Staff Selection Commission Combined Higher Secondary Level Exam
Question : The total discount on INR 1860 due after a certain time at 5% is INR 60. find the time after which it is due?
Option 1: 9 months
Option 2: 8 months
Option 3: 7 months
Option 4: 10 months
Correct Answer: 8 months
Solution : Amount = INR 1,860 Rate = 5% Total discount = INR 60 Principal, P = 1860 – 60 = 1,800 Let n be the time(in years). Simple interest, SI = $\frac{PnR}{100}$ ⇒ 60 = $\frac{1800 × n × 5}{100}$ ⇒ n = $\frac{6000}{9000}$ =
Question : A train is moving at the speed of 54 km/h. How many seconds it will take to cover a distance of 450 meters?
Option 1: 60
Option 2: 30
Option 3: 45
Option 4: 36
Correct Answer: 30
Solution : The speed of the train is 54 km/h = $\frac{54 \times 1000}{3600} = 15$ m/s. Distance = 450 meters The time taken to cover a distance is given by the formula: Time = $\frac{\text{Distance}}{\text{Speed}}$ Substituting the given values, Time = $\frac{450}{15} = 30$ seconds Hence,
Question : Directions: In the following question, a series is given, with one term missing. Choose the correct alternative from the given ones that will complete the series. AC, EG, IK, ?
Option 1: LM
Option 2: ON
Option 3: OP
Option 4: MO
Correct Answer: MO
Solution : Given: AC, EG, IK, ?
Add four to the place value of each letter to get the next term – AC; A (1) + 4 = E, C (3) + 4 = G→EG EG: E (5) + 4 = I, G (7) + 4 =
Question : The surface area of a sphere is 616 cm2. The volume of the sphere would be:
Option 1: $1437\frac{1}{3}$ cm3
Option 2: $2100$ cm3
Option 3: $2500$ cm3
Option 4: $1225\frac{3}{5}$ cm3
Correct Answer: $1437\frac{1}{3}$ cm3
Solution : Given: The surface area of a sphere = 616 cm$^2$ We know that, The surface area of a sphere of radius $r$ = $4\pi r^2$ ⇒ $4\pi r^2$ = 616 ⇒ $4×\frac{22}{7}× r^2$ = 616 ⇒ $r^2 = \frac{616×7}{4×22}= 49$ ⇒ $r =
Question : Which experiment was designed to trace the motion of the earth through the 'luminiferous aether', a theoretical substance necessary for the transmission of light?
Option 1: Maxwell and Hertz's experiment
Option 2: Faraday and Henry's experiment
Option 3: Michelson-Morley's experiment
Option 4: Marconi and Thomson's experiment
Correct Answer: Michelson-Morley's experiment
Solution : The correct option is Michelson-Morley's experiment.
The goal of the Michelson-Morley experiment was to determine how quickly the earth moved about the luminiferous aether, which was believed to be a medium that permeated space and carried light waves. Albert Michelson and Edward Morley
Question : A hemispherical dome of a building needs to be painted. If the circumference of the base of the dome is 154 cm, then find the cost of painting it if the cost of painting is INR 4 per 100 cm2. (Use$ ~\pi=\frac{22}{7}$).
Option 1: INR 150.92
Option 2: INR 150.66
Option 3: INR 105.29
Option 4: INR 105.66
Correct Answer: INR 150.92
Solution : Let $R$ be the radius. Circumference of the base of the dome = 154 cm $⇒2\pi R$ = $154$ $⇒R$ = $\frac{154×7}{2×22}$ = $\frac{49}{2}$ cm Surface area of hemispherical dome = $2\pi R^2$ = $2\pi R×R$ = $154×\frac{49}{2}$ = $3773$ cm2 Cost of
Question : In what ratio does a grocer mix tea at INR 26 per kg and INR 32 per kg so that by selling the mixture at INR 30 per kg he may gain 10%?
Option 1: 7 : 26
Option 2: 16 : 7
Option 3: 26 : 7
Option 4: 7 : 16
Correct Answer: 26 : 7
Solution : Given: A grocer mixes tea at INR 26 per kg and INR 32 per kg so that by selling the mixture at INR 30 per kg he may gain 10%. Selling price = INR 30 per kg and gain = 10%. So, the
Question : Two triangles XYZ and UVW are congruent. If the area of $\triangle$XYZ is 58 cm2, then the area of $\triangle$UVW will be:
Option 1: 58 cm2
Option 2: 116 cm2
Option 3: 29 cm2
Option 4: 15 cm2
Correct Answer: 58 cm2
Solution : Two triangles XYZ and UVW are congruent. The area of $\triangle$XYZ is 58 cm2. We know, The areas of two congruent triangles are equal. Hence, the correct answer is 58 cm2.
Question : Two circles touch each other internally. Their radii are 3 cm and 4 cm. What is the length of the biggest chord of the circle with radii of 4 cm which is outside the inner circle?
Option 1: $5 \sqrt{3} \mathrm{~cm}$
Option 2: $6 \sqrt{3} \mathrm{~cm}$
Option 3: $4 \sqrt{3} \mathrm{~cm}$
Option 4: $2 \sqrt{3} \mathrm{~cm}$
Correct Answer: $2 \sqrt{3} \mathrm{~cm}$
Solution : From the figure, MN is the diameter of the smaller circle and PQ is the biggest chord of the greater circle. O is the centre of the greater circle and O' is the centre of the inner circle. Now, OM = MN –
Question : The ratio of three numbers is 3 : 6 : 8. If their product is 9216, then what is the sum of the three numbers?
Option 1: 96
Option 2: 72
Option 3: 144
Option 4: 68
Correct Answer: 68
Solution : Given: The ratio of three numbers is 3 : 6 : 8. Their product is 9216. Let the numbers be $3k, 6k$, and $8k$. Product of $3k × 6k × 8k = 9216$ ⇒ $144k^{3}=9216$ ⇒ $k^{3}=\frac{9216}{144}$ ⇒ $k=\sqrt[3]{64}$ ⇒ $k=4$ The sum of the
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