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: prejudices

Solution : The correct choice to fill in the blanks is the fourth option.

Prejudice means opinions that are not experienced by oneself, are preconceived, and go correctly in the sentence, as the sentence implies that the brain has some opinions that may not be experienced in

Correct Answer: Shimsha River

Solution : The correct option is Shimsha River.

One of the Kaveri River's tributaries is the Shimsha. The river originates in Tumkur's Devarayanadurga hills. At Chamarajanagar, it enters the Cauvery after flowing for around 221 km from its source. After originating in the Tumkur district,

Correct Answer: has been steadily

Solution : The correct choice is the first option.

Explanation:

The original sentence has a grammatical error in the adverb, steady. The adverb steady should be modified to its adverbial form steadily to correctly describe the manner in which the action is taking

Correct Answer: Esteem

Solution : The first option is correct.

Ignominy: It denotes public shame and embarrassment.

Esteem: It denotes a good opinion of somebody.

The meanings of the other options are as follows:

• Disrepute: It denotes the situation when people no longer respect somebody or something.
• Stigma: It denotes

Correct Answer: cricket

Solution : The correct option is cricket.

Gurucharan Singh received the Padma Shri from the Government of India in 2023 for his contributions to the sport of cricket. He is a renowned cricket coach who has nurtured the careers of many international cricketers, including Kirti Azad,

Correct Answer: weathering

Solution : The correct option is weathering.

The breaking down of rock in situ is known as "weathering". Weathering is a natural process that occurs over time as they are exposed to various environmental factors. There are two main types of weathering: Mechanical weathering, and chemical

Correct Answer: Only III

Solution : Fractions with the same numerator are compared based on their denominators. The fraction with the smaller denominator is greater.
Fractions with the same denominator are compared based on their numerators. The fraction with the larger numerator is greater.
I. $\frac{5}{11} < \frac{5}{6}$ ($\frac{5}{11}$ is

Correct Answer: Jyotiba Phule

Solution : The correct answer is Jyotiba Phule.

Jyotiba Phule was a Maharashtrian social reformer. Jyotiba Phule founded Satyashodhak Sabha in 1873 in Pune, Maharashtra. It was a social reform society which helped to promote education, social rights, and Justice in deprived sections of the society.

Correct Answer: Husband's mother

Solution : Given:
A – F means A is the husband of F.
R # A means R is the mother of A.
F # H means F is the mother of H.

As per the given instructions, the family tree will be –

Here, the