Correct Answer: baab

Solution : Given:
aa_a_b_abaa_

To fill the series we have to divide the series→aa_ / a_b / _ab / aa_
Let's check each option –
First option: abab; aaa / abb / aab / aab (No repeated pattern has been found.)

Correct Answer:

Solution : Since the rotation is restricted. So, the embedded figure will have the same orientation as the main figure. By comparison of all the option figures, the given question figure is embedded only in the first option figure.

Hence, the first option is correct.

Correct Answer: $\operatorname{cosec} \theta+\cot \theta$

Solution : Given, $\frac{\cot \theta+\operatorname{cosec} \theta-1}{\cot \theta-\operatorname{cosec} \theta+1}$
We know, $\operatorname{cosec^2}θ−\cot^2θ=1$
$=\frac{\cot \theta+\operatorname{cosec} \theta-(\operatorname{cosec^2}θ−\cot^2θ)}{\cot \theta-\operatorname{cosec} \theta+1}$
$=\frac{\cot \theta+\operatorname{cosec} \theta-(\operatorname{cosec}θ−\cotθ)(\operatorname{cosec}θ+\cotθ)}{\cot \theta-\operatorname{cosec} \theta+1}$
$=\frac{(\operatorname{cosec}θ+\cotθ)[1-(\operatorname{cosec}θ-\cotθ)]}{\cot \theta-\operatorname{cosec} \theta+1}$
$=\frac{(\operatorname{cosec}θ+\cotθ)[1-\operatorname{cosec}θ+\cotθ)]}{\cot \theta-\operatorname{cosec} \theta+1}$
$=\operatorname{cosec}θ+\cotθ$
Hence, the correct answer is $\operatorname{cosec}θ+\cotθ$.

Correct Answer: 3241 – 5732

Solution : Let's check each option –
First option: (3241 – 5732); 5732 – 3241 = 2491≠ 2481
Second option: (2354 – 4835); 4835 – 2354 = 2481
Third option: (1326 – 3807); 3807 – 1326 = 2481
Fourth option: (2345 – 4826); 4826 –

Correct Answer: 200

Solution : Given series: 40960, 10240, 2560, 640, 200, 40, 10
The pattern is:
40960 ÷ 4 = 10240
10240 ÷ 4 = 2560
2560 ÷ 4 = 640
640 ÷ 4 = 160 ≠ 200
200 is the wrong number.
The correct number is 160.
160

Correct Answer: 48

Solution : Given:
34 is related to 70 and 56 is related to 114.

To find the second number, add 1 to the first number and then multiply it by 2.
Like, 34 is related to 70→34 + 1 = 35; 35 × 2 = 70
And,

Correct Answer: Extempore

Solution : The correct choice is the third option.

Explanation:

The term extempore refers to a speech or performance that is done without prior preparation or planning. It is characterised by being spontaneous and delivered on the spot. In the context provided, extempore accurately captures the meaning

Correct Answer: had been doing

Solution : The correct choice is the fourth option.

Explanation: The phrase "had been doing" is in the past perfect continuous tense, which is suitable for indicating a continuous action that was happening before another event in the past. In the context of the sentence,

Correct Answer: One

Solution : Given:
BITUMEN

When the letters of BITUMEN are arranged in alphabetical order, the letter cluster formed is BEIMNTU.

So, only 1 letter, i.e., B is at the same position as before. Hence, the first option is correct.

Correct Answer: Post of Vice President

Solution : The correct answer is Post of Vice President.

The position of the Vice President in the Indian Constitution is inspired by the United States Constitution. The office and role of the Vice President in India closely resemble the structure outlined in