Correct Answer: $1$

Solution : Given: $x\sin\theta=y\cos\theta$
And, $x\sin^{3}\theta +y\cos^{3}\theta=\sin\theta\cos\theta$
⇒ $x\sin\theta(\sin^{2}\theta) +y\cos\theta(\cos^{2}\theta)=\sin\theta\cos\theta$
Since, $x\sin\theta=y\cos\theta$ and $\sin^{2}\theta+\cos^{2}\theta=1$,
So, $x\sin\theta=y\cos\theta=\sin\theta\cos\theta$
⇒ $x=\cos\theta$ and $y=\sin\theta$
So, $x^{2}+y^{2}=\sin^{2}\theta+\cos^{2}\theta=1$
Hence, the correct answer is 1.

Correct Answer: 25

Solution : $\frac{2 p}{p^2-5 p+1}=\frac{1}{10}$
⇒ $p^2-5 p+1$ = $20p$
⇒ $p^2-25 p+1$ = $0$
⇒ $p+\frac{1}{p}-25$ = $0$
⇒ $p+\frac{1}{p}$ = $25$
Hence, the correct answer is 25.

Correct Answer: Vitasta

Solution : The correct option is Vitasta.

The ancient name of the river Jhelum was Vitasta. In Vedic times, the region where the Vedic Aryans lived, known as Sapt-Sindhu, included the land around seven rivers, and Vitasta (Jhelum) was one of these rivers. The Vedas and other

Correct Answer: $16$

Solution : Let the efficiency of 1 man and 1 boy be m and b respectively.
m = 2b
m : b = 2 : 1
We know that, work = efficiency × time
So, work done by 10 men in 8 days = 2 × 10

Correct Answer: BDFG

Solution : Let's check the options –
First option: ACEG; A + 2 = C; C + 2 = E; E + 2 = G
Second option: BDFG; B + 2 = D; D + 2 = F; F + 1 = G
Third option: JLNP; J

Correct Answer: Oslo

Solution : The correct option is - Oslo.

The Nobel Prizes in physics, chemistry, literature, and physiology or medicine are awarded in Stockholm, Sweden.

 while the Nobel Peace Prize is awarded in Oslo, Norway, as stated in the Swedish-born inventor and international industrialist Alfred Nobel's will, which

Correct Answer: Forward Bloc

Solution : The correct answer is Forward Bloc.

Subhas Chandra Bose founded the Forward Bloc. The Forward Bloc was established by Bose on May 3, 1939, as a breakaway faction of the Indian National Congress. Bose formed the Forward Bloc to advance a more radical approach

Correct Answer: Plutocracy

Solution : The correct answer is the fourth option.

It is derived from the Greek words "ploutos," which means wealth, and "kratia," which means rule or power. Therefore, it accurately represents a government that is primarily influenced or controlled by those with significant financial resources.

The meanings

Correct Answer: Baji Rao II

Solution : The Correct Answer is Baji Rao II

When Peshwa Baji Rao II was in power, the British abolished the Peshwaship. After the Third Anglo-Maratha War (1817–18), which saw the defeat of the Maratha power, this abolition was implemented. The British East India Company

Correct Answer: 1 3 2 4

Solution : The correct answer is 1 3 2 4.

Indira Col in the Siachen glacier is northernmost point of India and Indira point in the Andaman and Nicobar Islands is southernmost point of India. Bhubneshwar is in Odisha, Hyderabad is in Telangana, Cochin