Staff Selection Commission Combined Graduate Level Exam
Question : A lady sold an article for INR 960 at some profit. Had she sold it for INR 800, then there would have been a loss equal to $\frac{1}{3}$rd of the initial profit. What was the profit percentage of the article?
Option 1: $\frac{150}{7} \%$
Option 2: $\frac{50}{7} \%$
Option 3: $\frac{10}{7} \%$
Option 4: $\frac{100}{7} \%$
Correct Answer: $\frac{100}{7} \%$
Solution : Let the cost price of the article be $x$. According to the question, ⇒ $(x - 800) = \frac{1}{3}\times (960 - x)$ ⇒ $3(x - 800) = 960 - x$ ⇒ $3x - 2400 = 960 - x$ ⇒ $3x + x = 960
Question : What is the correct statement related to Avogadro?
Option 1: Avogadro discovered electrons
Option 2: Avogadro made a distinction between electrons and neutrons.
Option 3: Avogadro discovered a difference between animal and plant cells.
Option 4: Avogadro made a distinction between atoms and molecules.
Correct Answer: Avogadro made a distinction between atoms and molecules.
Solution : The correct option is Avogadro made a distinction between atoms and molecules.
Avogadro distinguished molecules from atoms for the first time in 1811. He also proposed Avogadro's Law: equal amounts of gas at the same pressure and
Question : 625 + 626 + 627 + 628 is divisible by:
Option 1: 256
Option 2: 254
Option 3: 255
Option 4: 259
Correct Answer: 259
Solution : 625 + 626 + 627 + 628 = 625(1 + 6 + 62 + 63) = 625(7 + 36 + 216) = 625(259) It is divisible by 259. Hence, the correct answer
Question : Expand and simplify the algebraic expression: $(x-5)^2+(x+3)^2+4x$
Option 1: $2\left(x^2-17\right)$
Option 2: $2\left(x^2+17\right)$
Option 3: $\left(x^2+17\right)$
Option 4: $2\left(x^2-5 x+17\right)$
Correct Answer: $2\left(x^2+17\right)$
Solution : $(x-5)^2+(x+3)^2+4x$ $=x^2-10x+25+x^2+6x+9+4x$ $= 2x^2+34$ $= 2(x^2+17)$ Hence, the correct answer is $2(x^2+17)$.
Question : Select the correct indirect form of the given sentence.
I said to the office boy, "Take these papers to the manager immediately."
Option 1: I requested the office boy to take these papers to the manager immediately.
Option 2: I said to the office boy to take these papers to the manager immediately.
Option 3: I told the office boy take those papers to the manager immediately.
Option 4: I ordered the office boy to take those papers to the manager immediately.
Correct Answer: I ordered the office boy to take those papers to the manager immediately.
Solution : The fourth option is the correct answer.
Narration Conversion:
Question : Directions: Starting from a point, a person travels 3 km towards the east and turns left and travels 4 km. Then again he turns to the left by 45° and moves straight. Which direction is he facing now?
Option 1: North-East
Option 2: North-West
Option 3: South-East
Option 4: South-West
Correct Answer: North-West
Solution : Firstly, we will draw the diagram as per the given instructions – Here, A is the starting point and D is the endpoint.
So, the person is facing in the northwest direction. Hence, the second option is correct.
Question : A man invests a total sum of INR 10,000 in a company. A part of the sum was invested at 10% simple interest per annum and the remaining part, at 15% simple interest per annum. If the total interest accrued in two years equals INR 2,400, the sum invested at 15% simple interest per annum is:
Option 1: INR 8000
Option 2: INR 4000
Option 3: INR 6000
Option 4: INR 5000
Correct Answer: INR 4000
Solution : Let the sum invested at 15% be $x$ and the sum invested at 10% be (10000 – $x$). Time = 2 years According to the question: $2400 =\frac{x×15×2}{100}$+$\frac{(10000-x)×10×2}{100}$ ⇒ $2400 =\frac{30x}{100}$+$\frac{(200000-20x)}{100}$ ⇒ $2400 = \frac{30x+200000-20x}{100}$ ⇒ $240000 = 10x + 200000$ ⇒ $40000 =
Question : In the first month, the income of Mohan increased by 30%. In the second month, his income decreased by 30%. What will be the percentage increase or decrease in the income after two months?
Option 1: 15% increase
Option 2: 9% increase
Option 3: 15% decrease
Option 4: 9% decrease
Correct Answer: 9% decrease
Solution : According to the question: In the first month, his income increased by 30%. In the second month, his income decreased by 30%. $\therefore$ Income of Mohan after 2 months = $30 +(-30) + \frac{30\times -(30)}{100} = - 9\%$ Hence, the correct answer is 9%
Question : If $\cos A+\cos^2 A=1$, then the value of $\sin^4 A+\sin^6 A$ is:
Option 1: $2$
Option 2: $\cos \mathrm{A}$
Option 3: $1$
Option 4: $\sin A$
Correct Answer: $\cos \mathrm{A}$
Solution : Given: $\cos A+\cos^2 A=1$ ⇒ $\cos A=1 - \cos^2 A$ ⇒ $\cos A= \sin^2 A$ Squaring both sides, ⇒ $\cos^2 A= \sin^4 A$ ⇒ $1-\sin^2 A= \sin^4 A$ Multiplying both sides by $\sin^2 A$, $\sin^2 A-\sin^4 A=\sin^6 A$ ⇒ $\sin^2 A=\sin^6 A+\sin^4 A$ ⇒
Question : River Indus originates from :
Option 1: Hindukush range
Option 2: Himalayan range
Option 3: Karakoram range
Option 4: Kailash range
Correct Answer: Kailash range
Solution : The correct answer is Kailash range
The Indus River originates from mountain springs northeast of Mount Kailash in Western Tibet, flows through the conflict region of Kashmir to the north, makes a sharp left turn after the Nanga Parbat massif, and then flows through
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