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Question : Pipes P and Q can fill a tank in 10 and 12 hours respectively and C can empty it in 6 hours. If all three are opened at 7 AM at what time will one-fourth of the tank be filled?
Option 1: 10 AM
Option 2: 10 PM
Option 3: 11 PM
Option 4: 11 AM
Correct Answer: 10 PM
Solution : Pipe P's hourly work = $\frac{1}{10}$ unit Pipe Q's hourly work = $\frac{1}{12}$ unit Pipe C's hourly work = $-\frac{1}{6}$ unit When all pipes are working together, let the tank be filled in $x$ hours. According to the question, $\frac{1}{10}+\frac{1}{12}-\frac{1}{6}=\frac{1}{x}$ $⇒\frac{1}{x}=\frac{6+5-10}{60}$ $⇒\frac{1}{x}=\frac{1}{60}$ $\therefore x
Question : The product of the two numbers is 38025 and their highest common factor is 65. What is the least common multiple of these numbers?
Option 1: 455
Option 2: 585
Option 3: 715
Option 4: 435
Correct Answer: 585
Solution : Let the two numbers be $a$ and $b$. $a \times b = 38025$ $\text{HCF}(a, b) = 65$ We know, $\text{HCF}(a, b) \times \text{LCM}(a, b) = a \times b$ $\therefore\text{LCM}(a, b) = \frac{a \times b}{\text{HCF}(a, b)} = \frac{38025}{65} = 585$ Hence, the correct answer is 585.
Question : The line chart given below shows the GDP of two countries P and Q in different five years.
L1 = The total GDP of country P in all 5 years. L2 = The total GDP of country Q in all 5 years. What is the value of (L2 – L1)?
Option 1: 180
Option 2: 240
Option 3: 280
Option 4: 160
Correct Answer: 240
Solution : L1 = The total GDP of country P in all 5 years. ⇒ L1 = 225 + 250 + 200 + 125 + 100 = 900 L2 = The total GDP of country Q in all 5 years. ⇒ L2 =
Question : During Quit India Movement, 'Parrallel Government' was constituted at :
Option 1: Varanasi
Option 2: Allahabad
Option 3: Lucknow
Option 4: Ballia
Correct Answer: Ballia
Solution : The Correct Answer is Ballia
The Quit India Movement is renowned for its local parallel government experiences. The 8th of August 1942 saw the beginning of the Quit India movement, which resulted in a number of notable events in the Ballia district of Uttar Pradesh
Question : Directions: A boy and a girl are playing in a park. The only daughter of the maternal grandfather of the girl is the sister of the boy's father. How is the boy related to the girl?
Option 1: Father
Option 2: Grandfather
Option 3: Son
Option 4: Cousin
Correct Answer: Cousin
Solution : As per the given instructions, the family tree will be drawn as shown below –
From the above family tree, the boy is the cousin of that girl. Hence, the fourth option is correct.
Question : How many numbers are there between 1 and 200 which are divisible by 3 but not by 7?
Option 1: 38
Option 2: 45
Option 3: 57
Option 4: 66
Correct Answer: 57
Solution : The numbers from 1 to 200 which are multiple of 3 are 3,6,9,...,198. The total number of multiples of 3 = $\frac{198 - 3 }{3}$ + 1 = 66 LCM of 3 and 7 is 21. The numbers from 1 to 200 which are multiples
Question : Select the correct idiom that can substitute the italicised group of words in the given sentence.
Shelley has been contemplating for a few days but still has not decided to quit the job.
Option 1: biting the dust
Option 2: chewing the cud
Option 3: cooling one’s heels
Option 4: getting into hot waters
Correct Answer: chewing the cud
Solution : The correct choice is the second option.
The idiom chewing the cud means to carefully consider or think about something, often at length. It's used when someone is deep in thought or contemplation, which is what the original sentence conveys.
The meanings
Question : Directions: In the following question, out of the four alternatives, select the alternative that will improve the bracketed part of the sentence. In case no improvement is needed, select "No Improvement".
My mother insists on setting (up) something every day for charity.
(1) on
(2) in
(3) aside
(4) No Improvement
Option 1: (1)
Option 2: (2)
Option 3: (3)
Option 4: (4)
Correct Answer: (3)
Solution : The sentence can be improved using the third option.
It conveys the idea that something is being set apart or allocated for charity. The original choice, "on" does not convey the same meaning.
The meanings of the other options are as follows:
Question : Select the correctly spelt word.
Option 1: Definitely
Option 2: Definately
Option 3: Defenately
Option 4: Difinately
Correct Answer: Definitely
Solution : The correctly spelled word is the first option
Explanation: The correct spelling is Definitely.
This word is often misspelled due to its pronunciation, leading to common misspellings like Definately, Defenately, or Difinately.
Paying attention to the correct placement of vowels and consonants in the word
Question : The given expression is equal to: $1-\frac{\tan ^2 \phi}{\sec ^2 \phi}$
Option 1: $\operatorname{sin}^2 \phi\cos ^2 \phi$
Option 2: $\operatorname{sin}^2 \phi\cot ^2 \phi$
Option 3: $\cot^2 \phi \cos^2 \phi$
Option 4: $\tan^2 \phi\cos^2 \phi$
Correct Answer: $\operatorname{sin}^2 \phi\cot ^2 \phi$
Solution : We know, $\sec^2 \phi-\tan^2 \phi$ = 1 and $\frac{\cos^2 \phi}{\sin^2 \phi}$ = $\cot^2 \phi$ So, $1-\frac{\tan^2 \phi}{\sec^2 \phi} $ = $\frac{\sec^2 \phi-\tan^2 \phi}{\sec^2 \phi}$ = $\frac{1}{\sec^2 \emptyset}$ = $\cos^2 \phi$ = $\frac{\sin^2 \phi\times{\cos^2 \phi}}{\sin^2 \phi}$ = $\sin^2 \phi\cot^2 \phi$ Hence, the correct
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