Staff Selection Commission Combined Graduate Level Exam
Question : The frequency distribution data is given below. If the average age is 17 years, the value of m is: Age (in years): 8, 20, 26, 29 Number of people: 3, 2, m, 1
Option 1: 1
Option 2: 2
Option 3: 3
Option 4: 4
Correct Answer: 1
Solution : Using frequency distribution table: Given: The average age = 17 years According to the question, $\frac{8 × 3+20×2+26×m+29×1}{3+2+m+1} = 17$ ⇒ $\frac{24+40+26m+29}{6+m} = 17$ ⇒ $93+26m = 102+17m$ ⇒ $9m=9$ $\therefore m=1$ Hence, the correct answer is 1.
Question : Article 1of the Constitution declares India as
Option 1: Federal State
Option 2: Quasi -Federal State
Option 3: Unitary State
Option 4: Union of States
Correct Answer: Union of States
Solution : The correct option is Union of States.
According to Article 1 of the Indian Constitution, India is a "Union of States." This proclamation represents India's federal structure, in which authority is shared between the central (Union) government and various states. It creates India
Question : In which year did John Newlands propound the 'Law of Octaves', an innovative concept proposing the periodicity of chemical elements arranged in the order of atomic weight?
Option 1: 1861
Option 2: 1863
Option 3: 1865
Option 4: 1867
Correct Answer: 1865
Solution : The correct option is 1865.
John Newlands introduced the "Law of Octaves" in 1865, which he formulated after noticing that when elements were arranged in ascending order of their atomic weights, every eighth element exhibited similar properties. This parallelism led him to draw an analogy
Question : In a right-angled triangle $\Delta PQR, PR$ is the hypotenuse of length 20 cm, $\angle PRQ = 30^{\circ}$, the area of the triangle is:
Option 1: $50\sqrt{3}\text{ cm}^{2}$
Option 2: $100\sqrt{3}\text{ cm}^{2}$
Option 3: $25\sqrt{3}\text{ cm}^{2}$
Option 4: $\frac{100}{\sqrt{3}}\text{ cm}^{2}$
Correct Answer: $50\sqrt{3}\text{ cm}^{2}$
Solution : $\sin 30^\circ=\frac{PQ}{PR}$ ⇒ $\frac{1}{2}=\frac{PQ}{20}$ ⇒ $PQ=\frac{20}{2}=10$ cm $\cos 30^\circ=\frac{QR}{PR}$ ⇒ $\frac{\sqrt3}{2}=\frac{QR}{20}$ ⇒ $QR=\frac{20\sqrt3}{2}=10\sqrt3$ cm Area of $\triangle PQR=\frac{1}{2}\times PQ \times QR$ $=\frac{1}{2}\times 10 \times10\sqrt3$ $=50\sqrt3\text{ cm}^2$ Hence, the correct answer is $50\sqrt3\text{ cm}^2$.
Question : The angle subtended by the largest chord of the circle to a point on the same circle measures:
Option 1: $<90^{\circ}$
Option 2: $180^{\circ}$
Option 3: $>90^{\circ}$
Option 4: $90^{\circ}$
Correct Answer: $90^{\circ}$
Solution : The angle subtended by the largest chord of the circle to a point on the same circle measures $90^{\circ}$ because the largest chord of a circle is itself the diameter of the circle which subtends $90^{\circ}$ to any point on the circle. Hence, the correct
Question : If a man walks at the rate of 5 km/hr, he misses a train by 7 minutes. However, if he walks at the rate of 6 km/h, he reaches the station 5 minutes before the arrival of the train. The distance he covered to reach the station is:
Option 1: 6 km
Option 2: 7 km
Option 3: 6.25 km
Option 4: 4 km
Correct Answer: 6 km
Solution : The required distance = $\frac{\text{Product of speeds in kmph}}{\text{Difference of speeds in kmph}}×\text{Difference in time in hours}$ = $\frac{5×6}{6-5}×\frac{7+5}{60}$ = 6 km So, the distance he covered to reach the station is 6 km. Hence, the correct answer is 6 km.
Question : A and B can do a piece of work in 8 days, B and C can do the same work in 12 days and A, B, and C complete it in 6 days. Find the number of days required to finish the work by A and C is:
Option 1: 16
Option 2: 8
Option 3: 12
Option 4: 24
Correct Answer: 8
Solution : Let the total work is 1 unit. The efficiency of A and B is $\frac{1}{8}$, the efficiency of B and C is $\frac{1}{12}$ and the efficiency of A, B, and C is $\frac{1}{6}$. Efficiency of A = Efficiency of (A, B, C) – Efficiency of
Question : Study the given triangle and find the length of BC.
Option 1: $\frac{5}{2}$
Option 2: 6
Option 3: 5
Option 4: 3
Correct Answer: 5
Solution : Given $\angle A = 30°$ We have to find the value of BC i.e., $x$. $\sin 30° = \frac{x}{10}$ ⇒ $\frac{1}{2}=\frac{x}{10}$ ⇒ $x=5$ units Hence, the correct answer is 5.
Question : If $\frac{x^2}{yz}+\frac{y^2}{zx}+\frac{z^2}{xy}=3$, then what is the value of $(x+y+z)^3$?
Option 1: 0
Option 2: 1
Option 3: 2
Correct Answer: 0
Solution : Given:$\frac{x^2}{yz}+\frac{y^2}{zx}+\frac{z^2}{xy}=3$ We know the identity, if $(x+y+z)=0$, then $(x^3+y^3+z^3)=3xyz$ Take the LCM of the given expression, we get– $\frac{x^3+y^3+z^3}{xyz}=3$ ${x^3+y^3+z^3}=3(xyz)$ So, $(x+y+z)=0$ The value of $(x+y+z)^3=0$ Hence, the correct answer is 0.
Question : Raman spends 80% of his income. If his income is increased by 25% and the expenditure increases by 10%, what will be the percentage increase in his savings?
Option 1: 17%
Option 2: 70%
Option 3: 77%
Option 4: 85%
Correct Answer: 85%
Solution : Let Raman's income be Rs. 100. Raman spends 80% = $\frac{80}{100}× 100$ = Rs. 80 Raman's savings = 100 – 80 = Rs. 20 If his income is increased by 25%, New income $=\frac{125}{100} × 100 = 125$ If his expenditure increases by 10%, New
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