Correct Answer: 38 years

Solution : Let the present age of the son be x years.

Two years ago, Aadhya was three times as old as his son, the equation becomes

⇒ Aadhya's age two years ago = 3 (x – 2) = 3x – 6

⇒ Aadhya's present age = 3x – 4 

Two years hence, twice her age will be equal to five times that of her son

⇒ 2 (3x – 2) = 5 (x + 2)

⇒ 6x – 4 = 5x + 10

⇒ x = 14

Aadhya's present age = 3x – 4 = (3 x 14) – 4 = 38 years.

Hence, option first is correct.

Correct Answer: Am I known to her?

Solution : The correct choice is the fourth option.

Passive voice is the voice in which the object experiences an action rather than the person who performs the action. Hence, the object in the active sentence becomes the subject in the passive voice.

The structure of the passive sentence in the case of the simple present interrogative sentence is: "Am + singular object + past participle form of the main verb + prepositional phrase?"

Therefore, the passive voice sentence would be: "Am I known to her?"

Correct Answer: 51

Solution : Given:
98 – 39 – 27 = 31; 87 – 38 – 34 = 20

Multiply the digits of each number of the L.H.S. and then subtract them to get the R.H.S.
Like, 98 – 39 – 27 = 31→(9 × 8) – (3 × 9) – (2 × 7) = 72 – 27 – 14 = 31
And, 87 – 38 – 34 = 20→(8 × 7) – (3 × 8) – (3 × 4) = 56 – 24 – 12 = 20
Similarly, follow the same pattern for 79 – 25 – 12→(7 × 9) – (2 × 5) – (1 × 2) = 63 – 10 – 2 = 51

Hence, the first option is correct.

Correct Answer: 30

Solution : Given: The number of pupils in a class = 55
Ratio of male and female = 5 : 6
Let the number of male and female pupils be 5x and 6x, respectively.
So, the total number of pupils = 5x + 6x = 11x
According to the question,
11x = 55
$\therefore$ x = 5
Number of female pupils = 6x = 6 × 5 = 30
Hence, the correct answer is 30.

Correct Answer: 172

Solution : Given:
214, 207, 193, ?, 144, 109

In the above-given series, subtract the multiples of 7 from the previous number to get the next number.
214 – 7 = 207; 207 – 14 = 193; 193 – 21 = 172; 172 – 28 = 144; 144 – 35 = 109

So, 172 is the missing number of the series. Hence, the first option is correct.

Correct Answer: 1833

Solution : The correct answer is 1833.

Carl Friedrich Gauss and Wilhelm Eduard Weber invented the first electromagnetic telegraph in 1833. Weber was appointed physics professor in Gottingen in 1831, having completed his studies in Halle and Gottingen. His attempts to create an absolute electrical unit system resulted in an advancement in electrical research.

Correct Answer: Arybhatta 

Solution : Correct Answer is Aryabhatta 

The concept of zero was transmitted from India and Babylon to Greece, Persia, and the Arab world over the course of hundreds of years. Zero was first used in calculations by Aryabhatta in the fifth century and Brahmagupta sometime around 628 BC. The concept of zero was thus invented by Aryabhatta. 

Correct Answer: idols

Solution : The correct choice is the first option.

Idols: Objects of adoration or worship, often referring to religious or celebrity figures.

The meanings of the other options are as follows:

• Idoles: Not a recognised English word.
• Ideals: Standards or principles that represent a perfect state, often used as a model to aspire to.
• Idles: Not engaged in work, activity, or purpose; inactive or doing nothing.

Therefore, the correct sentence is: They saw the beautiful idols of the gods in the temples.

Correct Answer: Article 21

Solution : The correct answer is Article 21.

The KA Najeeb vs. Union of India case is primarily concerned with a breach of Article 21 of the Indian Constitution. Article 21 of the Indian Constitution provides the right to life and personal liberty, and the courts have construed it to cover a variety of human rights and individual liberties.

Correct Answer: 2

Solution : Given: $(x-2)(x-p) = x^2-ax+6$
⇒ $x^2-px-2x+2p=x^2-ax+6$
⇒ $x^2-(p+2)x+2p=x^2-ax+6$
By comparing both sides of the equation,
$p+2=a$
⇒ $a-p=2$
Hence, the correct answer is 2.