Staff Selection Commission Combined Higher Secondary Level Exam
Question : The external fencing of a circular path around a circular plot of land is 33 m more than its interior fencing. The width of the path around the plot is:
Option 1: 5.52 m
Option 2: 5.25 m
Option 3: 2.55 m
Option 4: 2.25 m
Correct Answer: 5.25 m
Solution : Let the internal radius of the circular plot be $r$ m and the width of the path be $x$ m. According to the question, $2\pi (r+x)-2\pi r = 33$ ⇒ $2\pi x = 33$ ⇒ $x=33×\frac{7}{22}×\frac{1}{2}$ ⇒ $x=\frac{21}{4}$ ⇒ $x=$ 5.25 m Therefore, the
Question : The following table represents the number of candidates who appeared (A) and passed (P) in a screening test over four years from four different states. Read the table carefully and answer the question given below: What is the average number of appearing candidates in the screening test from all four states in the year 2021?
Option 1: 4000
Option 2: 3900
Option 3: 3850
Option 4: 3950
Correct Answer: 3950
Solution : Total appearing candidates in 4 states = 2900 + 4700 + 3400 + 4800 ⇒ Total appearing candidates in 4 states = 15800 Average number of appearing candidates in 4 states = $\frac{15800}{4}$ = 3950 Hence, the correct answer is 3950.
Question : Study the given pie chart and answer the question that follows. Percentage-wise distribution of teachers in six different subjects in a school is given in the pie chart. The total number of teachers is 600. The ratio of male and female teachers is 3: 1.
Find the ratio of teachers in English, Sanskrit, and Hindi to teachers in Mathematics, Biology, and Social Studies.
Option 1: 2 : 5
Option 2: 1 : 2
Option 3: 2 : 3
Option 4: 1 : 5
Correct Answer: 2 : 3
Solution : Number of teachers in English = $\frac{20}{100} \times 600$ = 120 Number of teachers in Sanskrit = $\frac{10}{100} \times 600$ = 60 Number of teachers in Hindi = $\frac{10}{100} \times 600$ = 60 Total number of teachers in English, Sanskrit, and Hindi =
Question : Parts of a sentence are given below in jumbled order. Arrange the parts in the correct order to form a meaningful sentence. (A) to simplify filing taxes (B) to a single flat rate (C) the current five rates (D) by narrowing (E) Forbes wanted
Option 1: EBDCA
Option 2: ECDAB
Option 3: EDACB
Option 4: EADCB
Correct Answer: EADCB
Solution : The correct order is the fourth option: EADCB.
Explanation:
Question : Which of the following sports was not played at Commonwealth Games 2022?
Option 1: Shooting
Option 2: Badminton
Option 3: Wrestling
Option 4: Cricket T20
Correct Answer: Shooting
Solution : The correct answer is Shooting.
The exclusion of shooting from the 2022 Birmingham Commonwealth Games was confirmed by Commonwealth Games Federation (CGF) Chief Louise Martin. This decision marks the first time since 1974 that shooting will not be part of the game's roster, attributed
Question : If $3\sin \theta +5\cos \theta =5$, then $5\sin \theta -3\cos \theta$ is equal to:
Option 1: $\pm 3$
Option 2: $\pm 5$
Option 3: $1$
Option 4: $\pm 2$
Correct Answer: $\pm 3$
Solution : Given, $3\sin\theta + 5\cos\theta =5$ squaring both sides, we get, $⇒9\sin^2\theta + 25\cos^2\theta+30\sin\theta \cos\theta =25$ $⇒ 30\sin\theta \cos\theta =25- 9\sin^2\theta - 25\cos^2\theta$--------------------------(1) To find $5\sin\theta-3\cos\theta$, $(5\sin\theta-3\cos\theta)^2 = 25\sin^2\theta+9\cos^2\theta-30\sin\theta \cos\theta$ Using equation(1), we get, $(5\sin\theta-3\cos\theta)^2 = 25\sin^2\theta+9\cos^2\theta-(25-9\sin^2\theta-25\cos^2\theta)$ $⇒ (5\sin\theta-3\cos\theta)^2 = 25\sin^2\theta+9\cos^2\theta-25+9\sin^2\theta+25\cos^2\theta$ $⇒ (5\sin\theta-3\cos\theta)^2 = 34\sin^2\theta+34\cos^2\theta-25$
Question : Directions: By Interchanging the given two numbers (not digits) which of the following equations will not be correct? 7 and 4 I. 4 × 3 – 7 + 8 ÷ 2 = 23 II. 7 × 5 – 9 ÷ 3 + 4 = 24
Option 1: Neither I nor II
Option 2: Only II
Option 3: Only I
Option 4: Both I and II
Correct Answer: Only I
Solution : Given: I. 4 × 3 – 7 + 8 ÷ 2 = 23 II. 7 × 5 – 9 ÷ 3 + 4 = 24
After interchanging the numbers 7 and 4 the equations become – I. 7 × 3 – 4 + 8
Question : In a circle of radius 14 cm, an arc subtends an angle of 90° at the centre. The length of are (in cm) is equal to: (Take $\pi=\frac{22}{7}$)
Option 1: 22
Option 2: 18
Option 3: 20
Option 4: 24
Correct Answer: 22
Solution : The length of an arc in a circle, where \(\theta\) is the angle that the arc subtends at the centre of the circle and \(r\) is the radius of the circle. $ = \frac{\theta}{360} \times 2\pi r$ Substituting the given values, The length of an
Question : Directions: In the following question, the sentence given with a blank is to be filled in with an appropriate word. Select the correct alternative out of the four.
With our _____ income, my wife and I can usually afford two vacations a year.
Option 1: modest
Option 2: simple
Option 3: timid
Option 4: discreet
Correct Answer: modest
Solution : The first option is the correct answer.
Modest income refers to not extravagant earnings i.e., not large but sufficient in size or amount, which is the correct intended meaning of the sentence that the speaker can usually go vacationing twice a year on account of
Question : Who was the first woman of Indian origin to go to space?
Option 1: Nagin Cox
Option 2: Yogita Shah
Option 3: Kalpana Chawla
Option 4: Sirisha Bandla
Correct Answer: Kalpana Chawla
Solution : The correct option is Kalpana Chawla.
The first woman of Indian origin to go to space was Kalpana Chawla. She achieved this milestone on November 19, 1997, when she flew aboard the Space Shuttle Columbia on mission STS-87. Kalpana Chawla, born in Karnal,
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