Staff Selection Commission Combined Graduate Level Exam
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
Question : If $a+b=3$, then the value of $a^{3}+b^{3}+9ab-27$ is:
Option 1: 24
Option 2: 25
Option 3: 0
Option 4: 27
Correct Answer: 0
Solution : Given: $a+b=3$ Cubing both sides, we get $(a+b)^3=3^3$ ⇒ $a^3+b^3+3ab(a+b)=27$ Putting, $(a+b)=3$ ⇒ $a^3+b^3+3ab×3=27$ ⇒ $a^3+b^3+9ab=27$ Thus, $a^3+b^3+9ab–27=0$ Hence, the correct answer is 0.
Question : Direction: In the following question, select the one which is different from other three alternatives.
Option 1: LNOR
Option 2: TRPS
Option 3: CEFI
Option 4: GIJM
Correct Answer: TRPS
Solution : Given:
First option:LNOR ; Follows alphabetical order
Second option:TRPS ; Does not follows alphabetical order
Third option:CEFI ; Follows alphabetical order
Fourth option:GIJM ; Follows alphabetical order
Hence, second option is correct.
Question : At a Christmas sale, all the goods in a shop are on sale at a 30% discount. If Jasmine buys a skirt marked at 800, how much would she need to pay?
Option 1: 476
Option 2: 400
Option 3: 770
Option 4: 560
Correct Answer: 560
Solution : Marked price = 800 Discount = 30% of marked price = 30% of 800 = 240 Selling price = 800 – 240 = 560 Hence, the correct answer is 560.
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