Correct Answer: $2,-\frac{1}{2}$

Solution : Given: $2(x^{2}+\frac{1}{x^{2}})-(x-\frac{1}{x})-7=0$
We know that, $x^{2}+\frac{1}{x^{2}} = (x-\frac{1}{x})^2+2$
⇒ $2[(x-\frac{1}{x})^2+2]-(x-\frac{1}{x})-7=0$
Put $x-\frac{1}{x}=t$
⇒ $2t^2+4-t-7=0$
⇒ $2t^2-t-3=0$
⇒ $2t^2-3t+2t-3=0$
⇒ $t(2t-3)+1(2t-3)=0$
⇒ $(2t-3)(t+1)=0$
$\therefore t=\frac{3}{2}$ or, $ -1$
Now if,
$x-\frac{1}{x}=\frac{3}{2}$
⇒ $2x^2-2=3x$
⇒ $2x^2-3x-2=0$
⇒ $2x^2-4x+x-2=0$
⇒ $2x(x-2)+1(x-2)=0$
⇒ $(x-2)(2x+1)=0$
$\therefore x = 2$ or,

Correct Answer: (1)

Solution : The sentence can be improved using the first option.

The verb help is typically followed by a gerund (-ing form of a verb) when it is used to express that someone can't avoid or refrain from doing something. In this context, the action is laughing,

Correct Answer: 206250

Solution : The diameter of the wheel of a cycle = 7 cm
Time taken to reach the destination = 75 minutes = 1.25 hr
Seed of cycle = 36.3 km/hr
Total distance = Time × Speed = 1.25 × 36.3 km
Number of revolutions = $\frac{\text{Total

Correct Answer: 42

Solution : Let's check the options –
First option: 24; 24 ÷ 4 = 6; 24 is divisible by 4.
Second option: 28; 28 ÷ 4 = 7; 28 is divisible by 4.
Third option: 42; 42 ÷ 4 = 10.5; 42 is not divisible by 4.

Correct Answer: $2(a^2+b^2)$

Solution : Given, $(a+b)^2+(a-b)^2$
= $a^2+b^2+2ab+a^2+b^2-2ab$
= $2(a^2+b^2)$
Hence, the correct answer is $2(a^2+b^2)$.

Correct Answer: Adani Wilmar

Solution : The correct answer is Adani Wilmar.

Adani Wilmar Limited is an Indian multinational food and beverage conglomerate based in Ahmedabad, Gujarat. The company was founded in 1999 as a joint venture between Adani Enterprises and Wilmar International. 

Adani Wilmar launched their IPO in

Correct Answer: batter

Solution : The first option is the correct choice.

Batter refers to the mixture of ingredients used for making the cake.

The meanings of the other options are as follows:

• Concoction refers to a mixture of various ingredients or elements, but it might not be the best

Correct Answer: HGHI

Solution : Given:
G_ IJG_HIJGGH_ IJGGHH _IJ

To fill the series we have to divide the series – G_ IJ/G_HIJ/GGH _ IJ/GGHH _IJ
Let's check each option –
First option: HIJG; GHIJ/GIHIJ/GGHJIJ/GGHHGIJ (No repeated pattern has been found.)
Second

Correct Answer: Unlikely

Solution : The correct choice is the first option.

The word credible refers to being capable of being believed or trusted, indicating reliability and trustworthiness. The opposite of credible would be something that is not likely to be believed or trusted.

The meanings of the other options

Correct Answer: Himachal Pradesh

Solution : The correct option is Himachal Pradesh.

Himachal Pradesh is not considered a major producer of fertilisers in India. Some of the major producers of fertilisers in India include states like Gujarat, Uttar Pradesh and Maharashtra. These states have significant manufacturing facilities and contribute