Correct Answer: 0

Solution : Given:
$⇒x+ \frac{1}{x} =2$
By squaring both sides,
$({x}+ \frac{1}{x})^{2} =({2})^{2}$
$⇒{x}^{2}+ \frac{1}{x^{2}}+2×x×\frac{1}{x} =4$
$⇒{x}^{2}+ \frac{1}{x^{2}}=2$
Similarly, we can find,
$({x}+ \frac{1}{x})^{3} =({2})^{3}$
$⇒{x}^{3}+ \frac{1}{x^{3}}+3×x×\frac{1}{x}(x+ \frac{1}{x}) =8$
$⇒{x}^{3}+ \frac{1}{x^{3}}+3×2 =8$
$⇒{x}^{3}+ \frac{1}{x^{3}}=2$
Similarly, we can find the value of,
$⇒{x}^{99}+ \frac{1}{x^{99}}=2$
$\therefore {x}^{99}+ \frac{1}{x^{99}} -2=0$

Correct Answer: Sardar Patel and V.P. Menon.

Solution : The correct answer is Sardar Patel and V P Menon.

Sardar Vallabhbhai Patel was the first Home minister of India and he played a pivotal role in the integration of princely states in the Indian union. As a member of constituent

Correct Answer: 8 : 6 : 3

Solution : Given: Three times the investment of A equals four times the investment of B.
So, 3A = 4B
⇒ A : B = 4 : 3
The capital of B is twice that of C
So, B = 2C
⇒ B

Correct Answer: 50%

Solution : Assume the sum of money is $P$.
It will become 5 times after 8 years = $5P$.
So, Simple interest = $5P - P = 4P$.
Rate = $r$
Simple interest = $\frac{\text{Principal×Rate×Time}}{100}$
⇒ $4P = \frac{P×r×8}{100}$
⇒ $r = 50$%
Hence, the correct answer

Correct Answer: 2, 4, 1, 3, 5

Solution : Given:
1. History 2. Historian 3. Hobnail 4. Historical 5. Hobnob

Step 1: Compare the first letter of each word. Since all the words start with the same letter H, then move on to the next letter.
Step 2: Next,

Correct Answer: Java trench

Solution : The correct answer is Java Trench.

Indian Ocean is the third largest ocean in the world. Deepest point in Indian ocean is Java trench with the depth of 7187 m. It is also known as Sunda double trench and is formed between the Australian

Correct Answer: 1 hour 30 minutes

Solution : Given:
Time = 7.5 hr
Speed = 72 km/hr
Distance = Time × Speed
Distance between two towns = 7.5 × 72 = 540 km
New speed = 72 + $\frac{25}{100}$ × 72 = 90 km/hr
Time taken = $\frac{540}{90}$ = 6

Correct Answer: 35 cm

Solution : Given, $\triangle ABC \sim \triangle DEF$
⇒ $\frac{\small\text{Perimeter of } \triangle ABC}{\small\text{Perimeter of }\triangle DEF}=\frac{AB}{DE}$
⇒ $\frac{\small\text{Perimeter of } \triangle ABC}{25}=\frac{9.1}{6.5}$
⇒ $\small\text{Perimeter of } \triangle ABC = \frac{9.1}{6.5}\times 25$
$\therefore \small\text{Perimeter of }\triangle ABC = 35$
Hence, the correct answer is 35 cm.

Correct Answer: Only conclusion II follows

Solution : The possible Venn diagram according to the given statements is as follows –

Let's analyse the conclusions –
Conclusion (I): All principals are students – From the Venn diagram, it is evident that the circles representing principals and students overlap each other

Correct Answer: General Agreement on Trade and Tariffs

Solution : The correct option is the General Agreement on Trade and Tariffs.

On October 30, 1947, 23 countries signed the General Agreement on Trade and Tariffs (GATT), which came into effect on January 1, 1948, in a provisional capacity. Its