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Correct Answer: $\frac{1}{b^8-1}$

Solution : $\frac{1}{8}[\frac{1}{b-1}-\frac{1}{b+1}-\frac{2}{b^2+1}-\frac{4}{b^4+1}]$
= $\frac{1}{8}[\frac{(b+1)-(b-1)}{b^2-1}-\frac{2}{b^2+1}-\frac{4}{b^4+1}]$
= $\frac{1}{8}[\frac{2}{b^2-1}-\frac{2}{b^2+1}-\frac{4}{b^4+1}]$
= $\frac{1}{8}[\frac{2(b^2+1)-2(b^2-1)}{b^4-1}-\frac{4}{b^4+1}]$
= $\frac{1}{8}[\frac{4}{b^4-1}-\frac{4}{b^4+1}]$
= $\frac{1}{8}[\frac{4(b^4+1)-4(b^4-1)}{b^8-1}]$
= $\frac{1}{8}[\frac{8}{b^8-1}]$
= $\frac{1}{b^8-1}$
Hence, the correct answer is $\frac{1}{b^8-1}$.

Correct Answer: 36 : 13

Solution :
DE : BC = 6 : 7
Theorem Used:
The ratios of the areas of two similar triangles are equal to the square of the ratio of their corresponding sides
Calculation:
Considering $\triangle$ABC and $\triangle$ADE
$\angle$A = $\angle$A (Common)
As DE || BC

Correct Answer: The Damodar

Solution : The correct answer is The Damodar.

The devastating floods that the River Damodar causes in the West Bengal plains have earned it the nickname "Bengal's sorrow." Because of the southwest monsoon, the Damodar River catchment area receives seasonal rains every year. Depending on the

Correct Answer: accidental

Solution : The second option is the correct choice.

Intentional means something done with purpose or intent, while accidental refers to something happening by chance or without intent.

The meanings of other options are as follows:

• Voluntary means something that is done willingly or by choice
• Designed 

Correct Answer: $\frac{15\sqrt 3}{2}\text{ cm}$

Solution : Given: The side of the triangle is 15 cm.
Let the altitude be $x$ cm.
The length of the altitude of an equilateral triangle = $\frac{\sqrt3}{2}$ × side of the triangle.
⇒ $x = \frac{\sqrt3}{2}\times15$
⇒ $x = \frac{15\sqrt3}{2}$
Hence, the correct answer

Correct Answer: (3)

Solution : The error lies in the third part of the sentence.

When a sentence uses the indefinite pronoun one, it should continue using the same pronoun or its supplementary forms i.e., one's in this case, as it is not correct to use other pronouns

Correct Answer: 279

Solution : Given: The first term is 7 and the last term is 55.
Using the formula, S₉ = $\frac{n}{2}(a+l)$
Where $a$ is the first term, $l$ is the last term of the A.P., and n is the number of terms.
By putting the value of

Correct Answer: Bopsi

Solution : Given:
1. Akram is further up the ladder than Bopsi.

2. Bopsi is in between Akram and Priya.

3. Tulsi is still further up than Akram.

So, the second person

Correct Answer: Twice

Solution : The correct answer is Twice.

In 1991, the Indian rupee was devalued in two steps. The Indian government devalued the rupee in July and again in July/August of 1991. These devaluations were aimed at boosting exports and addressing the external payment situation. The move

Correct Answer: 91486

Solution : Given:

Now, code the symbols with their respective numbers given in the question –

Thus by decoding the symbols, we will get the respective number 91486. Hence the first option is correct.