Correct Answer: analysis

Solution : The correct choice will be the fourth option.

Scrutiny means the careful and detailed examination of something in order to get information about it. Analysis denotes the result of a careful examination of something, making it a fitting synonym.

The meanings of the other words are:

Behaviour: It means the way that you act or behave.

Comprehensive: It means covering completely or broadly.

Trends: It means a general change or development.

According to the sentence, the correct synonym for scrutiny is analysis.

Correct Answer: 70

Solution : The average of 13 results = 70
The sum of all results = 13 × 70 = 910
The average of the first seven = 65, and the average of the last seven = 75
The sum of the first seven results = 7 × 65 = 455
The sum of the last seven results = 7 × 75 = 525
Seventh result = sum of first seven results + sum of last seven results – the sum of all results
= 455 + 525 – 910 = 70
Hence, the correct answer is 70.

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.