Correct Answer: PRS

Solution : Let's check the options –
First option: BDF; B + 2 = D; D + 2 = F
Second option: UWY; U + 2 = W; W + 2 = Y
Third option: IKM; I + 2 = K; K + 2 = M
Fourth option: PRS : P + 2; R + 1 = S

So, the fourth option is different from the other three options because the difference in the positional values of the letters is 2, 1 instead of 2, 2. Hence, the fourth option is correct.

Correct Answer: No Error

Solution : The third option is the correct answer.

The given sentence is correct and there is No error. The sentence simply describes the action of a crocodile swimming in a river.

Correct Answer: 111; 114; 117

Solution : Let the missing numbers in a table be a; b; c.

In a given table, the sum of all the numbers in a row and in a column is equal i.e. 342.

In the first row→113 + 118 + a = 342
⇒ a = 342 – 113 – 118 = 111
In the second row→112 + b + 116 = 342
⇒ b = 342 – 112 – 116 = 114
Similarly, in the third row→c + 110 + 115 = 342
⇒ c = 342 – 110 – 115 = 117

So, 111; 114; and 117 are the missing numbers in the given figure. Hence, the third option is correct.

Correct Answer: Bihar

Solution : The correct option is Bihar.

According to a survey conducted by the Geological Survey of India, the Jamui district in Bihar holds a significant gold reserve, totaling approximately 222.88 million metric tonnes, which includes 27.6 metric tonnes of mineral-rich ore. In terms of primary gold resources in India, Bihar emerges as the leading state, accounting for 44% of the total reserves, followed by Rajasthan (25%), Karnataka (21%), West Bengal (3%), Andhra Pradesh (3%), and Jharkhand (2%). The remaining 2% of gold ore resources are distributed across Chhattisgarh, Madhya Pradesh, Kerala, Maharashtra, and Tamil Nadu.

Correct Answer: they used chariots driven by horses

Solution : The Correct Answer is they used chariots driven by horses

Because they had superior Bronze and Iron tools and ox- and horse-drawn carts with light spoked wheels, Aryans were more successful than pre-Aryans. In order to create a new civilization, the pre-Aryans had previously destroyed and expelled some other population. Around 1500 BCE, the Aryans arrived on the Indian subcontinent. 

Correct Answer: 810000

Solution : Given:
Length = 12 m, Breadth = 9 m, Height = 7.5 m
Volume of cube = Length × Breadth × Height
⇒ Volume of cube = 12 × 9 × 7.5 = 810 m³
The amount of water held by 1 m³ tank = 1000 litres
So, the amount of water held by 810 m³ tank = 810 × 1000 = 810000 litres
Hence, the correct answer is 810000.

Correct Answer: $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$

Solution : $x\cos \theta -y\sin \theta =\sqrt{x^{2}+y^{2}}$ ..................................(1)
$\frac{\cos ^2{\theta }}{a^{2}}+\frac{\sin ^{2}\theta }{b^{2}}=\frac{1}{x^{2}+y^{2}}$ .......................................(2)
From equation (1),
$\frac{x\cos \theta}{\sqrt{x^{2}+y^{2}}} -\frac{y\sin \theta}{\sqrt{x^{2}+y^{2}}} =1$
Comparing with $\cos^2 \theta + \sin^2 \theta = 1$, we get,
$\sin \theta = -\frac{y}{\sqrt{x^{2}+y^{2}}}$ and $\cos \theta = \frac{x}{\sqrt{x^{2}+y^{2}}}$
Putting in (2),
$\frac{x^2}{(x^2 + y^2)a^2}+ \frac{y^2}{(x^2 + y^2)b^2} = \frac{1}{(x^2 + y^2)}$
⇒ $\frac{x^2}{a^2}+ \frac{y^2}{b^2} = 1$
Hence, the correct answer is $\frac{x^2}{a^2}+ \frac{y^2}{b^2} = 1$.

Correct Answer: 24

Solution : Given: Area = $84\ cm^2$
1st diagonal = 7 cm
2nd diagonal = $D_2$
We know that
Area of rhombus = $\frac{1}{2}\times$(Product of the diagonals)
⇒ $84 = \frac{1}{2}\times7\times D_2$
⇒ $D_2 = 24\ cm$
Hence, the correct answer is 24.

Correct Answer: the world's leading string quartet.

Solution : The error lies in the second option.

The phrase "one of" should be followed by a plural noun to maintain the agreement in the sentence. Thus, string quartet should be replaced with string quartets to make the sentence grammatically accurate, as "one of" is followed by a plural noun but requires a singular verb to agree with the noun phrase.

Therefore, the correct sentence is: The London-based Brodsky Quartet, meanwhile, is one of the world's leading string quartets.

Correct Answer: 1:4

Solution : The correct option is 1:4.

If the density of oxygen is 16 times that of hydrogen, the ratio of their velocities of sound will be the same as the ratio of their densities

The velocity of sound from oxygen to hydrogen is 1:4.

v=√γP/ρ.

• v is the speed of sound in the gas,
• γ is the heat capacity ratio 
• P is the pressure of the gas, and
• ρ is the density of the gas.

Vo₂/VH₂ = ρH₂/ρO₂

√1/16 = 1/4​​.