Staff Selection Commission Combined Graduate Level Exam
Question : If $A=\frac{\sqrt{0.0004} \times \sqrt[3]{0.000008}}{\sqrt[4]{16000} \times \sqrt[3]{125000} \times \sqrt[4]{810}}$ and $B=\frac{\sqrt[3]{0.729} \times \sqrt[4]{0.0016}}{\sqrt{0.16}}$, then what is $A \times B$?
Option 1: $6 \times 10^{–7}$
Option 2: $\frac{7}{4} \times 10^{–8}$
Option 3: $5 \times 10^{–8}$
Option 4: $\frac{7}{3} \times 10^{–7}$
Correct Answer: $6 \times 10^{–7}$
Solution : Given: The values of $A=\frac{\sqrt{0.0004} \times \sqrt[3]{0.000008}}{\sqrt[4]{16000} \times \sqrt[3]{125000} \times \sqrt[4]{810}}$ and $B=\frac{\sqrt[3]{0.729} \times \sqrt[4]{0.0016}}{\sqrt{0.16}}$. $A=\frac{\sqrt{0.0004} \times \sqrt[3]{0.000008}}{\sqrt[4]{16000} \times \sqrt[3]{125000} \times \sqrt[4]{810}}=\frac{\sqrt{(0.02)^2}\times\sqrt[3]{(0.02)^3}}{\sqrt[4]{2^4\times10^3}\times\sqrt[3]{(50)^3}\times{\sqrt[4]{3^4\times10}}}$ $=\frac{{0.02} \times {0.02}}{(2\times50\times3)\times{\sqrt[4]{(10)^3}}\times{\sqrt[4]{10}}}=\frac{{0.02} \times {0.02}}{300\times{{\sqrt[4]{(10)^3\times10}}}}$ ⇒ $A=\frac{{0.02} \times {0.02}}{300\times10}=\frac{0.0004}{3000}$ $B=\frac{\sqrt[3]{0.729} \times \sqrt[4]{0.0016}}{\sqrt{0.16}}=\frac{\sqrt[3]{(0.9)^3} \times \sqrt[4]{(0.2)^4}}{\sqrt{(0.4)^2}}$ ⇒ $B= \frac{0.9\times 0.2}{0.4}=\frac{0.9}{0.2}$ The value of
Question : Who introduced the Zamindari Settlement as a measure of land revenue administration?
Option 1: Lord Lytton
Option 2: Lord Curzon
Option 3: Lord Cornwallis
Option 4: Lord Wellesley
Correct Answer: Lord Cornwallis
Solution : The correct option is Lord Cornwallis.
In 1793, Lord Cornwallis, the Governor-General of India, proposed the Zamindari Settlement. This system was a significant reform in the land revenue administration of British India. The British East India Company acknowledged zamindars, or landowners, as the rightful
Question : Comprehension:
In the following passage, some words have been deleted. Read the passage carefully and select the most appropriate option to fill in each blank.
Ambition is a vital ingredient for success. Without ambition to push us, we will not be (1)_____of great achievements. We all need that special something (2)_____ourselves to give us the willpower to reach a higher goal (3)_____we imagine ourselves capable (4)_____Yet, ambition, (5)_____money and fire, is a good servant, but a bad master.
Select the most appropriate option to fill in the blank number 2.
Option 1: in
Option 2: with
Option 3: without
Option 4: within
Correct Answer: within
Solution : The correct choice is the fourth option.
"Within" in this context means the inner drive or motivation that comes from within oneself. It's what gives us the willpower to reach higher goals.
Question : An exterior angle of a triangle is 115° and one of the interior opposite angles is 45°. The other two angles are:
Option 1: 65° and 70°
Option 2: 60° and 75°
Option 3: 45° and 90°
Option 4: 50° and 85°
Correct Answer: 65° and 70°
Solution : Given: $\angle$ACD = 115°, $\angle$BAC = 45° We know, $\angle$ABC + $\angle$CAB = $\angle$ACD ⇒ $\angle$ABC = 115° - 45° $\therefore$ $\angle$ABC = 70° $\angle$ACB + $\angle$BAC + $\angle$ABC = 180° ⇒ $\angle$ACB + 45° + 70° = 180° $\therefore$ $\angle$ACB = 180°
Question : The tens digit of a two-digit number is larger than the unit digit by 7. If we subtract 63 from the number, the new number obtained is a number formed by the interchange of the digits. Find the number.
