Staff Selection Commission Combined Higher Secondary Level Exam
Question : In a circle, the length of a chord is 30 cm. The perpendicular distance of the chord from the centre of the circle is 8 cm. Find the diameter of the circle.
Option 1: 28 cm
Option 2: 34 cm
Option 3: 17 cm
Option 4: 30 cm
Correct Answer: 34 cm
Solution : Let AB be the chord and O be the center of the circle. Also, OP is perpendicular to AB In $\triangle$ OPB, OB2 = PB2 + OP2 ⇒ OB2 = 152 + 82 ⇒ OB2 = 225 + 64 ⇒ OB2 = 289 ⇒ OB = $\sqrt{289}$ ⇒ OB = 17 cm Diameter = 2 × OB = 2 × 17 = 34 cm ∴ The diameter of the circle is 34 cm. Hence, the correct answer is 34 cm.
Question : Gross primary deficit is equal to ____________.
Option 1: difference between gross fiscal deficit and interest payments
Option 2: difference between total expenditure and total receipts
Option 3: difference between net borrowings and net capital receipts
Option 4: difference between revenue deficit and capital expenditure
Correct Answer: difference between gross fiscal deficit and interest payments
Solution : The correct answer is the difference between the gross fiscal deficit and interest payments.
Gross primary deficit refers to the difference between the fiscal deficit of the current year and interest payments made on previous borrowings. It displays the government's budget deficit (interest payments excluded). The estimated borrowings of the nation's government represent the fiscal deficit; thus, the larger the deficit, the larger the government's borrowings will be.
Question : In a triangle ABC, two angles A and B are equal. If the exterior angle is at $\angle A = 115°$, find the measure of $\angle C$.
Option 1: $50^{\circ}$
Option 2: $130^{\circ}$
Option 3: $115^{\circ}$
Option 4: $65^{\circ}$
Correct Answer: $50^{\circ}$
Solution : $\angle A = 180° - 115° = 65°$ $\angle B = \angle A = 65°$ The sum of angles of the triangle = 180° $\angle C = 180° - \angle A - \angle B$ $⇒\angle C = 180° - 65°- 65°$ $\therefore\angle C = 50°$ Hence, the correct answer is $50°$.
Question : The 'Poorna Swaraj' resolution was adopted in the annual session of the Indian National Congress held at
Option 1: Bombay
Option 2: Lahore
Option 3: Calcutta
Option 4: Madras
Correct Answer: Lahore
Solution : The correct option is Lahore.
The "Poorna Swaraj" resolution was approved at the Indian National Congress' annual meeting on December 31, 1929, in Lahore. This resolution, known as "Poorna Swaraj," called for total independence (or "Poorna Swaraj") from British colonial rule, and it was a crucial turning point in the Indian independence struggle. The date was chosen by the Congress as India's Independence Day, and after the country gained its independence in 1947, it was changed to the Republic Day of India.
Question : Anil and Arun started for car race from the same point in the same direction and at the same time on a circular track of length 2575 m with speeds 72 km/hr and 90 km/hr, respectively. After how much time (in seconds) will they meet again for the first time?
Option 1: 520
Option 2: 525
Option 3: 510
Option 4: 515
Correct Answer: 515
Solution : Given that Anil and Arun are running in the same direction with the speed of 72 km/hr and 90 km/hr respectively. Length of circular track = 2575 m Relative Speed of Anil and Arun = 90 – 72 = 18 km/h = 18$\times\frac{5}{18} = 5$ m/s ⇒ Time taken by them to meet for the first time on the track while running in the same direction = $\frac{\text{Length of track}}{\text{Relative speed in same direction}}$ ⇒ $\frac{2575}{5}$ = 515 seconds Hence, the correct answer is 515.
Question : As a result of a higher rate of inflation in India, the US dollar will:
Option 1: depreciate
Option 2: constant
Option 3: negligible
Option 4: appreciate
Correct Answer: appreciate
Solution : The correct option is appreciated.
