Correct Answer: 2

Solution : The error lies in the second part of the sentence marked by the second option.

As per subject-verb agreement, their is a plural pronoun, and the helping verb was should be replaced with were to make the sentence grammatically correct. When a collective noun acts as an individual unit, it is treated as a singular noun, but when we are referring to the individual members in a group, it will be followed by a plural verb.

Therefore, the correct sentence should be: "The Management Committee were divided in their opinion."

Correct Answer: stoic

Solution : The second option is the correct answer.

A stoic refers to a person who can endure pain or hardship without showing their feelings or complaining. Stoicism is a philosophy that encourages self-control, resilience, and the acceptance of adversity with a calm and uncomplaining demeanour.

The meanings of the other options are as follows:

• Agnostic refers to a person who is unsure or sceptical about the existence of God or the supernatural.
• Ascetic refers to a person who practices severe self-discipline and abstains from indulgence, often for religious reasons.
• A pedant refers to a person who is excessively concerned with minor details and rules, often in a narrow or tedious way.

Therefore, the correct answer is stoic.

Correct Answer: 70

Solution : Given: 
× stands for +, + stands for ÷, – stands for × and ÷ stands for –
76 ÷ 5 – 6 + 3 × 4 = ?

After interchanging the given mathematical signs, the equation becomes –
76 – 5 × 6 ÷ 3 + 4
76 – 5 × 2 + 4
76 – 10 + 4
= 70

So, 70 is the answer to the given equation. Hence, the second option is correct.

Correct Answer: Helicase

Solution : The correct option is Helicase.

Catalysing the unwinding of the DNA helix during replication is an enzyme called DNA helicase. As a result of its ability to break hydrogen bonds between complementary base pairs, DNA helicase is crucial to DNA replication because it permits DNA strands to split, and provides templates for new strand composition.

Correct Answer: Madhya Pradesh

Solution : The correct answer is Madhya Pradesh.

Andhra Pradesh, Bihar, Karnataka, Maharashtra, Telangana, and Uttar Pradesh are the six states with bicameral legislatures. A bicameral legislature is not present in Madhya Pradesh. The two houses in a bicameral system are usually known as the Legislative Assembly (Vidhan Sabha) and the Legislative Council (Vidhan Parishad).

Correct Answer: 16 and 12; + and –

Solution : Given:
16 × 4 + 12 ÷ 4 – 15 = 59

Let's check each option –
First option: 4 and 12; × and ÷
Since there are two 4s in the given equation, it is not clear which 4 should be interchanged with 12. Therefore, this option is incorrect.
Second option: 12 and 15; ÷ and –
On interchanging the mathematical signs and numbers, we get –
16 × 4 + 15 – 4 ÷ 12 = 59
On solving the L.H.S. of the equation –
= 16 × 4 + 15 – 4 ÷ 12
= 16 × 4 + 15 – 0.33
= 64 + 15 – 0.33
= 78.67 ≠ 59
Third option: 16 and 12; + and –
On interchanging the mathematical signs and numbers, we get –
12 × 4 – 16 ÷ 4 + 15 = 59
On solving the L.H.S. of the equation –
= 12 × 4 – 16 ÷ 4 + 15
= 12 × 4 – 4 + 15
= 48 – 4 + 15
= 59
Fourth option: 15 and 16; × and +
On interchanging the mathematical signs and numbers, we get –
15 + 4 × 12 ÷ 4 – 16 = 59
On solving the L.H.S. of the equation –
= 15 + 4 × 12 ÷ 4 – 16
= 15 + 4 × 3 – 16 
= 15 + 12 – 16
= 11 ≠ 59

So, only the third option satisfies the equation. Hence, the third option is correct.

Correct Answer: Cattle : Barn

Solution : Given: 
Bird : Nest (The shelter place of a bird is called a nest.)

Let's check the options –
First option: Goat : Grass→Goat eats grass.
Second option: Tiger : Kennel→The shelter place of the tiger is called a lair.
Third option: Ant : Sugar→Ant eats sugar.
Fourth option: Cattle : Barn→The shelter place of cattle is called a barn.

So, only the fourth option follows the same pattern as the given pair. Hence, the fourth option is correct.

Correct Answer: Few sellers, Many buyers

Solution : The correct answer is Few sellers, Many buyers

In an oligopoly, there is limited competition in the market, shared by a small number of sellers and a large number of buyers. An oligopoly is described as an imperfect market because it has competition among a few sellers. In a monopoly, there is only one seller and many buyers.

Correct Answer: 60º

Solution :

In a triangle, the angles are in the ratio 2 : 2 : 5.
Let the angles are $2x$, $2x$, and $5x$ respectively, where $x$ is a constant.
Since the sum of the angles in a triangle is \(180^\circ\).
$⇒2x + 2x + 5x = 180^\circ$
$⇒x = 20^\circ$
$\angle P = \angle Q = 40^\circ$ and $\angle R = 100^\circ$.
Since a line AB parallel to QR is drawn which touches PQ and PR at A and B, by the corresponding angles theorem.
$⇒\angle PAB = \angle Q = 40^\circ$ and $\angle PBA = \angle R = 100^\circ$.
$⇒\angle PBA - \angle PAB = 100^\circ - 40^\circ = 60^\circ$
Hence, the correct answer is 60º.

Correct Answer:

$\frac{\pi}{3}$

Solution : Given: $0°<\theta<90°$ and $2\sec\theta =3 \operatorname{cosec}^2 \theta$
$2\sec\theta =3 \operatorname{cosec}^2 \theta$
$⇒\frac{2}{\cos\theta}=\frac{3}{\sin^2\theta}$
Squaring both sides, we get,
$\frac{4}{\cos^2\theta}=\frac{9}{\sin^4\theta}$
$⇒4\sin^4\theta+9\sin^2\theta-9=0$
$⇒(\sin^2\theta+3)(4\sin^2\theta-3)=0$
$\therefore \sin\theta= \sqrt{-3} , \frac{\sqrt{3}}{2}$
The value of $\sin\theta$ can't be $\sqrt{-3}$.
$⇒\sin\theta= \frac{\sqrt{3}}{2}=\sin60°$
$\therefore \theta=60°=\frac{\pi}{3}$
Hence, the correct answer is $\frac{\pi}{3}$.