Staff Selection Commission Combined Graduate Level Exam
Question : If the square of the sum of three positive consecutive natural numbers exceeds the sum of their squares by 292, what is the largest of the three numbers?
Option 1: 5
Option 2: 6
Option 3: 3
Option 4: 8
Correct Answer: 8
Solution : The consecutive natural numbers are a = (x – 1), b = x, and c = (x + 1). According to the question, (a + b + c)2 – (a2 + b2 + c2) = 292 ⇒ a2 +
Question : Acceptable "Noise Pollution Level" in India range between:
Option 1: 16 - 35 dec
Option 2: 40 - 45 dec
Option 3: 70 - 100 dec
Option 4: 10 - 15 dec
Correct Answer: 40 - 45 dec
Solution : The correct answer is 40 - 45 dec.
The higher levels of sound which is derogatory to human health is known as noise pollution or sound pollution. Sound is measured in Decibels. Noise pollution is usually caused by the transport noises, machinery
Question : The sum of the ages of the mother and her daughter is 60 years. 12 years ago, the mother was eight times as old as her daughter. How old is the daughter at present?
Option 1: 20 years
Option 2: 28 years
Option 3: 16 years
Option 4: 12 years
Correct Answer: 16 years
Solution : Let the current age of the mother be $x$ and the daughter be $y$. The sum of their current ages is $60$ years, ⇒ $x+ y = 60$...(i) $12$ years ago, the mother was eight times as old as the daughter. ⇒ $x -
Question : A petrol tank is of length 50 m, breadth 25 m and depth 10 m. How many litres of petrol can be accommodated in the tank when filled?
Option 1: 1,25,00,000
Option 2: 12,50,000
Option 3: 1,25,000
Option 4: 12,500
Correct Answer: 1,25,00,000
Solution : Volume of petrol tank = $l × b × h$ = 50 × 25 ×10 = 12500 m3 = 12500000 litres [1m3 = 1000 litres] Hence, the correct answer is 1,25,00,000.
Question : Select the correct direct form of the given sentence. Shravan said that the prisoner had slept throughout the journey.
Option 1: Shravan said, "The prisoner sleeps throughout the journey."
Option 2: Shravan said, "The prisoner had been sleeping throughout the journey."
Option 3: Shravan says, "The prisoner has slept throughout the journey."
Option 4: Shravan said, "The prisoner had slept throughout the journey."
Correct Answer: Shravan said, "The prisoner had slept throughout the journey."
Solution : The correct choice is the fourth option.
In direct speech, the reported words are directly quoted without any changes to the tense, pronouns, or other elements used in the reported speech.
The steps of conversion are
Question : If $P=7+4\sqrt3$ and $PQ=1$, then what is the value of $\frac{1}{P^{2}}+\frac{1}{Q^{2}}$?
Option 1: 196
Option 2: 194
Option 3: 206
Option 4: 182
Correct Answer: 194
Solution : Given: $PQ=1, P=7+4\sqrt3$ ⇒ $Q=\frac{1}{P}$ ⇒ $P^2=(7+4\sqrt3)^2=97+56\sqrt3$ Taking the inverse on both sides and rationalising the denominators, ⇒ $\frac{1}{P^2}={97 -56\sqrt{3}}$ ⇒ $\frac{1}{P^2}+ \frac{1}{Q^2}= \frac{1}{P^2}+ {P^2}$ ⇒ $\frac{1}{P^2}+ \frac{1}{Q^2}=(97 -56\sqrt{3} +97+56\sqrt{3})$ ⇒ $\frac{1}{P^2}+ \frac{1}{Q^2}= 194$ Hence, the correct answer is 194.
Question : In a school, there are 1500 students, 44% of whom are girls. The monthly fee for each boy is Rs. 540 and the fee for each girl is 25% less than that of a boy. The sum of the fees for both boys and girls is:
Option 1: Rs. 720600
Option 2: Rs. 720800
Option 3: Rs. 720900
Option 4: Rs. 721000
Correct Answer: Rs. 720900
Solution : Total number of students = 1500 44% of students are girls. Therefore, the number of girls $=\frac{44}{100} × 1500 = 660$ The number of boys = 1500 – 660 = 840 The monthly fee for each boy = Rs. 540 The monthly fee for
Question : Which of the following statements is/are correct regarding the changes made to small savings schemes by the Government of India in December 2022? A. The interest rate of a five-year National Saving Certificate has been increased to 7 per cent from 6.8 per cent. B. The interest rate on senior citizen saving schemes increased to 8 per cent from 7.6 per cent. C. The interest rate on the Public Provident Fund, Sukanya Samriddhi Account and Saving Deposit has been changed to 9% from 7.5%.
Option 1: B and C only
Option 2: A, B and C
Option 3: A and C only
Option 4: A and B only
Correct Answer: A and B only
Solution : The correct answer is A and B only.
The interest rate of a five-year National Saving Certificate has been increased to 7 per cent from 6.8 per cent. With a higher interest rate, individuals may find the National Saving Certificate more
Question : Directions: In the following question, one or two statements are given followed by two conclusions I and II. You have to consider the given statements to be true, even if they seem to be at variance from commonly known facts. You are to decide which of the given conclusions can be drawn from the given statements. Indicate your answer. Statements: 1. All boys are tall. 2. Rajiv is a boy. Conclusions: I. Rajiv is tall. II. Rajiv is not tall.
Option 1: Only conclusion I follows
Option 2: Only conclusion II follows
Option 3: Both conclusion I and conclusion II follow
Option 4: Neither conclusion I nor conclusion II follows
Correct Answer: Only conclusion I follows
Solution : As per the given information, let's analyse the conclusions – Conclusion I: Rajiv is tall – Based on the given statements, Rajiv is a boy, and all boys are tall. Therefore, from this, it can be concluded that Rajiv is tall. So,
Question : Directions: Study the following bar graph and answer the question. The bar graph gives the annual rates of inflation in percentage for 1975 and 1987. In the year 1987, the inflation rate in the Third World countries vis-à-vis the world jumped approximately by:
Option 1: 135%
Option 2: 126%
Option 3: 122%
Option 4: 200%
Correct Answer: 126%
Solution : As per the given graph: In the year 1987, The rate of inflation in the Third World = 36.2 The rate of inflation in the World = 16 The change in the rate of inflation in the year 1987 for the Third World and the
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