The US dollar will strengthen and the Indian rupee will weaken as a result of India's high rate of inflation. As a result, American goods will be imported into India at a higher rate and Indian goods will be exported to the United States at a lower rate, which will affect both the price of the Indian rupee in terms of dollars and the dollar exchange rate.
Question : Directions: In the following question, four number pairs are given. In each pair, the number on the left side of (–) is related to the number on the right side of (–) with some Logic/Rule/Relation. Three pairs are similar based on the same Logic/Rule/Relation. Select the odd one out from the given alternatives. (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.)
Option 1: 260 – 1560
Option 2: 540 – 3240
Option 3: 480 – 2860
Option 4: 320 – 1920
Correct Answer: 480 – 2860
Solution : Let's check each option – First option: 260 – 1560→260 × 6 = 1560 Second option: 540 – 3240→540 × 6 = 3240 Third option: 480 – 2860→480 × 6 = 2880 ≠ 2860 Fourth option: 320 – 1920→320 × 6 = 1920
So, the third option does not follow the pattern followed by the other three options. Hence, the third option is correct.
Question : By interchanging the digits of a two-digit number, we get a number which is four times the original number minus 24. If the digit at the unit's place of the original number exceeds its digit at ten's place by 7, then the original number is:
Option 1: 29
Option 2: 36
Option 3: 58
Option 4: 18
Correct Answer: 29
Solution : Let the digit in the ten's place and the digit in the unit's place be x and y respectively. Then the original number = 10x + y and the new number = 10y + x. According to the question, 10y + x = 4(10x + y) – 24 or, 10y + x = 40x + 4y– 24 or, 39x – 6y = 24 or, 13x – 2y = 8 -------------------------------(1) Also, given that y – x = 7 so, y = x + 7 -----------------------------------(2) Now, putting the value of y in (1) 13x – 2(x + 7) = 8 or, 13x – 2x – 14 = 8 or, 11x = 22 or, x = 2 Now, from (2) we get, y = 2 + 7 or, y = 9 Putting the value of x and y in the original number, we get, 10x + y = (10 × 2) + 9 = 29 Hence, the correct answer is 29.
Question : From which among the following rulers has the Government of India borrowed and adopted its symbols?
Option 1: Ashoka
Option 2: Krishnadevaraya
Option 3: Pulakeshin
Option 4: Kanishka
Correct Answer: Ashoka
Solution : The correct option is Ashoka.
The Mauryan ruler Ashoka's emblem was copied and used by the Government of India. The Ashoka Chakra is India's national symbol. It is a wheel with 24 spokes. The wheel is a symbol of Dharma, the Hindu notion of justice or responsibility. It is also a representation of the Buddhist notion of the Wheel of Law. The Ashoka Lion Capital is the focal point of the national symbol. It is a four-lion capital that was originally positioned atop the Sarnath pillar, which was constructed by Ashoka in the third century BCE. Lions are a sign of strength and power.
Question : Comprehension:
In the following passage, some words have been deleted. Fill in the blanks with the help of the alternatives given. Select the most appropriate option for each blank.
Teenage is a (1)______ of life that everyone goes through between childhood and adulthood. During this time, teenagers go through many changes, both physically and emotionally. They may experience mood swings, have difficulty expressing their feelings, and sometimes (2)_______ impulsively. Teenagers are also trying to figure out their place in the world and may face pressure from peers, parents, and society to (3)_______ to certain expectations. It is important for teenagers to have a support system that allows them to explore their interests, develop their own identities, and make healthy choices. Despite the challenges that come with being a teenager, it can also be an exciting and transformative time. Teenagers have the (4)_______ to learn new skills, make lifelong friends, and explore new experiences that can shape their future. It is important for parents, educators, and other adults to provide teenagers with guidance, support, and resources that can help them (5)______ the challenges of adolescence.
Select the most appropriate option to fill in the blank no. 5.
Option 1: correlate
Option 2: propagate
Option 3: conclude
Option 4: reduce
Correct Answer: reduce
Solution : The correct choice is the fourth option.
Challenges are addressed to reduce them and create more opportunities.
Therefore, reduce is the most suitable option, as we are talking about challenges related to adolescence.
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