SSC CGL 2024 PYQs

Question 1

If p cos A = 2q sin A and 2p cosec A - q sec A = 3, then the value ofp2+4q2is:

Accepted Answer

From p cos A = 2q sin A, find tan A = p/(2q). Substitute sin A and cos A in terms of p and q into the second equation. Simplify to get p^2 + 4q^2 = 4.

Question 2

A rectangular courtyard is 4m 95cm long and 16m 65cm broad. It is to be paved with the square tiles of the same size. Find the least number of such square tiles required to pave the rectangular courtyard.

Accepted Answer

Convert dimensions to cm: 495 cm and 1665 cm. Find HCF of 495 and 1665, which is 15 cm. Number of tiles = (495/15) * (1665/15) = 33 * 111 = 3663. Wait, the options are small. Let's recheck. Ah, the question asks for the LEAST number of tiles, which means the LARGEST possible tile size. HCF(495, 1665) = 15. So, side of square tile = 15 cm. Number of tiles = (495/15) * (1665/15) = 33 * 111 = 3663. This is not in the options. Let's re-read the question. "Find the least number of such square tiles required to pave the rectangular courtyard." This implies the largest possible tile size. Let's recheck HCF. 495 = 3^2 * 5 * 11. 1665 = 3 * 5 * 111 = 3 * 5 * 3 * 37 = 3^2 * 5 * 37. HCF = 3^2 * 5 = 45. So, side of square tile = 45 cm. Number of tiles = (495/45) * (1665/45) = 11 * 37 = 407.

Question 3

The following table shows scores in different subjects obtained by Akshay in school. Study the table and answer the question that follows.SubjectMarks obtainedTotal MarksEnglish73100Hindi5680Science4575Mathematics90125IT4560In which subject did he score the highest marks (in %)?

Accepted Answer

Calculate percentage for each subject: English (73%), Hindi (70%), Science (60%), Mathematics (72%), IT (75%). IT has the highest percentage.

Question 4

The classification of 100 students based on the marks obtained by them in English and Mathematics in an examination is given in the table below. Study the table and answer the question that follows.MARKS OUT OF 5040 and above30 and above20 and above10 and above0 and aboveENGLISH10318092100MATHEMATICS3236581100AGGREGATE7277387100If at least 40% marks in Mathematics are required for pursuing higher studies in Mathematics, how many students will be eligible to pursue higher studies in Mathematics?

Accepted Answer

To pursue higher studies, 40% marks in Mathematics are needed. Since the exam is out of 50, 40% of 50 is 20. From the table, 65 students scored 20 and above in Mathematics.

Question 5

Read the given information and answer the question that follows.The following table gives the percentage of marks obtained by seven students in six different subjects in an examination.The number in the brackets give the maximum marks in each subject.StudentMaths (150)Chemistry (130)Physics (120)Geography (100)History (60)Computer Science (40)Ayush905090607080Aman1008080408070Sajal906070709080Rohit806580806060Tanvi707565854070Tarun653550778080Muskan806585955090If someone secured all the highest scores that have been obtained by some student or the other in the six subjects as given in the table above, what would be the exact overall percentage score obtained by that student?

Accepted Answer

Calculate the highest marks obtained in each subject: Maths (100% of 150 = 150), Chemistry (80% of 130 = 104), Physics (90% of 120 = 108), Geography (95% of 100 = 95), History (90% of 60 = 54), Computer Science (90% of 40 = 36). Sum these highest scores (150+104+108+95+54+36 = 547). Total maximum marks are 150+130+120+100+60+40 = 600. Percentage = (547/600)*100 = 91.166...% which is 91 1/6%.

Question 6

What is the value of sec(t) if tan(t) = (1)/(3) ?

Accepted Answer

Use the identity sec²(t) = 1 + tan²(t). Substitute tan(t) = 1/3 to get sec²(t) = 1 + (1/3)² = 1 + 1/9 = 10/9. Thus, sec(t) = √(10/9) = √10/3.

Question 7

Kiran lent ₹4,000 to two persons such that one part of it at the rate of 8% per annum and the remaining part at the rate of 10% per annum. He got an annual simple interest of ₹352. Then the sum lent at 10% is:

Accepted Answer

Let the amount lent at 10% be X. Then the amount lent at 8% is (4000-X). Set up the equation: (X * 10 * 1)/100 + ((4000-X) * 8 * 1)/100 = 352. Solve for X to get ₹1,600.

Question 8

ΔEFG and ΔHIJ are similar. Also, ∠E = ∠H and ∠F = ∠I. If 3EF = HI and FG = 9 cm, then IJ is equal to ____.

