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Question : Which of the following was the capital of Mahajanapada 'Gandhara' in the 6th century BC?
Option 1: Hastinapur
Option 2: Mathura
Option 3: Taxila
Option 4: Varanasi
Correct Answer: Taxila
Solution : The correct answer is Taxila.
One of the sixteen Mahajanapadas, Taxila, was the capital of Gandhara. Located in modern-day Pakistan, Takshashila, commonly referred to as Taxila, was an old metropolis. In ancient India, it was a well-known educational institution and a significant hub of
Question : The average age of a husband and his wife 3 years ago was 39 years. The average age of the husband, wife, and child is 2 years hence will be 34 years. Find the present age of the child.
Option 1: 12 years
Option 2: 16 years
Option 3: 15 years
Option 4: 18 years
Correct Answer: 12 years
Solution : Let the present ages of the husband, wife, and child be $H$, $W$, and $C$ respectively. From the problem, we know that the average age of the husband and wife 3 years ago was 39 years. $⇒\frac{(H-3) + (W-3)}{2}$ = 39 $⇒H + W
Question : It takes 6 hours to clean a garden. In 2 hours 30 minutes, what part of the garden will be cleaned?
Option 1: $\frac{5}{2}$
Option 2: $\frac{5}{12}$
Option 3: $\frac{5}{8}$
Option 4: $\frac{5}{6}$
Correct Answer: $\frac{5}{12}$
Solution : Given: It takes 6 hours to clean a garden. In 6 hours 1 part of the garden can be cleaned So, in 2 hours 30 minutes i.e. 2.5 hours $\frac{2.5}{6} = \frac{5}{12}$ part can be cleaned. Hence, the correct answer is $\frac{5}{12}$.
Question : Directions: Which of the following interchanges of numbers and mathematical signs would make the given equation correct? 729 × 81 ÷ 20 + 16 − 6 = 50
Option 1: 6 and 20, × and ÷
Option 2: 20 and 50, + and −
Option 3: 16 and 50, × and +
Option 4: 16 and 20, + and ÷
Correct Answer: 6 and 20, × and ÷
Solution : Given: 729 × 81 ÷ 20 + 16 − 6 = 50
Let's check the given options – First option: 6 and 20, × and ÷ On interchanging the signs and numbers, we get – ⇒ 729 ÷ 81 ×
Question : Find the value of the following expression. $12\left(\sin^4 \theta+\cos^4 \theta\right)+18\left(\sin^6 \theta+\cos^6 \theta\right)+78 \sin^2 \theta \cos^2 \theta$
Option 1: 30
Option 2: 40
Option 3: 10
Option 4: 20
Correct Answer: 30
Solution : $12(\sin^4 \theta+\cos^4 \theta)+18(\sin^6 \theta+\cos^6 \theta)+78 \sin^2 \theta \cos^2 \theta$ $=12[(\sin^2 \theta+\cos^2\theta)^2-2\sin^2 \theta \cos^2 \theta]+18[(\sin^2 \theta+\cos^2 \theta)^3-3\sin^2 \theta \cos^2 \theta(\sin^2 \theta+\cos^2\theta)]+78 \sin^2 \theta \cos^2 \theta$ $=12[1-2\sin^2 \theta \cos^2 \theta]+18[1-3\sin^2 \theta \cos^2 \theta]+78 \sin^2 \theta \cos^2 \theta$ $= 12-24\sin^2 \theta \cos^2 \theta+18-54\sin^2 \theta \cos^2 \theta+78 \sin^2 \theta
Question : Directions: In the following question, select the related number from the given alternatives. 11 : 1210 :: 10 : ?
Option 1: 910
Option 2: 980
Option 3: 1000
Option 4: 970
Correct Answer: 1000
Solution : Given: 11 : 1210 :: 10 : ?
112 = 121 and 121 × 10 = 1210 Similarly, 102 = 100 and 100 × 10 = 1000
Hence, the third option is correct.
Question : Select the most appropriate ANTONYM to replace the underlined word in the following sentence. Darwin drew our attention to the gradual accumulation of unfavourable traits and its direct relationship with the survival of those presumed lucky species, which then serve as breeding grounds for more desirable traits.
Option 1: advantageous
Option 2: fulfilling
Option 3: steady
Option 4: negative
Correct Answer: advantageous
Solution : The correct answer is the fourth option.
The reason advantageous is the correct antonym for unfavourable is that it directly contrasts the idea of something being unfavourable or disadvantageous. Advantageous means favourable, beneficial, or providing an advantage.
The meanings of the other words are as
Question : The Revolutionary Socialist Party was established in _______.
Option 1: 1936
Option 2: 1925
Option 3: 1940
Option 4: 1929
Correct Answer: 1940
Solution : The correct answer is 1940.
The Revolutionary Socialist Party was established in 1940. It had its roots in the Bengali liberation movement and the Hindustan Socialist Republican Army. Tridib Chaudhuri was the founder of this party.
Question : Value of $\sec^2\theta-\frac{\sin^2\theta-2\sin^4\theta}{2\cos^4\theta-\cos^2\theta}$ is:
Option 1: 1
Option 2: 2
Option 3: –1
Option 4: 0
Correct Answer: 1
Solution : $\sec^2\theta-\frac{\sin^2\theta-2\sin^4\theta}{2\cos^4\theta-\cos^2\theta}$ $=\sec^2\theta-\frac{\sin^2\theta(1-2\sin^2\theta)}{\cos^2\theta(2\cos^2\theta-1)}$ $=\sec^2\theta-\frac{\sin^2\theta(1-2\sin^2\theta)}{\cos^2\theta[2(1-\sin^2\theta)-1]}$ $=\sec^2\theta-\frac{\sin^2\theta(1-2\sin^2\theta)}{\cos^2\theta(1-2\sin^2\theta)}$ $=\sec^2\theta-\tan^2\theta$ $=1$ Hence, the correct answer is 1.
Question : Divide Rs. 14136 among A, B, and C such that 2 times A's share, 3 times B's share and 5 times C's share are all equal. What is the share of C?
Option 1: Rs. 3680
Option 2: Rs. 456
Option 3: Rs. 2736
Option 4: Rs. 1413
Correct Answer: Rs. 2736
Solution : Given: Divide Rs. 14136 among A, B and C such that 2 times A's share, 3 times B's share and 5 times C's share are all equal. Let A's share, B's share and C's share are $x,y,$ and $z$ respectively. According to the question,
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