Correct Answer: By whom were my tickets stolen?

Solution : The correct choice is the third option.

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 subject in the passive voice.

The structure of the passive voice in the case of the simple past interrogative sentence is: "By + interrogative word 'whom' + were + plural object + past participle form of the verb?"

Therefore, the passive sentence would be: "By whom were my tickets stolen?"

Correct Answer: (3)

Solution : The correct choice is the third option.

Explanation:

"Either of" is the most appropriate choice, conveying the idea that one of the two options could be correct.

So, the correct sentence would be: "Either of these two options could be the correct answer."

Correct Answer: 3

Solution : The correct choice is the third option.

The preposition over should be replaced with across as across the state means from one end to the other end of the state. Across is often associated with a more direct or horizontal movement, while over can be used for both horizontal and vertical movements.

So, the correct sentence is: According to an official spokesperson, polling was held amid tight security arrangements in 29 municipal councils and panchayats across the state.

Correct Answer: are developed

Solution : The correct choice is the third option.

In the given sentence, since we are talking about childhood, we need to use the verb in the past participle form with an auxiliary verb. Therefore, are developed is the correct choice.

Correct Answer: $2\sec^2 \theta$

Solution : $\frac{1}{1+\cos(90^{\circ}- \theta)}$ + $\frac{1}{1-\cos(90^{\circ}- \theta)}$
= $\frac{1}{1+\sin \theta}$ + $\frac{1}{1-\sin \theta}$
= $\frac{(1-\sin \theta)+(1+\sin \theta)}{(1-\sin \theta)(1+\sin \theta)}$
= $\frac{2}{1-\sin ^2 \theta}$
= $\frac{2}{\cos ^2 \theta}$
= $2\sec^2 \theta$
Hence, the correct answer is $2\sec^2 \theta$.

Correct Answer: 1

Solution : Given:
$4x=\sqrt5+2$
⇒ $\frac{1}{4x}=\sqrt5-2$ (by rationalising)
⇒ $4x - \frac{1}{4x}=(\sqrt5+2)-(\sqrt5-2)$
⇒ $4x - \frac{1}{4x}=\sqrt5+2-\sqrt5+2$
⇒ $4x - \frac{1}{4x}=4$
Dividing both sides by 4, we get,
⇒ $\frac{4x}{4}-\frac{1}{4x×4}=\frac{4}{4}$
$\therefore x - \frac{1}{16x}=1$
Hence, the correct answer is 1.

Correct Answer: Father

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, the man is the father of that woman. Hence, the fourth option is correct.

Correct Answer: (125, 25, 100)

Solution : Given:
(23, 14, 9); (37, 19, 18)

Here, (23, 14, 9)→14 + 9 = 23
(37, 19, 18)→19 + 18 = 37

Let's check the options –
First option: (125, 25, 5)→25 + 5 = 30 ≠ 125
Second option: (125, 100, 5)→100 + 5 = 105 ≠ 125
Third option: (125, 25, 100)→25 + 100 = 125
Fourth option: (125, 5, 25)→5 + 25 = 30 ≠ 125

So, only the third option follows the same pattern as followed by the given set of numbers. Hence, the third option is correct.

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

Solution : Given: ABC is an equilateral triangle with a side of 12 cm.
The length of the inradius of the equilateral triangle = $\frac{\text{side}}{2\sqrt3}=\frac{12}{2\sqrt3}=2\sqrt3$ cm
Hence, the correct answer is $2\sqrt3$ cm.

Correct Answer: 15 : 9

Solution : Let's check the options –
First option: 20 : 11; (11 × 2) – 2 = 22 – 2 = 20
Second option: 6 : 4; (4 × 2) – 2 = 8 – 2 = 6
Third option: 15 : 9; (9 × 2) – 2 = 18 – 2 = 16 ≠ 15
Fourth option: 12 : 7; (7 × 2) – 2 = 14 – 2 = 12

So, only the third option is different from the other three. Hence, the third option is correct.