Staff Selection Commission Combined Higher Secondary Level Exam
Question : If the difference between the two numbers is 20 percent of their sum, then what is the ratio of larger number and smaller number?
Option 1: 6 : 5
Option 2: 5 : 4
Option 3: 4 : 3
Option 4: 3 : 2
Correct Answer: 3 : 2
Solution : Let the two numbers be $x$ and $y$. Then, $(x - y) = \frac{20}{100}\times(x + y)$ ⇒ $x - y = \frac{1}{5} (x + y)$ ⇒ $4x = 6y$ ⇒ $\frac{x}{y} = \frac{3}{2}$ Hence, the correct answer is 3 : 2.
Question : At a certain annual rate (rounded off to the nearest integer) of simple interest, a sum of money becomes nine times its original value in 21 years. By how much does the rate of interest change if the same sum of money has to become 12 times its original value in 25 years?
Option 1: Decreases by 6%
Option 2: Increases by 6%
Option 3: Increases by 8%
Option 4: Decreases by 8%
Correct Answer: Increases by 6%
Solution : Let the principal be $x$. In 21 years the simple interest is $9x-x=8x$ In 25 years the simple interest is $12x-x=11x$ Case I: Time = 21 years Simple interest = $\frac{\text{Principal × Rate × Time}}{100}$ ⇒ Rate = $\frac{8x×100}{21x}$ ⇒ Rate = $\frac{800}{21}\approx$
Question : Two trains 320 m and 205 m in length are running towards each other on parallel lines. One train runs at the rate of 70 kmph and the other train runs at the rate of 56 kmph. Find the time they will take to cross each other (in seconds).
Option 1: 10
Option 2: 20
Option 3: 12
Option 4: 15
Correct Answer: 15
Solution : Let $s$ be the relative speed of the trains, $d{_1}$ be the length of the first train, and $d{_2}$ be the length of the second train. ⇒ $s=70+56=126\mathrm{\ km/hr}=126\times \frac{5}{18}\mathrm{\ m/s}=35\mathrm{\ m/s}$ Time $=\frac{d{_1}+d{_2}}{s}=\frac{320+205}{35}=\frac{525}{35}=15$ seconds Hence, the correct answer is 15.
Question : A mixture of 70 litres of wine and water contains 10% of water. How much water must be added to make the water $12 \frac{1}{2}\%$ of the resulting mixture?
Option 1: 5 litres
Option 2: 3 litres
Option 3: 2 litres
Option 4: 4 litres
Correct Answer: 2 litres
Solution : Initial quantity of mixture = 70 litres Quantity of water in the initial mixture = 10% of 70 = 7 litres Let $x$ litres water be added. The final quantity of mixture = 70 + $x$ Quantity of water in the final mixture =
Question : Directions: Which one of the following responses would be a meaningful order of the following in ascending order? 1. Atom 2. Matter 3. Molecule 4. Electron
Option 1: 4, 1, 3, 2
Option 2: 3, 1, 4, 2
Option 3: 3, 4, 1, 2
Option 4: 1, 2, 3, 4
Correct Answer: 4, 1, 3, 2
Solution : Given: 1. Atom 2. Matter 3. Molecule 4. Electron
An electron is part of an atom, and when two or more atoms combine, it makes a molecule, and many more molecules when combined make a matter.
So, the order is 4, 1,
Question : Directions: The second number in the given number pairs is obtained by performing certain mathematical operations(s) on the first number. The same operation(s) are followed in all the number pairs except one. Find that odd number pair.
Option 1: 6 : 12
Option 2: 10 : 60
Option 3: 8 : 40
Option 4: 7 : 21
Correct Answer: 8 : 40
Solution : Let's check each option – First option: 6 : 12; (6 – 4) × 6 = 2 × 6 = 12 Second option: 10 : 60; (10 – 4) × 10 = 6 × 10 = 60 Third option: 8 : 40; (8
Question : The arc length of a sector of a circle that subtends a $22.5^{\circ}$ angle at the centre is given as $16.5$ cm. What will be the radius (in cm) of the circle? [Use $\pi=\frac{22}{7}$]
Option 1: 35
Option 2: 49
Option 3: 42
Option 4: 48
Correct Answer: 42
Solution : Given: Length of a sector = $16.5$ cm $\theta$ = $22.5^\circ$ We know that, Length of the sector = $\frac{\theta}{360^\circ}×2\pi r$ ⇒ $16.5 = \frac{22.5^\circ}{360^\circ}×2\pi r$ ⇒ $16.5 = \frac{1}{16}×2\pi r$ ⇒ $r = \frac{16×16.5×7}{2×22} = 42$ cm Hence, the correct answer is 42.
Question : Which of the following players won silver at the Tokyo Olympics 2020?
Option 1: Mirabai Chanu and Sushil Kumar
Option 2: P. V. Sindhu and Sushil Kumar
Option 3: Ravi Kumar Dahiya and Mirabai Chanu
Option 4: Ravi Kumar Dahiya and Sushil Kumar
Correct Answer: Ravi Kumar Dahiya and Mirabai Chanu
Solution : The correct answer is Ravi Kumar Dahiya and Mirabai Chanu.
Ravi Kumar Dahiya clinched the men's freestyle 57 kg wrestling silver, reaching the final but losing to a Russian Olympic Committee wrestler. Mirabai Chanu secured the women's weightlifting 49
Question : Directions: Which term from among the given options can replace the question mark (?) in the following series to make it logically complete? QX 10, ?, WD 30, ZG 26, CJ 130
Option 1: SB 15
Option 2: TA 6
Option 3: SC 12
Option 4: TB 18
Correct Answer: TA 6
Solution : Given: QX 10, ?, WD 30, ZG 26, CJ 130
In the above-given series, add 3 to the place values of the letters, subtract 4, and multiply 5 alternatively in the numbers to arrive at the next term of the series. First letter of
Question : Directions: In the following question, select the missing number from the given series. 16, 32, 64, 128, ?, 512
Option 1: 320
Option 2: 128
Option 3: 192
Option 4: 256
Correct Answer: 256
Solution : Given: 16, 32, 64, 128, ?, 512
In the above-given series, multiply the previous number by 2 to get the next number. 16 × 2 = 32; 32 × 2 = 64; 64 × 2 = 128; 128 × 2 = 256; 256 × 2
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