Correct Answer: 64 – 4032

Solution : Let's check each option –
First option: (64 – 4032); 64² = 4096 ≠ 4032
Second option: (38 – 1444); 38² = 1444
Third option: (42 – 1764); 42² = 1764
Fourth option: (52 – 2704); 52² = 2704

So, only the first option is different from the others. Hence, the first option is correct.

Correct Answer: 33

Solution : Given:
183, 173, 153, 123, 83, ?

Subtract multiples of 10 to the previous number to obtain the next number.
183 – 10 = 173, 173 – 20 = 153, 153 – 30 = 123, 123 – 40 = 83, 83 – 50 = 33

So, the missing number is 33. Hence, the second option is correct.

Correct Answer: $\frac{13}{12},\frac{13}{5}$

Solution : Given, $\tan A=\frac{12}{5}$
$\tan A = \frac{\text{perpendicular}}{\text{base}}$
Using pythagoras theorem,
$\small\text{Hypotenuse}^2=\text{Base}^2+\text{Perpendicular}^2$
⇒ $h^2=5^2+12^2$
⇒ $h^2=25+144$
⇒ $h^2=169$
⇒ $h=13$
$\therefore$ $\operatorname{cosec A}=\frac{\text{Hypotenuse}}{\text{Perpendicular}}=\frac{13}{12}$
And, $\sec A=\frac{\text{Hypotenuse}}{\text{Base}}=\frac{13}{5}$
Hence, the correct answer is $\frac{13}{12},\frac{13}{5}$.

Correct Answer: $\sqrt2-\sqrt3$

Solution : Given: $\operatorname{cosec}\theta=\sqrt3$
$⇒\frac{1}{\sin\theta}=\sqrt3$
$⇒\sin\theta=\frac{1}{\sqrt3}$
We know that,
$\cos\theta = \sqrt{1-\sin^2\theta}=\sqrt{1-(\frac{1}{\sqrt3})^2}=\sqrt{1-\frac{1}{3}}=\sqrt\frac{2}{3}$
So, $\cot\theta-\operatorname{cosec}\theta$
$=\frac{\cos\theta}{\sin\theta}-\operatorname{cosec}\theta$
$=\frac{\sqrt\frac{2}{3}}{\frac{1}{\sqrt3}}-\sqrt3$
$=\sqrt\frac{2}{3}×\sqrt3-\sqrt3$
$=\sqrt2-\sqrt3$
Hence, the correct answer is $\sqrt2-\sqrt3$.

Correct Answer: ZDW

Solution : Given:
HPA, FMZ, DJY, BGX, ?

Here, subtract 2, 3, and 1 in the first, second, and third letters respectively to obtain the letters of the next term.
HPA→H – 2 = F; P – 3 = M; A – 1 = Z→FMZ
FMZ→F – 2 = D; M – 3 = J; Z – 1 = Y→DJY
DJY→D – 2 = B; J – 3 = G; Y – 1 = X→BGX
BGX→B – 2 = Z; G – 3 = D; X – 1 = W→ZDW

ZDW is the missing term of the series. Hence, the first option is correct.

Correct Answer: MONR

Solution : Let's check the options –
First option: VNHK; None of the letters V, N, H, and K are vowels.
Second option: MONR; The letter O is a vowel.
Third option: NQMJ; None of the letters N, Q, M, and J are vowels.
Fourth option: NBJM; None of the letters N, B, J, and M are vowels.

So, the second option is different from the other three options as here vowel is present. Hence, the second option is correct.

Correct Answer: euphemism

Solution : The correct choice is the third option.

The most appropriate option to substitute the underlined segment in the sentence is euphemism.
Euphemism refers to the use of a word or phrase in place of one that might be considered too harsh, blunt, or unpleasant.

The meanings of the other options are as follows:

• Oxymoron: An oxymoron is a figure of speech that combines contradictory terms. For example, "jumbo shrimp" or "deafening silence."
• Metaphor: A metaphor is a figure of speech that implies a comparison between two unrelated things, suggesting a similarity between them without using "like" or "as."
• Hyperbole: Hyperbole refers to exaggerated statements or claims not meant to be taken literally but used for emphasis or effect.

Therefore, the correct answer is euphemism.

Correct Answer: into Indian equities have pushed

Solution : The correct answer is the fourth option.

According to the subject-verb agreement rule, the verb must agree with the subject in number. If the subject is singular, the verb should be singular, and if the subject is plural, the verb should be plural. In the given sentence, the subject of the verb is inflow, which is singular. So, has should be used instead of have to make it grammatically correct.

Therefore, the correct sentence is, "The inflow of foreign portfolio funds into Indian equities has pushed up price-earning multiples and valuation."

Correct Answer: DNA and proteins

Solution : The correct answer is DNA and proteins.

Chromosomes are made up of DNA and protein. DNA is the genetic material that holds the instructions for the construction and maintenance of an organism. Proteins are molecules that perform several critical roles in the body, including as tissue construction and repair, nutrition delivery, and catalysing chemical processes.

Correct Answer: Tuesday

Solution : Given:
19 June 2001 is a Tuesday.

Let's calculate the total number of days from the 19th of June 2001 to the 14th of August 2007 –

Number of days from 19 June 2001 to 31 December 2001 = 11 + 31 + 31 + 30 + 31 + 30 + 31 = 195
Number of days from 1 January 2002 to 31 December 2006 = (5 × 365) + 1 = 1826 (1 leap year)
Number of days from 1 January 2007 to 14 August 2007 = 31 + 28 + 31 + 30 + 31 + 30 + 31 +14 = 226
So, the total number of days from 19 June 2001 to 14 August 2007 = 195 + 1826 + 226 = 2247
Now, on dividing 2247 by 7, we get 321 as the quotient and 0 as the remainder.

Therefore, add 0 to Tuesday, Tuesday + 0 = Tuesday

So, the 14th of August 2007 will be Tuesday. Hence, the third option is correct.