Staff Selection Commission Combined Higher Secondary Level Exam
Question : $\triangle A B C$ inscribe in a circle with centre O. If AB = 9 cm, BC = 40 cm, and AC = 41 cm, then what is the circum-radius of the triangle?
Option 1: $20 \frac{1}{2} \mathrm{~cm}$
Option 2: $12 \frac{1}{2} \mathrm{~cm}$
Option 3: $18 \frac{1}{2} \mathrm{~cm}$
Option 4: $16 \frac{1}{2} \mathrm{~cm}$
Correct Answer: $20 \frac{1}{2} \mathrm{~cm}$
Solution : Given: $\triangle A B C$ inscribe in a circle with centre O. AB = 9 cm, BC = 40 cm, and AC = 41 cm Also, we can see $9^2+40^2=1681=41^2$ So, it is a right triangle. Hypotenuse = AC = 41 cm For
Question : Rearrange the parts of the sentence in the correct order. The Supreme Court P. must remind the state to act constitutionally, Q. lawfully and justly in every case across the R. country, especially in sensitive matters involving S. those who oppose the party in office with peaceful means
Option 1: PQRS
Option 2: PQSR
Option 3: QPSR
Option 4: QRSP
Correct Answer: PQRS
Solution : The correct choice is the first option: PQRS.
The logical flow of the order is as follows:
The sentence begins by introducing the subject, "The Supreme Court". It then establishes the directive or duty that the Supreme Court must fulfil, which is to "remind the
Question : The digit in the unit's place of the product 49237 × 3995 × 738 × 83 × 9 is:
Option 1: 0
Option 2: 7
Option 3: 5
Option 4: 6
Correct Answer: 0
Solution : The product of unit digits of the 2nd and 3rd numbers is (5 × 8) = 40. The unit digit of this product is 0. So, the digit in the unit's place of the product of 49237 × 3995 × 738 × 83 × 9
Question : The lengths of the two sides of a triangle are 14 cm and 9 cm. Which of the options below can be the length of the third side?
Option 1: 17 cm
Option 2: 23 cm
Option 3: 24 cm
Option 4: 5 cm
Correct Answer: 17 cm
Solution : We know that the sum of the length of either two sides of a triangle must be more than the third side. So, the third side < (14 + 9) Or, the third side < 23 Also, the difference in lengths of any two
Question : A car travels at a speed of 60 km/h and covers a particular distance in one hour. How long will it take for another car to cover the same distance at 40 km/h?
Option 1: 2.5 hours
Option 2: 2 hours
Option 3: 1.5 hours
Option 4: 1 hour
Correct Answer: 1.5 hours
Solution : The distance covered by the first car in one hour at 60 km/h. Distance = Speed × Time = 60 × 1 = 60 km. The time is taken to cover the same distance at a speed of 40 km/h. Time = $\frac{\text{Distance}}{\text{Speed}} =
Question : Directions: Select the option in which the numbers share the same relationship in the set as that shared by the numbers in 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.) (7, 21, 343) (8, 24, 512)
Option 1: (8, 50, 512)
Option 2: (5, 10, 225)
Option 3: (11, 66, 1331)
Option 4: (9, 27, 729)
Correct Answer: (9, 27, 729)
Solution : Given: (7, 21, 343); (8, 24, 512)
Multiply the first number by 3, to obtain the second number and find the cube of the first number, to obtain the third number in the given set of numbers – ⇒ (7, 21, 343)→7 ×
Question : Directions: Which answer figure will complete the pattern in the question figure?
Option 1:
Option 2:
Option 3:
Option 4:
Correct Answer:
Solution : On comparing the question figure and all the answer figures, the following figure will combine and make the complete pattern –
Hence, the second option is correct.
Question : If the angles $P, Q$ and $R$ of $\triangle PQR$ satisfy the relation $2 \angle R-\angle P=\angle Q-\angle R$, then find the measure of $\angle R$.
Option 1: $45^{\circ}$
Option 2: $60^{\circ}$
Option 3: $50^{\circ}$
Option 4: $55^0$
Correct Answer: $45^{\circ}$
Solution : We know that the sum of the angles of a triangle = $180^{\circ}$ Let $\angle R = x$ Given: $2 \angle R-\angle P=\angle Q-\angle R$ ⇒ $2x - \angle P = \angle Q -x$ ⇒ $3x = \angle Q+\angle P$ Now, $\angle R + \angle
Question : Directions: What should come in place of (?) in the given series based on the English alphabetical order? DRH, YOG, TLF, OIE, ?
Option 1: JFD
Option 2: KFE
Option 3: IDE
Option 4: KDD
Correct Answer: JFD
Solution : Given: DRH, YOG, TLF, OIE, ?
Subtract 5, 3, and 1 from the place value of the first, second, and third letters of the previous letter cluster to obtain the next letter cluster of the series. First letter of the series→D – 5 = Y;
Question : If the sum of three consecutive composite numbers is 36, then what is the product of the three numbers?
Option 1: 1460
Option 2: 1750
Option 3: 1680
Option 4: 1820
Correct Answer: 1680
Solution : Two consecutive numbers have a maximum difference of 2. So, the composite numbers that satisfy the given condition are 10, 12, and 14. The product of these three numbers = 10 × 12 × 14 = 1680 Hence, the correct answer is 1680.
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