Option 1: 81
Option 2: 18
Option 3: 62
Option 4: 26
Correct Answer: 81
Solution : Let the number be $(10x + y)$. According to the question, $x > y$ ⇒ $x - y = 7$ Now, ⇒ $(10x + y) - 63 =10y + x$ Options 1, 2, 3 i.e. (18, 62, 26) is lesser than 63, so we will
Question : Directions: Select the option that is related to the fifth letter cluster in the same way as the second letter cluster is related to the first letter cluster and the fourth letter cluster is related to the third letter cluster. DISMAY : SIDYAM :: DRIVER : IRDREV :: SAFARI : ?
Option 1: SAFIAR
Option 2: IRAFAS
Option 3: FASIRA
Option 4: FSAIRA
Correct Answer: FASIRA
Solution : Given: DISMAY : SIDYAM :: DRIVER : IRDREV :: SAFARI : ?
Split the words DISMAY and DRIVER into two parts. Then reverse the order of the letters of each part to get the required code.
Thus, DISMAY is related to SIDYAM.
Thus, DRIVER is
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.) (6, 16, 8) (5, 15, 9)
Option 1: (4, 12, 11)
Option 2: (3, 11, 11)
Option 3: (3, 19, 11)
Option 4: (4, 32, 8)
Correct Answer: (3, 11, 11)
Solution : Given: (6, 16, 8); (5, 15, 9)
Like, (6, 16, 8)→6 × 8 = 48 and 48 ÷ 3 = 16 (5, 15, 9)→5 × 9 = 45 and 45 ÷ 3 = 15
Let's check the options – First option: (4, 12,
Question : Six years ago, the ratio of ages of A to B was 7 : 5. 4 years from now, the ratio of their ages will be 11 : 9. What is A’s age at present?
Option 1: $24 \frac{1}{2}$ years
Option 2: $22 \frac{1}{2}$ years
Option 3: $23 \frac{1}{2}$ years
Option 4: $21 \frac{1}{2}$ years
Correct Answer: $23 \frac{1}{2}$ years
Solution : Six years ago, the ratio of ages of A to B was 7 : 5. Six years ago the ages of A and B were $7x$ and $5x$ respectively. 4 years from now, the ratio of their ages will be 11 : 9.
In the following passage, some words have been deleted. Read the passage carefully and select the most appropriate option to fill in each blank. The thing nodded vigorously; as it nodded, the left button-eye fell off and (1)_________ (2)__________ the concrete floor. The thing looked around (3)___________ with its one eye, as if it had lost her. The thing twisted bonelessly (4)____________. its one eye was again facing her. And it (5)_________ across the cellar towards her then. Select the most appropriate option to fill in the blank number 1.
Option 1: clattered
Option 2: hissed
Option 3: fizzed
Option 4: buzzed
Correct Answer: clattered
Solution : The first option is correct.
Explanation: The passage describes an object nodding vigorously, losing its left button-eye, and falling to the concrete floor. The most appropriate verb is clattered, which indicates a loud, rattling sound typically associated with objects falling or colliding.
Question : The value of $(0.3)^{[\frac {(200-146)}{(3 \times 3 \times 3)}-3]}$ is:
Option 1: $\frac{10}{3}$
Option 2: $\frac{5}{3}$
Option 3: $\frac{7}{3}$
Option 4: $\frac{8}{3}$
Correct Answer: $\frac{10}{3}$
Solution : Given: $(0.3)^{[\{\frac{(200-146)}{(3 \times 3 \times 3)}\}-3]}$ = $(0.3)^{[\{\frac{54}{27}\}-3]}$ = $(0.3)^{[2-3]}$ = $(0.3)^{-1}$ = $\frac{1}{0.3}$ = $\frac{10}{3}$ Hence, the correct answer is $\frac{10}{3}$.
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