Staff Selection Commission Combined Graduate Level Exam
Question : Three sides of a triangle are $\sqrt{a^2+b^2}, \sqrt{(2 a)^2+b^2}$, and $\sqrt{a^2+(2 b)^2}$ units. What is the area (in unit squares) of the triangle?
Option 1: $\frac{5}{2} ab $
Option 2: $3 ab$
Option 3: $4 ab$
Option 4: $\frac{3}{2} ab $
Correct Answer: $\frac{3}{2} ab $
Solution : Given that the three sides of a triangle are $\sqrt{a^2+b^2}$, $\sqrt{(2a)^2+b^2}$, and $\sqrt{a^2+(2b)^2}$ units. Let's assume that $a=b$. The sides of the triangle become = $\sqrt{2a^2}$, $\sqrt{5a^2}$, $\sqrt{5a^2} =a\sqrt{2}$, $a\sqrt{5}$, $a\sqrt{5}$. From this, we can say the triangle is an isosceles triangle with
Question : Find the least number which when divided separately by 15, 20, 36 and 48 leaves 3 as the remainder in each case.
Option 1: 183
Option 2: 243
Option 3: 483
Option 4: 723
Correct Answer: 723
Solution : 15 = 3 × 5 20 = 2 × 2 × 5 36 = 3 × 3 × 2 × 2 48 = 2 × 2 × 2 × 2 × 3 LCM = 3 × 3 × 2 × 2 × 2 × 2
Question : Directions: In the following question, a sentence is given with a blank that is to be filled in with an appropriate word. Four alternatives are suggested; choose the correct alternative out of them as your answer. The Prime Minister of England called____ the President of America.
Option 1: in
Option 2: out
Option 3: on
Option 4: at
Correct Answer: on
Solution : The third option is the correct answer.
"Call on" is a phrasal verb that means to pay a visit to someone formally to discuss a matter. The other options are not a correct fit for this scenario.
Therefore, the sentence is: "The Prime Minister of
Question : Pannalal Ghosh played which of the following musical instruments?
Option 1: Flute
Option 2: Sitar
Option 3: Violin
Option 4: Santoor
Correct Answer: Flute
Solution : The correct option is Flute
Amal Jyoti Ghosh, also known as Pandit Pannalal Ghosh, was an Indian composer and a famous flute player. He was a disciple of Allauddin Khan and is regarded as the "Pioneer of Indian Classical Flute" for popularising the
Question : Directions: Select the figure that will replace the question mark (?) in the following figure series.
Option 1:
Option 2:
Option 3:
Option 4:
Correct Answer:
Solution : The pattern followed here is that the shaded portion in the corner is shifting to the next corner in the anticlockwise direction, whereas the image in the centre remains the same. The following figure will complete the given pattern –
Hence, the second option is correct.
Question : If $\alpha$ and $\beta$ are the roots of equation $x^{2}-x+1=0$, then which equation will have roots $\alpha ^{3}$ and $\beta ^{3}?$
Option 1: $x^{2}+2x+1=0$
Option 2: $x^{2}-2x-1=0$
Option 3: $x^{2}+3x-1=0$
Option 4: $x^{2}-3x+1=0$
Correct Answer: $x^{2}+2x+1=0$
Solution : $\alpha$ and $\beta$ are roots of the equation $x^{2}-x+1=0$ ⇒ $\alpha+\beta=1$ and $\alpha\beta=1$ Now we need to find the equation whose roots are $\alpha ^{3}$ and $\beta ^{3}$. ⇒ $(\alpha^{3}+\beta^{3})=(\alpha+\beta)^{3}-3\alpha\beta\times(\alpha+\beta)$ ⇒ $(\alpha^{3}+\beta^{3})=(1)^{3}-3\times 1 \times (1)$ ⇒ Sum of roots = $(\alpha^{3}+\beta^{3})=-2$ Also, Product of roots
Question : Select the most appropriate option to fill in the blank. I am_________ after five years.
Option 1: making an exam
Option 2: taking an exam
Option 3: keeping an exam
Option 4: frying an exam
Correct Answer: taking an exam
Solution : The second option is correct.
Given the context of someone's engagement or action related to an exam five years from now, taking an exam is the appropriate choice to complete the sentence, indicating participation in an exam at that future time.
The meanings
Question : Directions: In the following question, select the odd letter cluster from the given alternatives.
Option 1: ADG
Option 2: HKN
Option 3: ORU
Option 4: BDF
Correct Answer: BDF
Solution : Let's check the options – First option: ADG; A + 3 = D; D + 3 = G Second option: HKN; H + 3 = K; K + 3 = N Third option: ORU; O + 3 = R; R + 3 = U Fourth
Question : For the year 2022, who among the following won the Indian Film Personality Award awarded by the International Film Festival of India (IFFI)?
Option 1: Chiranjeevi
Option 2: Prakash Raj
Option 3: Mahesh Babu
Option 4: Rajnikant
Correct Answer: Chiranjeevi
Solution : The correct answer is Chiranjeevi.
The Indian Film Personality Award was awarded to Chiranjeevi. He belongs to the Telugu industry. This was the 53rd edition of the International Film Festival of India (IFFI) award.
IFFI was first held in 1952, making it one of the
Question : How many job applicants had applied if the ratio of selected to rejected was 19 : 17? If 1200 less had been applied and 800 less were selected, then the ratio of selected to rejected would have been 1 : 1.
Option 1: 6000
Option 2: 7200
Option 3: 8400
Option 4: 4800
Correct Answer: 7200
Solution : Let there be 36x job applicants of whom 19x were selected, while 17x were rejected. If (36x – 1200) had applied and (19x – 800) were selected, then Rejected = (36x – 1200 – 19x + 800) = (17x – 400) Given, Rejected : Selected
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