Correct Answer: Kelvin

Solution : Given:
Electric current : Ampere :: Thermodynamic Temperature : ?

Like, the unit used to measure electric current is an ampere.
Similarly, the unit used to measure thermodynamic temperature is kelvin.

Hence, the second option is correct.

Correct Answer: Jawaharlal Nehru

Solution : The correct answer is Jawaharlal Nehru.

The Lahore Session of the Indian National Congress was held in 1929 and passed the historic Purna Swaraj, which means the total independence resolution under the presidency of Jawaharlal Nehru. The Indian National Congress selected January 26, 1930, as the day to celebrate as ‘’Independence Day’, and on the same day, the Constitution of India was enacted in 1950.

Correct Answer: Rs. 15,000

Solution : Let us assume Ram Babu's income is $x$.
According to the question,
$x \times\frac{97}{100}\times \frac{88}{100} = 12804$
⇒ $x$ = 15,000
Hence, the correct answer is Rs. 15,000.

Correct Answer: 423121

Solution : Given:
READER is written as 123421 and DIRTY is written as 49178.

On combining the letters of both the given words, the codes for each letter are –
Like, READER is written as 123421; R→1; E→2; A→3; D→4; E→2; R→1
And, DIRTY is written as 49178; D→4; I→9; R→1; T→7; Y→8
Similarly, DEARER; D→4; E→2; A→3; R→1; E→2; R→1

So, DEARER is coded as 423121 in the code language. Hence, the third option is correct.

Correct Answer: iv, v, ii, i, iii

Solution : Given:
i. Irrelevant ii. Invincible iii. Irresistible iv. Invariable v. Investigate

Step 1: Compare the first letter of each word. Since all the words start with the same letter I, we move on to the next letter.
Step 2: Let's move to the second letter of each word. The second letter of each word is r, n, r, n, n. Based on the alphabetical order of these letters, we can arrange them: Invincible, Invariable, Investigate Irrelevant, Irresistible.
Step 3: Since the third letter of (Invincible, Invariable, Investigate) is the same, move on to the next letter. Compare the fourth letter of  (Invincible, Invariable, Investigate). Invariable will come before Investigate and then Invincible in the sequence as a comes before e, and e comes before i in the alphabetical system.
Step 4: Compare the fifth letter of (Irrelevant, Irresistible). Irrelevant will come before Irresistible in the sequence as i comes before s in the alphabetical system.

So, the sequence is Invariable, Investigate, Invincible, Irrelevant, Irresistible, or (iv), (v), (ii), (i), (iii). Hence, the fourth option is correct.

Correct Answer: CI

Solution : Given:
AF : BE :: ? : DH

Subtract and add 1 alternatively to the letters of the second letter pair to get the first term.
Like, B – 1 = A; E + 1 = F
Similarly, D – 1 = C; H + 1 = I

So, DH is related to CI. Hence, the fourth option is correct.

Correct Answer: 3ab(a + b)

Solution : (a + b)³ – a³ – b³
= a³ + b³ + 3ab(a + b) – a³ – b³
= 3ab(a + b)
Hence, the correct answer is 3ab(a + b).

Correct Answer: $\triangle \mathrm{PQR} \sim \triangle \mathrm{FED}$

Solution :
$\because$ $\angle P=\angle F=52^0$
$\angle Q=\angle E=74^0$
And $\angle R=\angle D=54^0$
By AAA criteria, triangles are similar.
So, $\triangle \mathrm{PQR} \sim \triangle \mathrm{FED}$.
Hence, the correct answer is $\triangle \mathrm{PQR} \sim \triangle \mathrm{FED}$.

Correct Answer: Warren Hastings

Solution : The correct option is Warren Hastings.

Warren Hastings, the first Governor-General of British India, faced accusations of orchestrating the judicial murder of Raja Nand Kumar during the late 18th century. The trial of Raja Nand Kumar was marked by allegations of political motives and irregularities, contributing to the historical controversy surrounding Hastings' governance and the East India Company's influence in India.

Correct Answer: $1 \frac{64}{361}$

Solution : Given: $\tan \theta=\frac{8}{19}$
We know, $\sec ^2 \theta=1+\tan^2 \theta$
$⇒\sec ^2 \theta=1+(\frac{8}{19})^2$
$⇒\sec ^2 \theta=1+\frac{64}{361}$
$⇒\sec ^2 \theta=\frac{425}{361}$
$⇒\sec ^2 \theta=1\frac{64}{361}$
Hence, the correct answer is $1\frac{64}{361}$.