It's a Question of your Career!

Correct Answer: 15 : 5 : 3

Solution : We know,
Speed ∝ $\frac{1}{time}$
So, the ratio of time taken
= $1:\frac{1}{3}$ : $\frac{1}{5}$
= 15 : 5 : 3
Hence, the correct answer is 15 : 5 : 3.

Correct Answer: $441\sqrt{3}-693$

Solution :
The side length of the equilateral triangle $=2 \times 21 = 42\;\mathrm{cm}$
The area of the equilateral triangle $=\frac{\sqrt{3}}{4} \times (42)^2=441\sqrt3\;\mathrm{cm^2}$
Each angle of an equilateral triangle $=60^{\circ}$
The area of each sector $=\frac{60^{\circ}}{360^{\circ}} \times \pi \times (21)^2=231\;\mathrm{cm^2}$
The area of the portion enclosed by

Correct Answer: Manipuri

Solution : The correct answer is Manipuri.

The Manipuri dance form originated in the festival of Lai Haraoba. Guru Bipin Singh is related to Manipuri dance, which emphasises devotion. Guru Bipin Singh was a Manipuri dancer and was an awardee of the Sangeet Natak Akademi in 1966.

Correct Answer: 13,440

Solution : We have,
$A = 12000, r = 12\%, n = 1 $ (compounded annually) and $t = 3$ years.
$A = P \left(1+\frac{r}{100}\right)^{t}$
Substituting the given values into the formula,
$⇒12000 = P (1+\frac{12}{100})^{1×3}$
$⇒12000 = P (1.12)^{3}$---(i)
For $t = 4$ year 
$⇒ A

Correct Answer: Ahmad Shah I

Solution : The correct answer is Ahmad Shah I

The Gujarat Sultanate was ruled by Ahmad Shah I, also known as Ahmad Khan, a member of the Muzaffarid dynasty, from 1411 until he died in 1442. Because of Bidar's better climate and more advantageous location,

Correct Answer: Gautamiputra Satkami

Solution : The correct option is Gautamiputra Satkami.

Gautamiputra Satakarni, who ruled from 106 to 130 CE, was the greatest Satavahana king. He was a famous conqueror who greatly enlarged the Satavahana kingdom. He also supported the arts and sciences, and his reign is regarded as

Correct Answer: he spent many an hour playing the harp across the

Solution : The correct choice will be the first option.

The original sentence contains a grammatical error. The phrase many an hours should be corrected to many an hour. The use of many an. suggests a poetic or

Correct Answer: $0$

Solution : Given:
$\frac{\cos^{2}25^\circ-\sin^{2}65^\circ}{\cos^{2}25^\circ+\sin^{2}65^\circ}$
= $\frac{\cos^{2}25^\circ-\sin^{2}(90^\circ-25^\circ)}{\cos^{2}25^\circ+\sin^{2}(90^\circ-25^\circ)}$
= $\frac{\cos^{2}25°-\cos^{2}25°}{\cos^{2}25°+\cos^{2}25°}$
= $\frac{0}{2\cos^{2}25^\circ}$
= $0$
Hence, the correct answer is $0$.

Correct Answer: Neither I nor II

Solution : Statement I:
$\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\ldots \ldots \frac{1}{110}<\frac{5}{6}$
Expand LHS
$⇒\frac{1}{2}+\frac{1}{2\times{3}}+\frac{1}{3\times{4}}+\ldots \ldots \frac{1}{10\times{11}}<\frac{5}{6}$
$⇒\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\ldots \ldots \frac{1}{10}-\frac{1}{11}<\frac{5}{6}$
$⇒1-\frac{1}{11}<\frac{5}{6}$
$⇒\frac{10}{11}<\frac{5}{6}$
which is wrong,
So, statement I is incorrect.
Statement II:
$\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+\ldots \ldots \frac{1}{143}>\frac{7}{13}$
$⇒\frac{1}{3}+\frac{1}{3\times5}+\frac{1}{5\times7}+\ldots \ldots \frac{1}{11\times13}>\frac{7}{13}$
$⇒\frac{1}{3}+\frac{2}{2}[\frac{1}{3\times5}+\frac{1}{5\times7}+\ldots \ldots \frac{1}{11\times13}]>\frac{7}{13}$
$⇒\frac{1}{3}+\frac{1}{2}[\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\ldots \ldots \frac{1}{11}-\frac{1}{13}]>\frac{7}{13}$
$⇒\frac{1}{3}+\frac{1}{2}[\frac{1}{3}-\frac{1}{13}]>\frac{7}{13}$
$⇒\frac{1}{3}+\frac{5}{39}>\frac{7}{13}$
$⇒\frac{6}{13}>\frac{7}{13}$
which is

Correct Answer: 1959 A.D.

Solution : The correct answer is 1959 A.D.

The Panchayati Raj System, a three-tier structure, was introduced in the Nagaur district of Rajasthan on October 2, 1959. Later, in 1992, the system was added to the Constitution through the 73rd Constitutional Amendment Act.