SSC CHSL 2017 PYQs

Question 1

A carpenter can build a cupboard in 60 hours. After 15  hours he takes a break. What fraction of the cupboard is yet to be built?

Accepted Answer

The carpenter completes 1/60 of the cupboard per hour. In 15 hours, he completes 15/60 = 1/4 of the work. The remaining work is 1 - 1/4 = 3/4 or 0.75.

Question 2

If√(1+CosA)2=x,then find the value of x.

Accepted Answer

Use the identity 1 + cosA = 2cos²(A/2). Substitute this into the expression, simplify the square root, and divide by 2 to get cos(A/2).

Question 3

A student multiplied a number by 5/6 instead of 6/5. What is the percentage error in the calculation?

Accepted Answer

Let the number be x. Correct result is 6x/5. Incorrect result is 5x/6. Error = (6x/5 - 5x/6) = 11x/30. Percentage error = (Error / Correct Value) * 100 = (11x/30) / (6x/5) * 100 = (11/30) * (5/6) * 100 = 30.56%.

Question 4

If x + y = 12 and xy = 32, then what is the value ofx2+y2

Accepted Answer

Use the identity (x+y)² = x² + y² + 2xy. Substitute the given values: 12² = x² + y² + 2(32). This simplifies to 144 = x² + y² + 64. Subtract 64 from 144 to get x² + y² = 80.

Question 5

What is the equation of the line passing through the  point (2,-3) and making an angle of -45°with the positive X-axis?

Accepted Answer

The slope (m) is tan(-45°) = -1. Using the point-slope form y - y1 = m(x - x1) with (2, -3), we get y - (-3) = -1(x - 2), which simplifies to y + 3 = -x + 2, or x + y = -1.

Question 6

If1√(Cosec2A−1)=x,then value of x is

Accepted Answer

Use the identity Cosec²A - 1 = Cot²A. Substitute this into the expression, then simplify the square root and reciprocal to get tanA.

Question 7

Factors of48x3−8x2−93x−45Factors of

Accepted Answer

Test the options by multiplying them out or by substituting a value for x. Option 3 yields the given polynomial 48x³ - 8x² - 93x - 45.

Question 8

Rearrange the parts of the sentence in correct order.The arbitrationPdented China's interestsQin multiple waysRaward has, nevertheless,

Accepted Answer

Start with 'R' (Award has, nevertheless,) as it introduces the subject. Follow with 'P' (dented China's interests) to complete the action. Conclude with 'Q' (in multiple ways) to specify the manner.

Question 9

Choose the antonym of analogue

Accepted Answer

Analogue means similar or comparable. Therefore, its antonym is 'difference,' which implies dissimilarity or distinction.

Question 10

There is 75% increase in an amount in 5 years at simple interest. What will be the compound interest of Rs 40000 after 2 years at the same rate?

Accepted Answer

First, calculate the simple interest rate: 75% increase in 5 years means 15% per year. Then, use this rate to find the compound interest on Rs 40000 for 2 years using the CI formula.

Question 11

P and Q can do a project in 150 and 100 days respectively.  In how many days can they complete 60% of the project if they work together?

Accepted Answer

P's 1-day work = 1/150, Q's 1-day work = 1/100. Combined 1-day work = 1/150 + 1/100 = 5/300 = 1/60. They complete 60% of work in 60 * 0.60 = 36 days.

Question 12

The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 12% per annum is Rs 900. What is the  value of given sum (in Rs)?

Accepted Answer

Use the formula for the difference between CI and SI for 2 years: P(R/100)^2 = Difference. Substitute the given values: P(12/100)^2 = 900. Solve for P to get 62500.

Question 13

Which of the following numbers is completely divisible by 99?

Accepted Answer

A number divisible by 99 must be divisible by both 9 and 11. Check option 1: Sum of digits (5+1+5+7+9=27) is divisible by 9. Alternating sum (9-7+5-1+5=11) is divisible by 11. Thus, 51579 is divisible by 99.

Question 14

If 2(3x-2) < 6-3x and 6x + 2(6-x) > 2x-2, then x can take which of the following values?

Accepted Answer

Solve both inequalities: 6x-4 < 6-3x gives 9x < 10, so x < 10/9. And 6x+12-2x > 2x-2 gives 4x+12 > 2x-2, so 2x > -14, or x > -7. The common range is -7 < x < 10/9. Only -5 satisfies this.

Question 15

Pradeep has done 1/4th of a job in 14 days, Saquib  completes the rest of the job in 56 days. In how many days can they together complete the job?

Accepted Answer

Pradeep does 1/4 work in 14 days, so total work in 56 days. Saquib does 3/4 work in 56 days, so total work in 56 * (4/3) = 224/3 days. Combined rate: 1/56 + 3/224 = 4/224 + 3/224 = 7/224 = 1/32. Together they complete it in 32 days.

Question 16

x and y are two numbers such that their mean  proportion is 8 and third proportion is 512. What is the  value of x and y?

Accepted Answer

Mean proportion of x and y is sqrt(xy) = 8, so xy = 64. Third proportion is y^2/x = 512. Substitute x = 64/y into the second equation to find y=32, then x=2.

Question 17

Improve the bracketed part of the sentence. Any bad habit must be nipped (on) the bud.

Accepted Answer

The correct idiom is 'nip in the bud', meaning to stop something at an early stage. Therefore, 'in' is the appropriate preposition.

Question 18

Which of the following equations has the sum of its roots as 5?

Accepted Answer

For a quadratic equation ax²+bx+c=0, the sum of roots is -b/a. In option 1, a=1, b=-5, so sum = -(-5)/1 = 5.

Question 19

If secA + tanA = x, then find the value of x.

Accepted Answer

We know sec²A - tan²A = 1. Factor this as (secA - tanA)(secA + tanA) = 1. Given secA + tanA = x, so secA - tanA = 1/x. Solving these two equations for secA gives secA = (x + 1/x)/2. Express secA in terms of sinA to find the correct option.

Question 20

Given: 6x + 2(6-x) > 2x -2 < 5x/2 - 3x/4; then x can take which of the following values?

Accepted Answer

Solve the two inequalities separately: 6x + 12 - 2x > 2x - 2 gives x > -7. And 2x - 2 < 10x/4 - 3x/4 simplifies to 2x - 2 < 7x/4, which gives x < 8. So, -7 < x < 8. The only option in this range is 5.