Correct Answer: 2 : 3

Solution : According to the question
For maths:
⇒ $\theta$ for maths = $\frac{20}{100}$ × 360° = 72°
For Science
⇒ $\theta$ for science = $\frac{30}{100}$ × 360° = 108°
Ratio = $\frac{\theta ~\text {for maths}}{\theta ~\text{for science}}$ = $\frac{72°}{108°}$  = $\frac{2}{3}$ = 2 : 3
Hence,  the correct answer is 2 : 3.

Correct Answer: 1782

Solution : The correct answer is 1782.

The Treaty of Salbai, which ended the First Anglo-Maratha War, was signed on 17 May 1782 between the British East India Company and the Marathas. The first Anglo-Maratha War started in 1775. The Treaty of Salbai led to the establishment of the status quo which was restored between the English and Marathas.

Correct Answer: 2, 1, 3, 5, 4

Solution : Given:
1. Earth 2. Venus 3. Mars 4. Saturn 5. Jupiter

The correct order of planets based on their distance from the sun is Venus, Earth, Mars, Jupiter, and Saturn.

Thus, the order is 2, 1, 3, 5, 4. Hence, the third option is correct.

Correct Answer: $47$

Solution : Given: $x^2-3x+1=0$
Divide both sides by $x$, we get,
$⇒ x-3+\frac{1}{x}=0$
$\therefore x+\frac{1}{x}=3$
Squaring both sides, we get,
$⇒(x+\frac{1}{x})^2=3^2$
$⇒x^2+\frac{1}{x^2}+2×x×\frac{1}{x}=9$
$\therefore x^2+\frac{1}{x^2}=7$
Again squaring both sides, we get,
$⇒(x^2+\frac{1}{x^2})^2=7^2$
$⇒x^4+\frac{1}{x^4}+2×x^2×\frac{1}{x^2}=49$
$⇒(x^4+\frac{1}{x^4})=49-2$
$\therefore(x^4+\frac{1}{x^4})=47$
Hence, the correct answer is $47$.

Correct Answer: (2)

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

"Engaged tone" should be preceded by the indefinite article "an" to indicate that it is referring to one of the several possible engaged tones that someone might hear. Moreover, the article "an" is used with words starting with a vowel sound.

Therefore, the correct sentence is: "If you hear an engaged tone, replace the receiver and dial again."

Correct Answer: 72 km/h

Solution : Let the speed of the car be $x$ km/h.
According to the question,
Relative speed $= (x - 42)$ km/h
Distance $= 30 + 60 = 90$ km
Now the speed of the car will be
$⇒ x - 42 = \frac{90}{3}$
$⇒ x - 42 = 30$
$⇒ x = 30 + 42 = 72$ km/h
Hence, the correct answer is 72 km/h.

Correct Answer: Mirabai

Solution : The correct answer is Mirabai.

Mirabai was a Rajput princess and a prominent figure in the Bhakti movement of medieval India. She was born into the Rathore clan of Rajputs in the late 15th century. Mirabai is renowned for her unwavering devotion to Lord Krishna, and her devotional songs, known as bhajans, are dedicated to him.

Correct Answer: A person of the age of 30 years can become the Governor

Solution : The correct option is A person of the age of 30 years can become the Governor.

The President appoints the Governor. The Governor holds office at the pleasure of the President. A person can run for Governor once they become 35. To be a governor, he or she must be an Indian citizen. The President receives the resignation of the Governor.

Correct Answer: despoil

Solution : The first option is correct.

Ruin means to cause severe damage, and despoil refers to the act of plundering. Both involve causing harm or damage, so despoil is the appropriate synonym for the word ruin.

The meanings of the other options are as follows:

• Fix means to repair or mend something that is broken.
• Revamp means to give a new and improved form to something.
• Recover means to become completely well again.

Therefore, the correct answer is despoil.

Correct Answer: 18 sq. units

Solution :
$9x+4y=36$ can be written as
$\frac{9x+4y}{36}=1$
$⇒\frac{x}{4} + \frac{y}{9} = 1$
$\therefore$ Area = $\frac{1}{2}\times OA\times OB=\frac{1}{2}\times 4 \times 9$ = 18 sq. units
Hence, the correct answer is 18 sq. units.