Staff Selection Commission Combined Graduate Level Exam
Question : In a trapezium ABCD, AB and DC are parallel to each other with a perpendicular distance of 8 m between them. Also, AD = BC = 10 m, and AB = 15 m < DC. What is the perimeter (in m) of the trapezium ABCD?
Option 1: 50
Option 2: 66
Option 3: 62
Option 4: 58
Correct Answer: 62
Solution : ⇒ AD = BC = 10 m ⇒ AB = EF = 15 m ⇒ AE = BF = 8 m In $\triangle$ADE, By Pythagoras theorem, AD2 = AE2 + DE2 DE = $\sqrt{10^2-8^2}$ = $\sqrt{100-64}$ = $\sqrt{36}$ = 6 m ⇒
Question : Select the option that expresses the given sentence in passive voice. The mistress appointed him monitor.
Option 1: Monitor had been appointed as mistress.
Option 2: He had been appointed as monitor.
Option 3: He was appointed monitor by the mistress.
Option 4: He appointed mistress as monitor.
Correct Answer: He was appointed monitor by the mistress.
Solution : The third option is correct.
In the original sentence, the structure is in active voice. The passive voice is the voice in which the object experiences an action rather than the person who performs the action. Hence, the object
Question : If $x^2-5 x+1=0$, then the value of $\frac{x^6+x^4+x^2+1}{5 x^3}=?$
Option 1: 30
Option 2: 25
Option 3: 23
Option 4: 28
Correct Answer: 23
Solution : Given, $x^2-5 x+1=0$ $⇒x^2+1=5 x$----(i) Multiplying whole equation by $x^4$, we get: $⇒x^6+x^4=5 x^5$ Also dividing equation (i) by $x$, we get, $x+\frac{1}{x}=5$ Now, $\frac{x^6+x^4+x^2+1}{5 x^3}$ = $\frac{5 x^5+5 x}{5 x^3}$ = $x^2+\frac{1}{x^2}$ = $(x+\frac{1}{x})^2-2$ = $5^2-2$ = $23$ Hence, the correct answer is 23.
Question : Ram sold a plot for Rs. 4,00,000 at a 20% loss. For what price should he sell the plot to gain a 5% profit?
Option 1: Rs. 5,25,000
Option 2: Rs. 5,20,000
Option 3: Rs. 5,00,000
Option 4: Rs. 5,05,000
Correct Answer: Rs. 5,25,000
Solution : Here CP denotes the cost price, and SP denotes the selling price. Let CP be Rs. $100x$. Now, SP after 20% loss $= 100x × (100 – 20)$% $=80x$ And, SP after 5% profit $= 100x × (100 + 5)$% $=105x$ According to the
Question : Directions: Select the set in which the numbers are related in the same way as the numbers of the given set. (NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits. E.g. 13 – Operations on 13 such as adding/subtracting/multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.) (4, 7, 165) (14, 26, 600)
Option 1: (23, 29, 567)
Option 2: (5, 19, 225)
Option 3: (3, 6, 135)
Option 4: (17, 6, 325)
Correct Answer: (3, 6, 135)
Solution : Given: (4, 7, 165); (14, 26, 600)
Like, (4, 7, 165)→(165 ÷ 15) – 4 = 11 – 4 = 7 (14, 26, 600)→(600 ÷ 15) – 14 = 40 – 14 = 26
Let's check the options – First option: (23, 29,
Question : The Wheeler Island has been renamed as
Option 1: Vikram Sarabhai Island
Option 2: Satish Dhawan Island
Option 3: Abdul Kalam Island
Option 4: C.V. Raman Island
Correct Answer: Abdul Kalam Island
Solution : The correct answer is Abdul Kalam Island.
Wheeler Island is located 150 km off the coast of Odisha in Bay of Bengal. Recently it has been renamed as Abdul Kalam Island in honour of the former President of India. It is also famous
Question : Directions: In this question, a part of the sentence is in bold. Below are given alternatives to the bold part at (1), (2), and (3) which may improve the sentence. Choose the correct alternative. In case, no improvement is needed your answer is (4).
She has that rare character- the ability to listen to people.
(1) rare ear
(2) rare characteristic
(3) rare sense
(4) No Improvement
Option 1: (1)
Option 2: (2)
Option 3: (3)
Option 4: (4)
Correct Answer: (3)
Solution : The correct option is the third option.
Rare sense implies a unique and uncommon quality that the sentence intends to convey. This option provides a more suitable and idiomatic word choice.
Therefore, the correct sentence is, "She has that rare sense - the ability
Question : Directions: Select the option that represents the correct order of the given words as they would appear in an English dictionary. 1. Effluent 2. Edifice 3. Effleurage 4. Edacious 5. Effeminate 6. Eccentric 7. Effulgent
Option 1: 6, 4, 2, 5, 3, 1, 7
Option 2: 6, 4, 2, 3, 5, 1, 7
Option 3: 6, 4, 2, 5, 1, 3, 7
Option 4: 6, 4, 2, 5, 7, 3, 1
Correct Answer: 6, 4, 2, 5, 3, 1, 7
Solution : Given: 1. Effluent 2. Edifice 3. Effleurage 4. Edacious 5. Effeminate 6. Eccentric 7. Effulgent
Step 1: Compare the first letter of each word. Since all the words start with the same letter E. So, move on to
Question : Directions: Select the option that represents the letters that, when placed from left to right in the following blanks, will complete the letter series. _ V J R W B _ _ R W B V L _ _ B V _ _ W
Option 1: B V K R W M R
Option 2: A V K R W M R
Option 3: A W K R X N R
Option 4: B W K R W M R
Correct Answer: B V K R W M R
Solution : Given: _ V J R W B _ _ R W B V L _ _ B V _ _ W
To fill the series we have to divide the series – _ V J R W / B
Question : Directions: In the following question, the statement is followed by two conclusions. Which of the two conclusions is/are true? Statement: M < K > I < J > H = G ≤ F Conclusions: I. H = F II. J > G
Option 1: Only conclusion I is true
Option 2: Both conclusions I and II are true
Option 3: Only conclusion II is true
Option 4: Neither conclusion I nor II is true
Correct Answer: Only conclusion II is true
Solution : Given: Statement: M < K > I < J > H = G ≤ F
Let's analyse the conclusions – Conclusion (I): H = F→This conclusion is false as H = G ≤ F ⇒ H ≤ F Conclusion (II): J
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