Staff Selection Commission Combined Graduate Level Exam
Question : If $x+y=5$, $x^{3}+ y^{3}=35$, what is the positive difference between $x$ and $y$?
Option 1: 0
Option 2: 1
Option 3: 5
Option 4: 6
Correct Answer: 1
Solution : Given: $x+y=5$ and $x^{3}+ y^{3}=35$ We know, $(x+y)^{3}=x^{3}+y^{3}+3xy(x+y)$ $⇒5^{3}=35+3xy(5)$ $⇒xy=6$ Now, $|x-y|=\sqrt{(x-y)^{2}}$ $⇒|x-y|=\sqrt{(x+y)^{2}-4xy}$ $\therefore|x-y|=\sqrt{(5)^{2}-4\times 6}=1$ Hence, the correct answer is 1.
Question : Directions: Select the set in which the numbers are related similarly to the numbers of the following 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.) (85, 24, 133) (97, 36, 145)
Option 1: (79, 18, 127)
Option 2: (71, 15, 124)
Option 3: (86, 23, 135)
Option 4: (67, 12, 111)
Correct Answer: (79, 18, 127)
Solution : Given: (85, 24, 133); (97, 36, 145)
In the given sets, subtract the first number by 61, to obtain the second number and add the second number to 109 to obtain the third number. (85, 24, 133)→85 – 61 = 24; 24 +
Question : A watch is sold at a profit of 25%. Had it been sold for Rs.120 less then, there would have been a loss of 15%. What is the cost price in rupees?
Option 1: Rs. 400
Option 2: Rs. 350
Option 3: Rs. 200
Option 4: Rs. 300
Correct Answer: Rs. 300
Solution : Let's denote the cost price (CP) of the watch as $x$. The selling price with a 25% profit = CP + ($\frac{25}{100}\times$CP) So, SP = $x+0.25x=1.25x$ The selling price with a 15% loss = CP − ($\frac{15}{100}\times$CP) So, SP = $x−0.15x=0.85x$ According to the
Question : Select the appropriate idiom that can replace the underlined phrase in the following sentence. My father's office is at a close distance from home.
Option 1: from hand to mouth
Option 2: a part and parcel
Option 3: at a stone's throw
Option 4: at sixes and sevens
Correct Answer: at a stone's throw
Solution : The correct choice is the third option.
Explanation: At a stone's throw means a very short distance away, emphasising proximity.
Question : Directions: In a certain code language, RAIN is written as OHBQ. How is SUMMER written in that code language?
Option 1: QFLNTT
Option 2: QDLLTR
Option 3: SFNNVT
Option 4: SDNLVR
Correct Answer: SDNLVR
Solution : Given: RAIN is written as OHBQ.
Subtract and add 1 alternatively from the place values of the letters of RAIN and then reverse their order to get the required code – R – 1 = Q; A + 1 = B; I – 1 =
Question : The area of the square inscribed in a circle of radius 8 cm is:
Option 1: $256\;\mathrm{cm^2}$
Option 2: $250\;\mathrm{cm^2}$
Option 3: $128\;\mathrm{cm^2}$
Option 4: $125\;\mathrm{cm^2}$
Correct Answer: $128\;\mathrm{cm^2}$
Solution : The diagonal of the square is equal to the diameter of the circle. The diameter of this circle $= 2×8 = 16 \;\mathrm{cm}$ In a square, where the diagonal $(d)$ and the side $(s)$, $d = s\sqrt{2}$ The side of the square, $s = \frac{d}{\sqrt{2}}
Question : Directions: In the following question, the sentence given with a blank is to be filled in with an appropriate word. Select the correct alternative out of the four. To ensure a _____ reply, please include all pertinent details in your email.
Option 1: prompt
Option 2: efficient
Option 3: tardy
Option 4: strange
Correct Answer: prompt
Solution : The first option is the correct answer for this sentence because 'prompt' means 'abrupt/very quick' and contextually fits in the sentence and makes the explanation of the sentence as 'please include all the related details in the email for a quick reply.
The other optons
Question : If $\sin \theta-\cos \theta=\frac{4}{5}$, then find the value of $\sin \theta+\cos \theta$.
Option 1: $ \frac{5}{\sqrt{34}} $
Option 2: $ \frac{5}{\sqrt{24}} $
Option 3: $ \frac{\sqrt{34}}{5} $
Option 4: $ \frac{\sqrt{24}}{5}$
Correct Answer: $ \frac{\sqrt{34}}{5} $
Solution : $\sin \theta-\cos \theta=\frac{4}{5}$ ⇒ $(\sin \theta-\cos \theta)^2=(\frac{4}{5})^2$ ⇒ $\sin^2 \theta + \cos^2 \theta -2\sin \theta \cos \theta = \frac{16}{25}$ ⇒ $1-2\sin \theta \cos \theta = \frac{16}{25}$ ⇒ $2\sin \theta \cos \theta = \frac{25-16}{25}$ ⇒ $2\sin \theta \cos \theta = \frac{9}{25}$ -------------(i) Adding $\sin^2
Question : Directions: In the following question, some parts of the sentence may have errors. Find out which part of the sentence has an error and select the appropriate option. If the sentence is free from error, select "No Error".
The internal and external environment we (1) / experience in our thoughts, feelings and the (2) / world around us also has an affect. (3) / No Error (4)
Option 1: (1)
Option 2: (2)
Option 3: (3)
Option 4: (4)
Correct Answer: (3)
The word "affect" should be replaced by "effect". "Affect" is a verb that means to produce a change or influence something, while "effect" is a noun that refers to a change that occurred as a result of
Question : Directions: Which of the following numbers will replace the question mark (?) in the given series? 11, ?, 20, 29, 41, 56
Option 1: 16
Option 2: 13
Option 3: 15
Option 4: 14
Correct Answer: 14
Solution : Given: 11, ?, 20, 29, 41, 56
Add the multiples of 3 to the previous number to get the following number – 11 + 3 = 14; 14 + 6 = 20; 20 + 9 = 29; 29 + 12 = 41; 41 + 15
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