Accepted Answer

For similar triangles, the ratio of corresponding sides is equal. Given 3EF = HI, so HI/EF = 3. Thus, IJ/FG = 3. Since FG = 9 cm, IJ = 3 * 9 = 27 cm.

Question 9

A circular track's inner and outer radii are 25 m and 28 m respectively. The cost (in ₹) of levelling the track at ₹28 per m² is: [Use π = 22/7]

Accepted Answer

Calculate the track's area using π(R² - r²). Substitute R=28, r=25, and π=22/7. Multiply the area by the cost per m² (₹28) to find the total cost.

Question 10

How many years will it take for ₹8,400 to amount to ₹11,928 at a simple interest rate of 7% per annum?

Accepted Answer

Calculate simple interest (11928-8400 = 3528). Use SI = (P*R*T)/100 to find time T. T = (3528 * 100) / (8400 * 7) = 6 years.

Question 11

In triangles ABC and DEF, AB = FD and ∠A = ∠D. The two triangles are congruent by SAS criterion if:

Accepted Answer

For SAS congruence, two sides and the included angle must be equal. Given AB = FD and ∠A = ∠D, the included sides must be AC and DE respectively for congruence.

Question 12

The value of sin230 – sin240 + sin245 – sin255 – sin235 + sin245 – sin250 + sin260 is:

Accepted Answer

Use the identity sin(90-x) = cos(x) and sin^2(x) + cos^2(x) = 1. Pair terms like sin^2(30) and sin^2(60) (which is cos^2(30)) to cancel out, resulting in 0.

Question 13

The points P and S are on the same side of the line segment QR, such that∠PQR=90∘,∠SRQ=90∘andPQ=SR. Select the correct statement.

Accepted Answer

Given ∠PQR = ∠SRQ = 90°, PQ = SR, and QR is common. By SAS congruence (Side-Angle-Side), ∆PQR ≅ ∆SRQ. The angle is included between the sides.

Question 14

X, Y, and Z are three points on a plane with XY = 11 cm, YZ = 13 cm, and XZ = 24 cm. The number of circles that travel through points X, Y, and Z is:

Accepted Answer

For three points to form a circle, they must be non-collinear. Here, XY + YZ = 11 + 13 = 24 cm, which equals XZ. This means X, Y, and Z are collinear, so no circle can pass through them.

Question 15

Study the given bar-graph and answer the question that follows.The bar-graph shows the sales of books (in thousands) from six branches (B1, B2, B3, B4, B5 and B6) of a publishingcompany during two consecutive years 2000 and 2001.The total sales of branch B6 for both the years is what percentage of the total sales of branch B3 for both the years (correct up to two decimal places)?

Accepted Answer

Calculate total sales for B6 (70+80=150) and B3 (95+110=205). Then, divide B6 sales by B3 sales and multiply by 100: (150/205) * 100 = 73.17%.

Question 16

There are two pipes to fill a tank. Together, they can fill the tank in 15 minutes. If one pipe can fill the tank in one and a half times as fast as the other, the faster pipe alone can fill the tank in:

Accepted Answer

Let the slower pipe take 'x' minutes. The faster pipe takes 'x/1.5' = '2x/3' minutes. Their combined rate is 1/x + 3/2x = 1/15. Solving for x gives x=25 minutes for the faster pipe.

Question 17

Find the area of a square, one of whose diagonals is 4.8 m long.

Accepted Answer

The area of a square can be found using the formula (diagonal^2)/2. So, (4.8 * 4.8) / 2 = 23.04 / 2 = 11.52 m^2.

Question 18

Two pipes, A and B, can fill a tank in 10 minutes and 20 minutes, respectively. The pipe C can empty the tank in 30 minutes. All the three pipes are opened at a time in the beginning. However, pipe C is closed 2 minutes before the tank is filled. In what time, will the tank be full (in minutes)?

Accepted Answer

Calculate the combined filling rate of A and B, and the emptying rate of C. For the last 2 minutes, only A and B work. Calculate the remaining work and the time taken by all three pipes together.

Question 19

The value of cos229° + cos261° is :

Accepted Answer

Use the identity cos(90°-θ) = sin(θ). So, cos(61°) = cos(90°-29°) = sin(29°). The expression becomes cos²29° + sin²29°, which equals 1.

Question 20

The marked price of an article is 26% more than its cost price. If a discount of 32% is given, what will be the loss percentage?

Accepted Answer

Assume CP is 100. MP = 100 + 26% of 100 = 126. Selling Price = 126 - 32% of 126 = 126 - 40.32 = 85.68. Loss = 100 - 85.68 = 14.32. Loss percentage is 14.32%.