Correct Answer: 1

Solution : Given expression,
$x^4+x^{-4}=47$
⇒ $x^4+\frac{1}{x^4}=47$
Adding 2 on both sides,
⇒ $x^4+\frac{1}{x^4}+2=47+2$
⇒ $x^4+\frac{1}{x^4}+2\times x^2\times\frac{1}{x^2}=49$
⇒ $(x^2+\frac{1}{x^2})^2=7^2$ [As $a^2+b^2+2ab=(a+b)^2$]
⇒ $x^2+\frac{1}{x^2}=7$
Again adding 2 on both sides,
⇒ $x^2+\frac{1}{x^2}+2=7+2$
⇒ $x^2+\frac{1}{x^2}+2\times x\times\frac1x=9$
⇒ $(x+\frac1x)^2=3^2$
⇒ $x+\frac1x=3$
⇒ $x+\frac1x-2=3-2$
$\therefore x+\frac1x-2=1$
Hence, the correct answer is 1.

Correct Answer: that

Solution : The fourth option is the correct answer.

That in the sentence indicates that the dog being referred to is identical to the one that was previously seen running on the road.

The prepositions whose, who, and whom are relative pronouns used to refer to people and not animals and are hence incorrect.

Therefore, the complete sentence is: This is the same dog that was running on the road.

Correct Answer: 2 hours

Solution : Amount of work done by A and B in 1 hour = $\frac{2}{9}$
Amount of work done by B and C in 1 hour = $\frac{1}{3}$
Amount of work done by A and C in 1 hour = $\frac{4}{9}$
Adding all the equations, we have:
⇒ 2 × (A + B + C)'s 1 hour work = $\frac{2}{9}+\frac{1}{3}+\frac{4}{9}$
⇒ 2 × (A + B + C)'s 1 hour work = $\frac{2+3+4}{9}=1$
⇒ (A + B + C)'s 1 hour work = $\frac{1}{2}$
(A + B + C) can finish $\frac{1}{2}$ work in 1 hour.
(A + B + C) can finish the total work in 2 hours.
Hence, the correct answer is 2 hours.

Correct Answer: 2

Solution : The given figure can be labeled as shown below –

There are 2 quadrilaterals in the above figure. They are ABFE and ABCE.

Hence, the first option is correct.

Correct Answer:

Solution : On comparing the question figure and all the answer figures, the following figure will combine and make the complete pattern –

Hence, the first option is correct.

Correct Answer: Ghadar Movement

Solution : The correct answer is the Ghadar Movement.

Lala Har Dayal inspired many Indians in the United States, and Canada to oppose the British Empire. He declined a position in Indian civil service to join the National Movement. He founded the Ghadar Party in the United States in 1913 as a revolutionary. He was arrested by US officials for spreading anarchy. He finally migrated to Berlin and taught Indian philosophy in Sweden for eleven years.

Correct Answer: tie down

Solution : The correct choice is the second option.

In military terms, tie down means to restrict the movement or activities of the enemy, to keep them occupied or engaged in a particular area. In the given sentence, if the battalion operating from the mountain was able to tie down three enemy divisions, it suggests that the battalion successfully restricted the enemy divisions' movements or activities.

The meanings of other options are as follows:

• Tie up: This phrase generally means to secure something or someone by fastening it with a knot or a similar device.

• Tie on: This phrase doesn't fit the context of military operations in this sentence.

• Tie with: This phrase is not the appropriate choice for this context.

Therefore, the correct sentence is: "The battalion operating from the mountain was able to tie down three enemy divisions."

Correct Answer: 78

Solution : Given:
BABY is coded as 29, and GENDER is coded as 52. 

Add the positional value of the letters of the word BABY and subtract one from the resultant to obtain the required code –
B→2, A→1, B→2, Y→25
(2 + 1 + 2 + 25) – 1 = 30 – 1 = 29
Thus, BABY is coded as 29.
And GENDER is coded as 52 –
G→7, E→5, N→14, D→4, E→5, R→18
(7 + 5 + 14 + 4 + 5 + 18) – 1 = 53 – 1 = 52
Thus, GENDER is coded as 52.
Similarly, follow the same pattern for CRIPPLE –
C→3, R→18, I→9, P→16, P→16, L→12, E→5
(3 + 18 + 9 + 16 + 16 + 12 + 5) – 1 = 79 – 1 = 78

Thus, CRIPPLE is coded as 78. Hence, the third option is correct.

Correct Answer: $33\frac{1}{3}$

Solution : Let the cost price of 1 article be Rs. $x$.
Selling price of 1 article $=\frac{212}{318}x$
Loss percentage $=\frac{x-\frac{212}{318}x}{x} × 100 = 33\frac{1}{3}$%
Hence, the correct answer is $33\frac{1}{3}$.

Correct Answer: 10

Solution :
The ladder leaning against the wall makes an angle $\theta$ with the horizontal ground such that $\tan \theta = \frac{12}{5}$.
The height of the top of the ladder from the wall is = 24 m
Concept Used:
$\tan \theta = \frac{\text{Height}}{\text{Base}}$
Accordingly,
Let the base = x which means the distance of the foot of the ladder from the wall is x
$\tan \theta = \frac{12}{5}$
$⇒\frac{24}{\text{x}} = \frac{12}{5}$
$⇒\text{x} = 10$ m
$\therefore$ The distance of the foot of the ladder from the wall is 10 m.
Hence, the correct answer is 10 m.