SSC CHSL 2017 PYQs

Question 1

The mean of marks secured by 30 students in division-A of class X is 67, 55 students of division-B is 63 and that of 40 students of division-C is 61. What is the mean of marks of the students of three divisions of Class X?

Accepted Answer

Calculate the total marks for each division (students × mean). Sum these totals and divide by the total number of students (30+55+40 = 125) to find the overall mean.

Question 2

Chords PQ and RS of a circle extended externally intersect  at point T. Length of the segment PT, if lengths of QT, RT and ST are 9 cm, 18 cm and 6 cm respectively, is

Accepted Answer

Apply the intersecting chords theorem for external intersection: PT × QT = RT × ST. Substitute the given values: PT × 9 = 18 × 6. Solve for PT: PT = (18 × 6) / 9 = 12 cm.

Question 3

Select the synonym of 'splayed'

Accepted Answer

'Splayed' means to spread out or apart, especially awkwardly. Therefore, 'spread' is the most direct synonym, indicating an outward extension.

Question 4

Select the synonym of incinerate

Accepted Answer

Incinerate means to destroy by burning. Ignite means to set on fire or to cause to burn. Thus, ignite is the closest synonym.

Question 5

If a merchant offers a discount of 20% on the list price, then she makes a loss of 16%. What % profit or % loss will she make if she sells goods at a discount of 10% of the list price?

Accepted Answer

Assume list price is 100. Selling price at 20% discount is 80. If 80 is 84% of cost price (100-16), then CP is 80/0.84 ≈ 95.24. At 10% discount, SP is 90. Loss = (95.24 - 90) / 95.24 ≈ 5.5%.

Question 6

If 5A = 13B = 7C; find the value of A : B : C.

Accepted Answer

Let 5A = 13B = 7C = k. Then A = k/5, B = k/13, C = k/7. The ratio A:B:C is 1/5 : 1/13 : 1/7. Multiply by LCM(5,13,7) = 455 to get 91:35:65.

Question 7

In an army selection process, the ratio of selected to unselected candidates was 9:2. If 80 less had applied and 20 less selected, the ratio of selected to unselected would have been 5:1. How many candidates had applied for the process?

Accepted Answer

Let selected be 9x and unselected 2x. Total applicants = 11x. In the second scenario, (9x-20) / (2x-60) = 5/1. Solving this equation gives x=280. Total applicants = 11 * 280 = 3080.

Question 8

If tanA - cotA = x, then value of x is?

Accepted Answer

Convert tanA and cotA to sinA/cosA and cosA/sinA respectively. Combine them to get (sin²A - cos²A)/(sinAcosA). Use sin²A = 1 - cos²A to simplify the numerator to (1 - 2cos²A).

Question 9

If cot(A + B) = x, then value of x is

Accepted Answer

The trigonometric identity for cot(A + B) is (cotA cotB - 1) / (cotB + cotA). Comparing this with the given equation, x equals this expression.

Question 10

ABCD is a parallelogram. Co-ordinates of A, B and C are  (5,0), (-2,3) and (-1,4) respectively. What will be the equation of line AD?

Accepted Answer

In a parallelogram, diagonals bisect each other. Find the midpoint of AC and use it to find D. Then, calculate the slope of AD and use point-slope form to get the equation.

Question 11

If a + b = 11 anda2+b2=61, then value of ab is

Accepted Answer

Use the identity (a+b)² = a² + b² + 2ab. Substitute the given values: 11² = 61 + 2ab. This simplifies to 121 = 61 + 2ab, so 2ab = 60, and ab = 30.

Question 12

Select the antonym of ogle

Accepted Answer

To 'ogle' means to stare in a lecherous or unpleasant way. The direct opposite is to 'ignore', meaning to pay no attention to someone or something.

Question 13

The sum of all prime numbers between 30 and 42 is

Accepted Answer

Identify prime numbers between 30 and 42: 31, 37, 41. Sum them up: 31 + 37 + 41 = 109. This is the correct answer.

Question 14

To travel 708 km, an Express train takes 6 hours more than Rajdhani train. If however, the speed of the Express train is doubled, it takes 3 hours less than  Rajdhani train. What is the speed of Rajdhani train?

Accepted Answer

Let Rajdhani's speed be R and Express's speed be E. Formulate equations based on time differences. Solve the system of equations to find R. The correct speed is 59 km/hr.

Question 15

If sin 30° + cos 45° = X, then the value of X.

Accepted Answer

Substitute the standard values: sin 30° = 1/2 and cos 45° = 1/√2. Add them to get X = 1/2 + 1/√2. Rationalize and simplify to (1+√2)/2.

Question 16

What is the equation of the line passing through the point (-1,3) and having x-intercept of 4 units?

Accepted Answer

The x-intercept is 4, so the line passes through (4,0). Using the two-point form with (-1,3) and (4,0), the slope is (0-3)/(4-(-1)) = -3/5. The equation is y - 0 = (-3/5)(x - 4), which simplifies to 5y = -3x + 12, or 3x + 5y = 12.

Question 17

A shopkeeper, sold almonds at the rate Rs 1250 per kg and bears a loss of 7%. Now if he decides to sell it at Rs 1375 per kg, what will be the result?

Accepted Answer

First, calculate the cost price (CP) using the initial selling price (SP) and loss percentage. Then, use this CP and the new SP to find the new profit/loss percentage.

Question 18

At what rate of compound interest per annum will a sum  of Rs 50000 become Rs 73205 in 2 years?

Accepted Answer

Use the compound interest formula A = P(1 + R/100)^T. Substitute A=73205, P=50000, T=2. Solve for R. (1+R/100)^2 = 73205/50000 = 1.4641. Taking square root, 1+R/100 = 1.21, so R = 21%.

Question 19

What is the value of tan-240°?

Accepted Answer

tan(-240°) = -tan(240°). Since 240° is in the third quadrant, tan(240°) = tan(180° + 60°) = tan(60°) = √3. Thus, -tan(240°) = -√3.

Question 20

Improve the bracketed part of the sentence. The patient died (of a wound and not of) cancer.

Accepted Answer

When referring to death caused by an injury or external cause, 'from' is used. For diseases, 'of' is correct. So, 'from a wound and not of cancer' is the right usage.