Staff Selection Commission Combined Graduate Level Exam
Question : Directions: In a row of people all facing north, Prince is 5th from the right end. Amit is 15th from the right end. Amit is exactly between Prince and Aditya. If Aditya is sixth from the left end of the line, how many people are there in the row?
Option 1: 29
Option 2: 31
Option 3: 30
Option 4: 32
Correct Answer: 30
Solution : Given: Prince is 5th from the right end. Amit is 15th from the right end. Amit is exactly between Prince and Aditya. Aditya is sixth from the left end of the line.
→The number of people between Amit and Prince = (Position of Amit from
Question : A coconut tree swings with the wind in such a manner that the angle covered by its trunk is 18°. If the topmost portion of the tree covers a distance of 44 metres, find the length of the tree. ( $\tan 18°$ = 0.3249).
Option 1: 120 metres
Option 2: 210 metres
Option 3: 140 metres
Option 4: 70 metres
Correct Answer: 140 metres
Solution : Let the length of the tree be $l$ metres. According to the question, $2\pi l×\frac{18°}{360°}=44$ ⇒ $\frac{44l}{7}×\frac{1}{20}=44$ ⇒ $l=140$ metres Hence, the correct answer is 140 metres.
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) is/are followed in all the number pairs except one. Find that odd number pair.
Option 1: 7 : 46
Option 2: 13 : 166
Option 3: 9 : 78
Option 4: 48 : 144
Correct Answer: 48 : 144
Solution : Let's check the options – First option: 7 : 46→(7)2 – 3 = 49 – 3 = 46 Second option: 13 : 166→(13)2 – 3 = 169 – 3 = 166 Third option: 9 : 78→(9)2 – 3 = 81
Question : The area of triangle formed by the straight line $3x + 2y = 6$ and the co-ordinate axes is:
Option 1: 3 square units
Option 2: 6 square units
Option 3: 4 square units
Option 4: 8 square units
Correct Answer: 3 square units
Solution : The area of a triangle formed by a line and the coordinate axes $=\frac{1}{2} \times \text{base} \times \text{height}$ The line $3x + 2y = 6$ At $y = 0⇒x = \frac{6}{3} = 2$ At $x = 0⇒y = \frac{6}{2} = 3$ So, the
Question : If $\left(y+\frac{1}{y}\right)=4$, then find the value of $\left(y^6+\frac{1}{y^6}\right)$.
Option 1: 2702
Option 2: 2704
Option 3: 4096
Option 4: 2706
Correct Answer: 2702
Solution : Given: $\left(y+\frac{1}{y}\right)=4$ Squaring both sides, we get ⇒ $\left(y+\frac{1}{y}\right)^{2}=4^{2}$ ⇒ $y^{2}+\frac{1}{y^{2}}=16-2$ ⇒ $y^{2}+\frac{1}{y^{2}}=14$ Cubing both sides, we get ⇒ $(y^{2}+\frac{1}{y^{2}})^3=14^3$ ⇒ $\left(y^6+\frac{1}{y^6}\right)+3×\left(y^2×\frac{1}{y^2}\right)×\left(y^2+\frac{1}{y^2}\right)=2744$ ⇒ $\left(y^6+\frac{1}{y^6}\right)+3×14=2744$ ⇒ $\left(y^6+\frac{1}{y^6}\right)=2744-42$ $\therefore \left(y^6+\frac{1}{y^6}\right)=2702$ Hence, the correct answer is 2702.
Question : If $a+b+c$ = 6 and $ab+bc+ca$ = 11, then the value of $bc(b+c)+ca(c+a)+ab(a+b)+3abc$ is:
Option 1: 33
Option 2: 66
Option 3: 55
Option 4: 23
Correct Answer: 66
Solution : Given: $a+b+c$ = 6 and $ab+bc+ca$ = 11 To find: $bc(b+c)+ca(c+a)+ab(a+b)+3abc$ = $b^2c+bc^2+c^2a+ca^2+a^2b+ab^2+abc+abc+abc$ = $bc(a+b+c)+ac(a+b+c)+ab(a+b+c)$ = $(a+b+c)(ab+bc+ac)$ Putting the values, we get ⇒ 6$×$11 = 66 Hence, the correct answer is 66.
Question : Potato is a_____.
Option 1: root
Option 2: stem
Option 3: bud
Option 4: fruit
Correct Answer: stem
Solution : The answer is a stem.
Potato (Solanum tuberosum) is a starchy, edible tuber that is a modified underground stem, also known as a tuber. A tuber is an expanded storage structure used by plants to store nutrients. Potato plants grow underground and produce these tubers
Question : Directions: A watch company produces four different products. The sale of these products in lakhs during 2005 and 2010 is shown in the following bar diagram. Study the graph and answer the question.
The sales of table clocks in 2010 were less than the sales of wall clocks in 2010 nearly by:
Option 1: 70.5%
Option 2: 69.05%
Option 3: 68.05%
Option 4: 62.05%
Correct Answer: 69.05%
Solution : As per the given graph, The sales of table clocks in 2010 = 9.5 lakh The sales of wall clocks in 2010 = 30.7 lakh The required percentage = $\frac{30.7-9.5}{30.7}$ × 100 = $\frac{21.2}{30.7}$ × 100 = 69.05% Hence, the correct answer is 69.05%.
Question : An electronic store owner allows two successive discounts of 20% and 25% on each item. The store has a reward points scheme that enables a customer to get free shopping worth INR 0.10 on every 1 reward point credited to the customer's account on previous purchases from the store. A customer decides to buy a laptop that is marked at INR 72,000. What will be its net selling price if he has 2850 reward points to his credit?
Option 1: INR 43,200
Option 2: INR 42,915
Option 3: INR 42,215
Option 4: INR 42,942
Correct Answer: INR 42,915
Solution : The first discount is 20% on the marked price. Price after the first discount = 80% × marked price = 0.8 × 72,000 = INR 57,600 The second discount is 25% on the price after the first discount. Price after the second discount =
Question : Find the Simple Interest on INR 27,000 at $14 \frac{2}{3}$% per annum for 8 months.
Option 1: INR 2,600
Option 2: INR 2,630
Option 3: INR 2,610
Option 4: INR 2,640
Correct Answer: INR 2,640
Solution : Given: Principal = INR 27,000 Rate of interest = $14 \frac{2}{3}$% Time period = 8 months = $\frac{8}{12}=\frac{2}{3}$ year. Simple interest = $\frac{\text{Principal × Rate × Time}}{100}$ = $\frac{27000×\frac{44}{3}×\frac{2}{3}}{100}$ = 60 × 44 = INR 2,640. Hence, the correct answer is INR 2,640.
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