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Question : A can do a work in 48 days. What part of the total work can be done by A in 18 days?
Option 1: $\frac{5}{6}$
Option 2: $\frac{3}{5}$
Option 3: $\frac{3}{8}$
Option 4: $\frac{4}{9}$
Correct Answer: $\frac{3}{8}$
Solution : A can complete the work in 48 days. ⇒ 1 day work of A = $\frac{1}{48}$ Work done by A in 18 days = $\frac{1}{48}×18$ = $\frac{18}{48} = \frac{3}{8}$ Hence, the correct answer is $\frac{3}{8}$.
Question : Comprehension: In the following passage, some words have been deleted. Read the passage carefully and select the most appropriate option to fill in each blank.
It was a matter of (1)_________ pleasure that the Chief of Police himself came up to us and congratulated us on our successful efforts in reducing the (2)___________ of child marriages in our area. We were also (3) _________ by other (4) _________ present at the event. Our dear leader, the founder of our NGO, Mr. Kumar, was (5) _________ by the mayor with a bouquet.
Question: Select the most appropriate option to fill in the blank number 2.
Option 1: aggregate
Option 2: limit
Option 3: number
Option 4: quota
Correct Answer: number
Solution : The correct choice is the third option.
Number is the appropriate word, as it helps convey that the Chief of Police congratulated them on reducing the number of child marriages in their area.
Question : What is the difference of the factors of the expression $x^2+\frac{1}{x^2}-6$?
Option 1: 0
Option 2: 1
Option 3: 2
Option 4: 4
Correct Answer: 4
Solution : $x^2+\frac{1}{x^2}-6$ = $x^2+\frac{1}{x^2}-2-4$ = $x^2+\frac{1}{x^2}-2×x^2×\frac{1}{x^2}-(2)^2$ = $(x-\frac{1}{x}^2)-(2)^2$ = $(x-\frac{1}{x}+2)(x-\frac{1}{x}-2)$ These are the two factors. So, the difference between them is $(x-\frac{1}{x}+2-x+\frac{1}{x}+2)=4$ Hence, the correct answer is 4.
Question : Directions: What will come in place of the question mark (?) in the following equation if + and – are interchanged and × and ÷ are interchanged? 11 ÷ 4 + 8 × 2 – 1 = ?
Option 1: 41
Option 2: 40
Option 3: 39
Option 4: 43
Correct Answer: 41
Solution : Given: 11 ÷ 4 + 8 × 2 – 1 = ?
After interchanging + with – and × with ÷, the equation becomes – = 11 × 4 – 8 ÷ 2 + 1 = 11 × 4 – 4 + 1 = 44
Question : The following sentence has been divided into parts. One of them may contain an error. Select the part that contains the error from the given options. If you don't find any error, mark 'No Error' as your answer.
Can you not / knock so louder / in the morning?
Option 1: No Error
Option 2: knock so louder
Option 3: in the morning
Option 4: Can you not
Correct Answer: knock so louder
Solution : The correct choice is the second option.
The adjective "loud" should be modified using the adverb form "loudly" in the comparative construction "so loudly" instead of "so louder". This correction adheres to proper grammatical structure, specifically in terms of forming comparatives and expressing
Question : The perimeter of two similar triangles ABC and PQR are 36 cm and 24 cm respectively. If PQ = 10 cm. then the length of AB is:
Option 1: 18 cm
Option 2: 12 cm
Option 3: 15 cm
Option 4: 30 cm
Correct Answer: 15 cm
Solution : Since the ratio of the corresponding sides of similar triangles is the same as the ratio of their perimeters. $\triangle{ABC} \sim\triangle{PQR}$ $\Rightarrow \mathrm{\frac{AB}{PQ} = \frac{BC}{QR} = \frac{AC}{PR} = \frac{36}{24}}\\$ $\Rightarrow\mathrm{\frac{AB}{PQ} = \frac{36\;\mathrm{cm}}{24\;\mathrm{cm}}}\\$ $\Rightarrow \mathrm{\frac{AB}{10\;\mathrm{cm}} = \frac{36\;\mathrm{cm}}{24\;\mathrm{cm}}}\\$ $\Rightarrow \mathrm{AB = \frac{36\;\mathrm{cm} \times 10\;\mathrm{cm}}{24\;\mathrm{cm}} = 15\;\mathrm{cm}}$
Question : Directions: Two different positions of the same dice are shown, the six faces of which are numbered from 1 to 6. Select the number that will be on the face opposite to the face showing 3.
Option 1: 4
Option 2: 2
Option 3: 5
Option 4: 1
Solution : Taking dice positions 1 and 2 with 4 as the common face.
Moving clockwise from the common face with 4 –
So, the opposite pairs are –
Therefore, the opposite face of the 3 is 4. Hence, the first option is correct.
Question : Directions: Seven people, A, B, C, D, E, F, and G are sitting in a straight row facing the north. Only two people sit to the left of C. Only two people sit between A and B. B sits to the left of A. E is an immediate neighbour of A to the right. Only one person sits to the right of D. F is not an immediate neighbour of B. Who sits at the centre?
Option 1: C
Option 2: E
Option 3: D
Option 4: A
Correct Answer: A
Solution : Given: Only two people sit to the left of C. Only two people sit between A and B. B sits to the left of A. E is an immediate neighbour of A to the right. Only one person sits to the right of D. F
Question : Direction: Which one of the given responses would be a meaningful order of the following?
(A) Ghee
(B) Milk
(C) Curd
(D) Cow
(E) Butter
Option 1: (E), (A), (B), (D), (C)
Option 2: (D), (B), (E), (C), (A)
Option 3: (D), (B), (C), (E), (A)
Option 4: (C), (B), (E), (D), (A)
Correct Answer: (D), (B), (C), (E), (A)
Solution : Given:
Question : Which of the following statements is correct? I. The death rate in India was 7.2 per 1000 in 2011. II. Life expectancy at birth was 72.6 years in 2012.
Option 1: Only II
Option 2: Both I and II
Option 3: Neither I nor II
Option 4: Only I
Correct Answer: Only I
Solution : The correct answer is Only I.
In 2011, the death rate in India was 7.2 per 1000, which was 25 per 1000 in 1951. This drastic decline was due to the various campaigns, and the efforts applied by the different governments. Life expectancy
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