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 $\frac{\pi}{3}$.

Correct Answer: Hydro-electricity

Solution : The correct option is Hydroelectricity.

Sometimes the term "white coal" refers to hydroelectricity. Hydroelectricity is produced by harnessing the energy of moving or falling water, often via the use of dams and turbines to transform the kinetic energy of the water into electrical energy. It is seen as a clean and renewable source of energy, in the same way that coal is regarded as a fossil fuel. When compared to regular coal, which is a non-renewable and polluting energy source, the term "white coal" emphasises the ecologically favourable and renewable qualities of hydroelectric electricity.
 

Correct Answer: Cerebellum

Solution : The correct answer is Cerebellum.

The top region of the brain is called the cerebrum. It receives information from the sensory organs, interprets it, and commands the body. Additionally, the cerebrum is main in mental processes like thinking, emotion regulation and remembering. Taking a pencil off a table is one instance of this.

Correct Answer: Jalandhar, India

Solution : The correct option is Jalandhar, India.

The 1979 Asian Wrestling Championships were organized by the Asian Associated Wrestling Committee (AAWC) for the first time in Jalandhar, India. The championship starts with the men's events, but female events were added in 1996. Iran has the highest number of medals, which is 317.

Correct Answer: 250

Solution : Given:
14, 29, 60, 123,?

Multiply the previous term by 2 and then add consecutive natural numbers to obtain the next term in the series –
14 × 2 + 1 = 29
29 × 2 + 2 = 60
60 × 2 + 3 = 123
123 × 2 + 4 = 250

So, 250 is the missing term of the series. Hence, the second option is correct.

Correct Answer: Article 22

Solution : The correct answer is Article 22.

Article 22 of the Indian Constitution (1950) safeguards the rights of individuals arrested. It ensures that a person, upon arrest, must be promptly informed of the grounds for arrest and has the right to consult and be defended by a legal practitioner of their choice. Additionally, anyone arrested must be brought before the nearest magistrate within 24 hours, excluding travel time, and cannot be held in custody beyond this period without magistrate authorisation.