
Let AB be the chord of the smaller circle which is tangent to a smaller circle.
Since the tangent is perpendicular to the radius at its point of contact, angle OMA is a right angle.
By Pythagoras theorem,
OA² = AM² + OM²
⇒ 13² = AM² + 12²
⇒ AM² = 25
⇒ AM = 5 cm
Also, perpendicular from the centre to a chord bisects the chord.
AB = 2 × AM = 2 × 5 = 10 cm
Hence, the correct answer is 10 cm.

Correct Answer: To give great importance to trifles.

Solution : The third option is correct.

To make a mountain out of a molehill is an idiom referring to over-reactive, histrionic behaviour where a person makes too much of a minor issue.

Therefore, the correct answer is, to give great importance to trifles.

Correct Answer: 4%

Solution : Given: Principal = INR 7,400
Time = 36 months = 3 years
Simple interest after 3 years = INR 888
Let the rate of interest be $r$%.
We know, Simple interest = $\frac{\text{Principal × Rate × Time}}{100}$
⇒ $888=\frac{7400\times r\times 3}{100}$
$\therefore r=4$%
Hence, the correct answer is 4%.

Correct Answer: Mother Teresa

Solution : The correct option is Mother Teresa.

In 1992, Mother Teresa was presented with the first Rajiv Gandhi National Sadbhavna Award. The award was established by the Indian National Congress Party's All India Congress Committee in 1992 to recognise the long-lasting contribution made by the late Prime Minister Rajiv Gandhi.

Correct Answer: hostile

Solution : The correct choice is the third option.

The most appropriate antonym for affable is hostile, because affable denotes pleasant or friendly, while hostile means having very strong feelings against somebody or something.

The meanings of other options are as follows:

• Aggravate: It denotes making something worse.
• Sardonic: It denotes showing that you think you are better than other people and not taking others seriously.
• Amicable: It denotes something made or done in a friendly way, without argument.

Correct Answer: JEOW

Solution : Given:
DMTS is related to FOVU and KGQO is related to MISQ.

Add 2 to the place value of each letter of DMTS and KGQO to obtain their respective codes –
DMTS→D + 2 = F; M + 2 = O; T + 2 = V; S + 2 = U
Thus, DMTS is coded as FOVU.
KGQO→K + 2 = M; G + 2 = I; Q + 2 = S; O + 2 = Q
Thus, KGQO is coded as MISQ.
Similarly, follow the same pattern for HCMU –
H + 2 = J; C + 2 = E; M + 2 = O; U + 2 = W

So, HCMU is coded as JEOW. Hence, the third option is correct.

Correct Answer: 2

Solution : The correct choice is the second option.

Explanation: When we express admiration or emphasise the quality of something, we often use the structure "What a [adjective] [noun]!". The addition of the article "a" in this case is grammatically correct and aligns with the pattern of exclamatory sentences that emphasise a particular quality or attribute.

Therefore, the correct sentence would be: "What a delicious flavour these mangoes have!"

Correct Answer: Brother

Solution : As per the given information, the family tree will be as follows –

Here, the quadrilateral represents the male, and the circular figure represents the female in the figure.

So, from the above family tree, E is the brother of G. Hence, the first option is correct.

Correct Answer:

$10\%$

Solution : Let the selling price of one orange = Re. 1
The selling price of 36 oranges = Rs. 36
Loss on 36 oranges = Rs. 4
The cost price of 36 oranges = 36 + 4 = Rs. 40
Loss percentage = $\frac{\text{Loss}}{\text {Cost Price}}$ × 100
Loss percent = $\frac{4}{40}$ × 100 = 10%
Hence, the correct answer is $10\%$.

Correct Answer: 64 – 4032

Solution : Let's check each option –
First option: (64 – 4032); 64² = 4096 ≠ 4032
Second option: (38 – 1444); 38² = 1444
Third option: (42 – 1764); 42² = 1764
Fourth option: (52 – 2704); 52² = 2704

So, only the first option is different from the others. Hence, the first option is correct.