Staff Selection Commission Combined Graduate Level Exam
Question : Directions: A * B means multiply A by B, A @ B means divide A by B, A ? B means add B to A, and A = B means subtract B from A. Then, find the value of – 10 * 10 = 5 * 10 ? 50 @ 10
Option 1: 100
Option 2: 45
Option 3: 1000
Option 4: 55
Correct Answer: 55
Solution : Given: 10 * 10 = 5 * 10 ? 50 @ 10
After replacing the symbols with the mathematical signs as per the direction, the equation becomes – 10 × 10 – 5 × 10 + 50 ÷ 10 = 10 × 10 – 5
Question : Raja and Rocky together can complete painting work in 5 days. Together they both start painting, but after 2 days, Rocky falls sick and leaves the work. If Raja completes the remaining painting in 4 days, find the number of days in which Rocky alone can do the work.
Option 1: 12 days
Option 2: 15 days
Option 3: 20 days
Option 4: 10 days
Correct Answer: 20 days
Solution : Let total work = LCM of 5, 2 and 4 = 20 units 1 day's work of Raja and Rocky together = $\frac{20}{5} = 4$ units Two days work of Raja and Rocky together = 4 × 2 = 8 units $\therefore$ Remaining work
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".
An education in handling money would imply the ability to (oversee) the consequences of overspending or over-borrowing.
(1) foresee
(2) overlook
(3) overvalue
(4) No Improvement
Option 1: (1)
Option 2: (2)
Option 3: (3)
Option 4: (4)
Correct Answer: (1)
Solution : The sentence can be improved using the first option.
Oversee suggests that the person is simply watching over the consequences, without necessarily taking any action to prevent them. Foresee is more precise in this context, as it implies that the person is able to anticipate
Question : Someity is related to which of the following events?
Option 1: Tokyo Olympics 2020
Option 2: Winter Olympics 2022
Option 3: Commonwealth Games 2022
Option 4: Tokyo paralympic 2020
Correct Answer: Tokyo paralympic 2020
Solution : The correct answer is Tokyo Paralympic 2020.
The Tokyo 2020 Paralympics has a mascot named Someity. This name is a combination of the words 'so mighty' and the name of a famous cherry tree type called Somei-yoshino. The mascot represents the Paralympic athletes
Question : Directions: In the following question a series is given, with one number missing. Choose the correct alternative from the given ones that will complete the series. 14, 27, 52, 101, 198, ?
Option 1: 381
Option 2: 395
Option 3: 391
Option 4: 394
Correct Answer: 391
Solution : Given: 14, 27, 52, 101, 198, ?
Multiply each number by 2 and subtract consecutive natural numbers from it to find the next term – (14 × 2) – 1 = 28 – 1 = 27; (27 × 2) – 2 = 54 – 2
Question : If $2x+\frac{9}{x}=9$, what is the minimum value of $x^2+\frac{1}{x^2}$?
Option 1: $\frac{95}{36}$
Option 2: $\frac{97}{36}$
Option 3: $\frac{86}{25}$
Option 4: $\frac{623}{27}$
Correct Answer: $\frac{97}{36}$
Solution : Given: $2x+\frac{9}{x}=9$ Multiplying both sides by $x$, we get, $⇒2x^2-9x+9=0$ $⇒(2x-3)(x-3)=0$ So, $x= \frac{3}{2},3$ Putting the values of $x$ in the equation, we get When $x=\frac{3}{2}$, $x^2+\frac{1}{x^2}=(\frac{3}{2})^2+\frac{1}{(\frac{3}{2})^2}=\frac{97}{36}=2.69$ When $x=3$, $x^2+\frac{1}{x^2}=3^2+\frac{1}{3^2}=\frac{82}{9}=9.11$ So, the minimum value is $\frac{97}{36}$. Hence, the correct answer is $\frac{97}{36}$.
Question : If $\left(x+\frac{1}{x}\right)=2 \sqrt{2}$ and $x>1$, what is the value of $\left(x^6-\frac{1}{x^6}\right)$?
Option 1: $140\sqrt{2}$
Option 2: $116\sqrt{2}$
Option 3: $144\sqrt{2}$
Option 4: $128\sqrt{2}$
Correct Answer: $140\sqrt{2}$
Solution : $\left(x+\frac{1}{x}\right)=2 \sqrt{2}$ Squaring both sides. ⇒ $ (x+\frac{1}{x})^2= 8$ ⇒ $(x-\frac{1}{x})^2 = (x+\frac{1}{x})^2-4$ ⇒ $(x-\frac{1}{x})^2=8-4=4$ ⇒ $(x-\frac{1}{x})= 2$ So, $(x^2-\frac{1}{x^2})=(x+\frac{1}{x})(x-\frac{1}{x})= 2\sqrt{2}×2=4\sqrt{2}$ Cubing both sides, we get ⇒ $x^6-\frac{1}{x^6}-3(x^2-\frac{1}{x^2})=64×(2\sqrt{2})$ ⇒ $x^6-\frac{1}{x^6}-3(4\sqrt{2})=128\sqrt{2}$ ⇒ $x^6-\frac{1}{x^6}=140\sqrt{2}$ Hence, the correct answer is $140\sqrt{2}$.
Question : Directions: How many rectangles are there in the given figure?
Option 1: 9
Option 2: 10
Option 3: 11
Option 4: 12
Correct Answer: 11
Solution : The given figure can be labeled as shown below –
There are a total of 11 rectangles in the above figure. They are ABCD, EFGH, IJKL, MFNQ, EMQR, EFNR, QNOD, NJPO, QJPD, RNGH, MFOD.
Hence, the third option is correct.
Question : A television and a refrigerator were sold for Rs. 12,000 each. If the television was sold at a loss of 20% of the cost and the refrigerator at a gain of 20% of the cost, the entire transaction resulted in:
Option 1: no loss or gain
Option 2: loss of Rs. 1000
Option 3: gain of Rs. 1,000
Option 4: loss of Rs. 2,000
Correct Answer: loss of Rs. 1000
Solution : Let the cost price of the television be $x$ and the cost price of the refrigerator be $y$. Given that the television was sold at a loss of 20% of the cost. $⇒12000 = x - 0.20x = 0.80x$ $⇒x = \frac{12000}{0.80}
Question : Select the incorrect statement about Gymnosperms.
Option 1: Gymnosperms are found as woody shrubs, trees or lianas and include no true aquatics and few epiphytes.
Option 2: Gymnosperms are seedless flowering plants.
Option 3: Gymnosperms are typically slow in terms of reproduction; up to a year may pass between pollination and fertilisation and seed maturation may require 3 years.
Option 4: Gymnosperms exhibit cones or strobili and naked seeds, but not flowers.
Correct Answer: Gymnosperms are seedless flowering plants.
Solution : The correct answer is Gymnosperms are seedless flowering plants.
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