Staff Selection Commission Combined Higher Secondary Level Exam
Question : If $\sin 2\theta=\frac{\sqrt{3}}{2}$, then the value of $\sin 3\theta$ is equal to $(0^{\circ}\leq \theta\leq 90^{\circ})$:
Option 1: $\frac{1}{2}$
Option 2: $1$
Option 3: $0$
Option 4: $\frac{\sqrt{3}}{2}$
Correct Answer: $1$
Solution : $\sin 2\theta=\frac{\sqrt{3}}{2}=\sin 60^{\circ}$ $⇒2\theta = 60^{\circ}$ $⇒\theta = 30^{\circ}$ We know that, $\sin 3\theta = \sin 90^{\circ} = 1$ Hence, the correct answer is $1$.
Question : Who among the following Indian Grandmasters defeated the world number one Magnus Carlsen and became the FTX Crypto Cup 2022 runner-up?
Option 1: Saketh Myneni
Option 2: Vishwanathan Anand
Option 3: R Praggnanandhaa
Option 4: P. Harikrishna
Correct Answer: R Praggnanandhaa
Solution : The correct option is R Praggnanandhaa.
R Praggnanandhaa, the Indian Grandmaster, defeated Magnus Carlsen in the FTX Crypto Cup 2022, securing the runner-up position. Praggnanandhaa had previously triumphed over Carlsen twice in 2022. In the Tata Steel Chess Tournament 2023, he achieved his first
Question : The altitude drawn to the base of an isosceles triangle is 8 cm and its perimeter is 64 cm. The area (in cm2) of the triangle is:
Option 1: 240
Option 2: 180
Option 3: 360
Option 4: 120
Correct Answer: 120
Solution : Let the base of the isosceles triangle as $b\operatorname{ cm }$ and each of the equal sides as $a\operatorname{ cm }$. The altitude drawn to the base = $8\operatorname{ cm }$ The perimeter of the isosceles triangle = $64\operatorname{ cm }$ In an isosceles triangle,
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. AD, EI, JN, PS, ?
Option 1: WY
Option 2: XX
Option 3: WX
Option 4: WW
Correct Answer: WX
Solution : Given: AD, EI, JN, PS, ?
Add consecutive numbers to the place values of the first letters and 5 to the place values of the second letters of the previous term to obtain the next term of the series – AD→A + 4 = E;
Question : Improve the underlined part of the sentence. Choose 'No improvement' as an answer if the sentence is grammatically correct. His father was few proud of his power over the horse.
Option 1: No improvement
Option 2: much proudest
Option 3: very proud
Option 4: very proudly
Correct Answer: very proud
Solution : The correct answer is the third option.
The underlined part of the sentence is improved by adding the word "very" to convey a stronger degree of pride. The addition of "very" enhances the intensity of the pride his father feels. This modification results in
Question : What is the value of $\frac{8 \times 5 \div 25}{7 \div 14 \times 2}-\frac{14 \div 7-5}{7 \div 14-25} ?$
Option 1: $\frac{362}{245}$
Option 2: $\frac{115}{245}$
Option 3: $\frac{306}{245}$
Option 4: $\frac{106}{245}$
Correct Answer: $\frac{362}{245}$
Solution : $\frac{8 \times 5 \div 25}{7 \div 14 \times 2}-\frac{14 \div 7-5}{7 \div 14-25} $ $=\frac{\frac{8}{5}}{1}-\frac{2-5}{\frac{1}{2}-25} $ $=\frac{8}{5}-\frac{-3}{-\frac{49}{2}} $ $=\frac{8}{5}-\frac{6}{49}$ $=\frac{392-30}{245}$ $=\frac{362}{245}$ Hence, the correct answer is $\frac{362}{245}$.
Question : Directions: 34 is related to 15 following a certain logic. Following the same logic, 44 is related to 20. Which of the following is 52 related to, following the same logic?
Option 1: 32
Option 2: 54
Option 3: 20
Option 4: 24
Correct Answer: 24
Solution : Given: 34 is related to 15 and 44 is related to 20.
Like, 34 is related to 15→(34 – 4) ÷ 2 = 30 ÷ 2 = 15 44 is related to 20→(44 – 4) ÷ 2 = 40 ÷ 2 = 20 Similarly, follow
Question : Directions: Select the option that is related to the first number in the same way as the third number is related to the fourth number and the fifth number is related to the sixth number. 12 : ? :: 15 : 1728 :: 11: 512
Option 1: 216
Option 2: 81
Option 3: 729
Option 4: 6561
Correct Answer: 729
Solution : Given: 12 : ? :: 15 : 1728 :: 11 : 512
Like, (15 : 1728)→(15 – 3)3 = (12)3 = 1728 (11 : 512)→(11 – 3)3 = (8)3 = 512 Similarly, follow the same pattern for (12 : ?)→(12 –
Question : Who invented the electric bulb?
Option 1: Thomas More
Option 2: Thomas Alva Edison
Option 3: James Watt
Option 4: None of these
Correct Answer: Thomas Alva Edison
Solution : The correct answer is Thomas Alva Edison.
An electric light, lamp, or light bulb is an electrical component that produces light. It is the most common form of artificial lighting. Thomas Alva Edison created the first electric light bulb for commercial use. A
Question : Directions: A series is given below with one term missing. Choose the correct alternative from the given ones that will complete the series. AN, DQ, GT, JW, ?
Option 1: MA
Option 2: NZ
Option 3: MZ
Option 4: LY
Correct Answer: MZ
Solution : Given: AN, DQ, GT, JW, ?
Add 3 to the place value of each letter of the previous term to obtain the next term in the series – First letter of the series→A + 3 = D; D + 3 = G; G + 3
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