Correct Answer: $\pm\frac{2}{\sqrt{5}}$

Solution : Given: $x-\frac{1}{x}=1$
$⇒x^{2}-1=x$
$⇒x^{2}+1=x+2$
$\left (\frac{1}{x-1}-\frac{1}{x+1}+\frac{1}{x^{2}+1}-\frac{1}{x^{2}-1} \right)$
$=(\frac{2}{x^{2}-1}+\frac{1}{x^{2}+1}-\frac{1}{x^{2}-1})$
$=(\frac{1}{x^{2}-1}+\frac{1}{x^{2}+1})$
$=(\frac{2x^{2}}{(x^{2}-1)(x^{2}+1)})$
Using $x^{2}-1=x$ and $x^{2}+1=x+2$, we get,
$=(\frac{2x^{2}}{(x)(x+2)})$
$=\frac{2x}{x+2}$
Solving $x^{2}-x-1=0$, we get $x=\frac{1\pm\sqrt{5}}{2}$
So, $x+2=\frac{5\pm\sqrt{5}}{2}$
When $x=\frac{1+\sqrt{5}}{2}$, $\frac{2x}{x+2}=\frac{2}{\sqrt{5}}$
When $x=\frac{1-\sqrt{5}}{2}$, $\frac{2x}{x+2}=-\frac{2}{\sqrt{5}}$
Hence, the correct answer is $\pm\frac{2}{\sqrt{5}}$.

Correct Answer: a programming language

Solution :  Correct Answer is - a programming language.

Danish computer scientist Bjarne Stroustrup developed the general-purpose programming language C++ for the development of software. This language is object-oriented. In other words, it places more emphasis on using object data fields with distinctive attributes than

Correct Answer: 875

Solution : Given:

25 : 625 :: 35 : ?

Like, 25 × 25 = 625; 25 is multiplied by 25 to get the second number.

Similarly, 35 × 25 = 875; 35 is multiplied by 25 to get the second number.

Hence, the first option is

Correct Answer:

Solution : As per the mirror image properties, closer things appear closer to the mirror in the reflection.
So, according to the above property and the information provided, the mirror is placed on the right side of the figure (on line AB). So, the left side of the

Correct Answer:

Solution : According to the given figure series, in every alternate box, the geometrical figures/ numbers/ letters shift their position following the below patterns –
1. From Box 1 to Box 2 – Top left ⇔ Bottom left; Bottom right ⇔ Top right; Centre-left→Centre of the box→Centre-right→Centre-left; Top

Correct Answer: 1

Solution : According to the dice rule, if two or three positions of the same dice are given with two common faces but in different orientations, then out of those two common faces the faces that are not common are opposite to each other.
In Figures 1

Correct Answer: $60^{\circ}$

Solution :
Since $\triangle PQR$ is an equilateral triangle,
$\angle PQR = \angle QRP = \angle RPQ = 60°$
Angles subtended by a chord on the same side of a circle are equal.
Here, $\angle QRP$ and $\angle PSQ$ are angles subtended on the circle by chord

Correct Answer: Father said that on the news that night, they had mentioned a possibility of a power strike.”

Solution : The first option is the correct choice.

The steps of conversion are as follows:

• There would be no change in the reporting verb "said".
• The simple past tense "mentioned"

Correct Answer: Mint

Solution : The correct choice is the third option.

A mint is a place where coins, medals, or tokens are manufactured.

The meanings of the other options are as follows:

• Hutch: It refers to a cage or coop for small animals, such as rabbits.

• Hangar: It refers

Correct Answer: all the mouse

Solution : The correct choice is the first option.

Explanation: The error in the sentence lies in the incorrect use of the word "mouse". When referring to more than one mouse, the plural form should be used, which is "mice". The