Staff Selection Commission Combined Graduate Level Exam
Question : Which of the following is TRUE? I. $\sqrt[3]{11}>\sqrt{7}>\sqrt[4]{45}$ II. $\sqrt{7}>\sqrt[3]{11}>\sqrt[4]{45}$ III. $\sqrt{7}>\sqrt[4]{45}>\sqrt[3]{11}$ IV. $\sqrt[4]{45}>\sqrt{7}>\sqrt[3]{11}$
Option 1: Only I
Option 2: Only II
Option 3: Only III
Option 4: Only IV
Correct Answer: Only III
Solution : LCM of 3, 2, and 4 is 12. After taking the 12th power, $\sqrt[3]{11}$ → $11^4=14641$ $\sqrt{7}→7^6→49^3=117649$ $\sqrt[4]{45}→45^3=91125$ Comparing the above three terms, we can conclude that $\sqrt{7}>\sqrt[4]{45}>\sqrt[3]{11}$ Hence, the correct answer is 'Only III'.
Question : Litmus is obtained from
Option 1: a bacterium
Option 2: a fungus
Option 3: an alga
Option 4: lichen
Correct Answer: lichen
Solution : The correct option is lichen.
Litmus is a water-soluble natural dye extracted from lichens, which are symbiotic organisms composed of a fungus and an alga or cyanobacterium. Specifically, litmus is obtained from certain species of lichens, such as Roccella tinctoria and related varieties. The lichen
Question : In a circle with centre O, AB is the diameter. P and Q are two points on the circle on the same side of the diameter AB. AQ and BP intersect at C. If $\angle {POQ}=54^{\circ}$, then the measure of $\angle {PCA}$ is:
Option 1: 63º
Option 2: 56º
Option 3: 54º
Option 4: 72º
Correct Answer: 63º
Solution : A circle with the centre O and diameter AB. P and Q are two points on the circle, and $\angle$POQ = 54$^\circ$ Concept used: The angle subtended by the chord at the circumference would be half of the angle subtended at the centre Calculation: We
Question : The average of five positive numbers is 56. If the first number is three-fourths of the sum of the last four numbers, then the average of the last four numbers is:
Option 1: 35
Option 2: 40
Option 3: 30
Option 4: 50
Correct Answer: 40
Solution : Given: The average of five positive numbers is 56. The first number is three-fourths of the sum of the last four numbers. Use the formula, $\text{Average}=\frac{\text{The sum of values}}{\text{The total number of values}}$. Let the sum of the last four numbers be $4x$. ⇒ The
Question : If a certain number of two digits is divided by the sum of its digits, the quotient is 6 and the remainder is 3. If the digits are reversed and the resulting number is divided by the sum of the digits, the quotient is 4 and the remainder is 9. The sum of the digits of the number is:
Option 1: 6
Option 2: 9
Option 3: 12
Option 4: 4
Correct Answer: 12
Solution : Let the number be $10x + y$. Dividend = Divisor × Quotient + Remainder $10x + y = 6(x + y) + 3$ ⇒ $10x + y = 6x + 6y + 3$ ⇒ $10x – 6x + y – 6y = 3$ ⇒ $4x
Question : The book "Azad Bachpan Ki Aur" is written by which author?
Option 1: Kailash Satyarthi
Option 2: Radhakant Bharti
Option 3: Dipak Misra
Option 4: Subhash Chandra
Correct Answer: Kailash Satyarthi
Solution : The correct option is Kailash Satyarthi.
The author of Azad Bachpan ki Aur is Indian Nobel Peace Prize winner Kailash Satyarthi. The book is an anthology of essays by Satyarthi discussing important movements, court decisions, and policy changes that he spearheaded in his pursuit
Question : Two ships are on the opposite of a lighthouse such that all three of them are collinear. The angles of depression of the two ships from the top of the lighthouse are 30° and 60°. If the ships are $230 \sqrt{3}$ m apart, then find the height of the lighthouse (in m).
Option 1: 175.4
Option 2: 165.2
Option 3: 172.5
Option 4: 180.5
Correct Answer: 172.5
Solution : Given: The distance between the ships is BC = $230\sqrt3$ m Let the height of the lighthouse AD be $h$ m. From $\triangle$ABD we get, $\tan30°=\frac{AD}{BD}$ ⇒ BD = $h\sqrt3$ Again from $\triangle$ACD we get, $\tan60°=\frac{AD}{CD}$ ⇒ CD = $\frac{h}{\sqrt3}$ According to the question, $h\sqrt3+\frac{h}{\sqrt3}=230\sqrt3$
Question : With which Australian University Indian Railways has signed an agreement for Dedicated freight corridor?
Option 1: Monash University
Option 2: Victoria University
Option 3: University of Canberra
Option 4: Universit of Sydney
Correct Answer: Monash University
Solution : The correct option is Monash University.
In March 2017, an agreement was made between Monash University's Institute of Railway Technology and the Indian Ministry of Railways Corporation to collaborate on the establishment of a cutting edge railway research and development institute as part of
Question : If $\frac{10x}{3}+\frac{5}{2}(2-\frac{x}{3})=\frac{7}{2}$, then the value of $x$ is:
Option 1: $\frac{3}{5}$
Option 2: $-\frac{5}{3}$
Option 3: $\frac{5}{3}$
Option 4: $-\frac{3}{5}$
Correct Answer: $-\frac{3}{5}$
Solution : Given: $\frac{10x}{3}+\frac{5}{2}(2-\frac{x}{3})=\frac{7}{2}$ ⇒ $\frac{10x}{3}+(5-\frac{5x}{6})=\frac{7}{2}$ ⇒ $\frac{10x}{3}-\frac{5x}{6}=\frac{7}{2}-5$ ⇒ $\frac{20x-5x}{6}=\frac{7-10}{2}$ ⇒ $\frac{15x}{6}=-\frac{3}{2}$ ⇒ $x=-\frac{3}{5}$ Hence, the correct answer is $-\frac{3}{5}$.
Question : Directions: A is D's brother. D is B's father. B and C are sisters. How is C related to A?
Option 1: Cousin
Option 2: Niece
Option 3: Aunt
Option 4: Nephew
Correct Answer: Niece
Solution : As per the given information, the family tree will be as follows –
Here, the quadrilateral represents the male, and the circular figure represents the female in the figure.
So, from the above family tree, C is the niece of A. Hence, the second option
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