Staff Selection Commission Combined Graduate Level Exam
Question : In the given figure, $\angle ABC=81^{\circ}$ and $\angle ACB=9^{\circ}$. What is the value of $\angle BDC$?
Option 1: 80°
Option 2: 90°
Option 3: 70°
Option 4: 60°
Correct Answer: 90°
Solution : The angles at the circumference subtended by the same arc are equal. In $\triangle ABC$, $\angle ABC + \angle BCA + \angle ACB = 180°$ ⇒ $81° + 9° +\angle BAC= 180°$ ⇒ $\angle BAC = 90°$ Now, $\angle BAC = \angle BDC = 90°$
Question : Identify the segment in the sentence which contains a grammatical error.
The seat which you are sitting on is my.
Option 1: which you
Option 2: is my
Option 3: The seat
Option 4: are sitting on
Correct Answer: is my
Solution : The correct choice is the second option.
My should be replaced with mine to make the sentence grammatically accurate, as my is usually followed by a noun, whereas mine is used without a following noun to indicate ownership.
Therefore, the correct sentence is:
Question : Directions: Which answer figure will combine the pattern in the question figure?
Option 1:
Option 2:
Option 3:
Option 4:
Correct Answer:
Solution : On comparing the question figure and all the answer figures, the following figure will combine and make the complete pattern –
Hence, the first option is correct.
Question : Directions: The second number in the given number pairs is obtained by performing certain mathematical operation(s) on the first number. The same operation(s) are followed in all the number pairs except one. Find that odd number pair.
Option 1: 4 : 70
Option 2: 3 : 30
Option 3: 6 : 222
Option 4: 7 : 350
Correct Answer: 4 : 70
Solution : Let's check the options – First option: 4 : 70; 70 is not divisible by 4. Second option: 3 : 30; 30 ÷ 3 = 10; 30 is divisible by 3. Third option: 6 : 222; 222 ÷ 6 = 37; 222 is
Question : A man and a woman can finish a work together in half the time taken by a woman and a boy together. A boy can finish the work alone in 20 days and 2 women together can finish it in 30 days. In how many days will the work be finished by 4 men?
Option 1: 2
Option 2: 2.14
Option 3: 2.5
Option 4: 3
Correct Answer: 2.14
Solution : Given: Time taken by a man and a woman = $\frac{1}{2}$ (Time taken by a woman and a boy) Time taken by a boy to complete the work = 20 days Time taken by 2 women to complete the work = 30 days Time taken
Question : If $x=1+\sqrt2+\sqrt3$, then find the value of $x^{2}-2x+4$.
Option 1: $2(7+\sqrt6)$
Option 2: $2(4+\sqrt6)$
Option 3: $2(3+\sqrt7)$
Option 4: $(4+\sqrt6)$
Correct Answer: $2(4+\sqrt6)$
Solution : $x=1+\sqrt{2}+\sqrt{3}$ ⇒ $x-1=\sqrt{2}+\sqrt{3}$ Squaring both sides ⇒ $(x-1)^2=(\sqrt{2}+\sqrt{3})^2$ ⇒ $(x^2+1-2x)=(2+3+2\sqrt{6})$ ⇒ $(x^2+1-2x)=(5+2\sqrt{6})$ adding 3 to both sides, we get, ⇒ $(x^2+1-2x)+3=(5+2\sqrt{6})+3$ ⇒ $(x^2+4-2x)=(8+2\sqrt{6})$ $\therefore (x^2+4-2x)=2(4+\sqrt{6})$ Hence, the correct answer is $2(4+\sqrt{6})$.
Question : Directions: In the following question, out of the four alternatives, select the alternative that will improve the bracketed part of the sentence. In case no improvement is needed, select "No Improvement".
I had not completed my project, so I thought I was (done with) when the manager asked me to hand it in.
(1) done for
(2) done in
(3) done on
(4) No Improvement
Option 1: 1
Option 2: 2
Option 3: 3
Option 4: 4
Correct Answer: 1
Solution : The appropriate answer is the first option because "done with" means 'to bring an end to something' and should be replaced with "done for" which means 'to be in a difficult situation that it is impossible to get out.'
"Done
Question : Which of the following offices was not held by the poet Harishena?
Option 1: Sandhi-vigrahika
Option 2: Maha-danda-nayaka
Option 3: Nagara-Shreshthi
Option 4: Kumar-amatya
Correct Answer: Nagara-Shreshthi
Solution : The correct answer is Nagara-Shreshthi.
Harishena did not hold the office of Nagara-Shreshthi. The offices held by Harishena include Sandhi-Vigrahika (negotiator), Maha-Danda-Nayaka (chief of the great staff), and Kumar-amatya (chief minister or prince). Nagara-Shreshthi refers to the chief merchant, and it was not among the
Question : The average of 11 numbers is 36, whereas the average of 9 of them is 34. If the remaining two numbers are in the ratio of 2 : 3, find the value of the smaller number (between the remaining two numbers).
Option 1: 45
Option 2: 48
Option 3: 54
Option 4: 36
Correct Answer: 36
Solution : Given: The average of 11 numbers is 36. ⇒ Total of 11 numbers = 36 × 11 = 396 The average of 9 of them is 34. ⇒ Total of 9 numbers = 34 × 9 = 306 $\therefore$ Total of the remaining two numbers
Question : Directions: A & B means A is the son of B; A # B means A is the sister of B; A @ B means A is the brother of B; A % B means A is the father of B; A – B means A is the daughter of B; A * B means A is the wife of B. If C # D @ E % Z & L # M – N * P, then how is L related to P?
Option 1: Wife
Option 2: Daughter
Option 3: Daughter-in-law
Option 4: Sister
Correct Answer: Daughter
Solution : Given: A & B ⇒ A is the son of B A # B ⇒ A is the sister of B A @ B ⇒ A is the brother of B A % B ⇒ A is the father of B A – B ⇒
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