Correct Answer: 2

Solution : Given: $(x^2-2x+1)=0$
⇒ $x^2+1=2x$
Divide the given equation by $x$ on both sides, we get,
⇒ $x+\frac{1}{x}=2$
On squaring the above equation on both sides, we get,
⇒ $x^2+\frac{1}{x^2}+2=4$
⇒ $x^2+\frac{1}{x^2}=2$
On squaring the above equation on both sides, we get,
⇒ $(x^2+\frac{1}{x^2})^2=2^2$
⇒ $(x^4+\frac{1}{x^4})+2=4$

Correct Answer: 18

Solution : Given: $\frac{8+2 \sqrt{3}}{3 \sqrt{3}+5}=a \sqrt{3}–b$
Rationalize the given fraction,
$\frac{(8+2 \sqrt{3})\times(3\sqrt3–5)}{(3 \sqrt{3}+5)\times (3\sqrt3–5)}=\frac{24\sqrt3–40+18–10\sqrt3}{27–25}$
⇒ $\frac{14\sqrt3–22}{2}=7\sqrt3–11$
Now, compare the value with the given expression $a \sqrt{3}–b$, we get,
$7\sqrt3–11=a \sqrt{3}–b$
⇒ $a=7,b=11$
The value of $a + b=7+11=18$.
Hence, the correct answer is 18.

Correct Answer:

Solution : Both bonuses and dividends are a part of profits. But, bonuses and dividends are not related to each other in any way.

So, All bonuses are profits; All dividends are profits; No bonuses are dividends.

Based on the above statements, the Venn diagram will be

Hence,

Correct Answer: MCP

Solution : Let's check the options –

First option: OQS→O + 2 = Q; Q + 2 = S
Second option: JLN→J + 2 = L; L + 2 = N
Third option: HJL→H + 2 = J; J + 2 = L
Fourth option: MCP→M –

Correct Answer: The troops were ordered to march ahead by the commanding officer.

Solution : The correct option is the second option.

Explanation: 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

Correct Answer: Saroj Khan

Solution : The correct option is Saroj Khan.

Saroj Khan won the National Award for Best Choreography three times in the mentioned years and indeed worked on Bollywood films, including "Devdas," directed by Sanjay Leela Bhansali. She is known for her exceptional work in the

Correct Answer: $10$

Solution : In a trapezium, if one diagonal divides the other in the ratio $2:9$, then the parallel sides are divided in the same ratio. 
Given that the length of the larger parallel side is $45\;\mathrm{cm}$.
Let the length of the smaller parallel side be $x$.
$⇒\frac{x}{45}

Correct Answer: Raghav asked Meera if she was upset with him.

Solution : The second option is the correct choice.

Narration conversion:

• "Said" is changed to "asked".
• "Are" is changed to "was".
• "You" becomes "she".
• The question changes to a statement.
• The two clauses are connected by "if".

Person's Rule:

Correct Answer: 11, 88, 99, 22

Solution : Given:
LION

Number representations of each letter:
L → 40, 11, 32, 03, 24
I → 65, 66, 97, 88, 79
O → 85, 76, 67, 58, 99
N → 30, 01, 22, 43, 14

First option: 03, 55, 76, 33
I

Correct Answer: 2CaSO₄.H₂O

Solution : The correct option is 2CaSO₄. 2H₂O.

The compound 2CaSO₄·2H₂O is known as Plaster of Paris. Plaster of Paris is a common name for calcium sulphate hemihydrate, and its chemical formula is exactly