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

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

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 –

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;

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

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

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,

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 +