Correct Answer: (3)

Solution : The correct choice is the third option.

In this context, when referring to job reservations, it is more appropriate to use "in" to indicate that reservations are related to jobs. "At" is less suitable in this context, as it defines specification.

So, the correct

Correct Answer: 1924

Solution : Given:
$x=-5$ and $y=-7$
$\left(27 x^3-58 x^2 y+31 x y^2-8 y^3\right)$
$= (3x)^3-3×(3x)^2×2y+3×3x×(2y)^2-(2y)^3-4x^2y-5xy^2$
$= (3x-2y)^3-xy(4x+5y)$
$= (3×(-5)-2×(-7))^3-(-5×(-7))(4×(-5)+5×(-7))$
$=-1-35(-20-35)$
$= -1-35(-55)$
$= -1+1925$
$= 1924$
Hence, the correct answer is 1924.

Correct Answer: 3

Solution : The given number is 756896.
Sum of digits in odd places = 7 + 6 + 9 = 22
Sum of digits in even places = 5 + 8 + 6 = 19
Difference in sums = 22 – 19 = 3
If we add

Correct Answer: Pleasant

Solution : The correct choice is the third option.

Explanation: Repulsive is an adjective used to describe something that causes a strong feeling of disgust or aversion. Its antonym, pleasant, denotes the opposite meaning by representing something that is agreeable, enjoyable, or pleasing. 

The meanings of

Correct Answer: 1

Solution : The sentence is already correct and does not need any improvement because the original phrase "acquired experience through age" effectively conveys the idea that the old man has gained knowledge and wisdom over time, which is the intended meaning. Therefore, the correct answer is:

No

Correct Answer: $45(\sqrt{3}+2)$

Solution :

Let OP = $h$ m
In $\triangle$OPQ,
$\tan60°=\frac{h}{OQ}$
⇒ $OQ=\frac{h}{\sqrt3}$ ------------------(equation 1)
In $\triangle$OPR,
$\tan30^\circ=\frac{h}{OR}$
⇒ $OR=h\sqrt3$ ----------------------(equation 2)
According to the question,
$h\sqrt3+\frac{h}{\sqrt3}=180$
⇒ $3h+h=180\sqrt3$
⇒ $h=\frac{180\sqrt3}{4}$
⇒ $h=45\sqrt3$ m
Now, in $\triangle$OPQ,
$\sin60^\circ=\frac{h}{PQ}$
⇒ $PQ=45\sqrt3×\frac{2}{\sqrt3}$
⇒ PQ = 90 m
So, the total

Correct Answer: (2)

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

The use of the preposition "than" after "superior" is incorrect. To express comparison, we use "superior to" as superior is followed by the preposition to and not than.

Therefore, the correct sentence would be:

Correct Answer: – 6726

Solution : Given:
$x+\frac{1}{x}=-6$ ---------------------------------------(1)
Squaring both sides of equation (1)
So, $(x+\frac{1}{x})^2=(-6)^2$
⇒ $x^2+\frac{1}{x^2}=36-2=34$
Cubing both sides of equation (1)
$(x+\frac{1}{x})^3=(-6)^3$
⇒ $x^3+\frac{1}{x^3}+3×x×\frac{1}{x}(x+\frac{1}{x})=-216$
⇒ $x^3+\frac{1}{x^3}+3(-6)=-216$
⇒ $x^3+\frac{1}{x^3}=-216+18=-198$
So, $x^5+\frac{1}{x^5}$
= $(x^2+\frac{1}{x^2})(x^3+\frac{1}{x^3})-(x+\frac{1}{x})$
= $34×(-198)-(-6)$
= $-6732+6$
= $-6726$
Hence, the correct answer is – 6726.

Correct Answer: 48.23%

Solution : As per the given graph:
The total populations of both males and females in the year 1991 = 44 + 41 = 85 crore
The population of females in the year 1991 = 41 crore
The percentage of female population in India during the year

Correct Answer: 3

Solution : The sentence is already correct and does not need any improvement. The phrase "could not help but laugh" is an idiomatic expression that means she couldn't resist laughing, Therefore, the correct answer is:

No Improvement