Q: Simplify: $\frac{(x^2 - 9)}{x + 3} $, Options are a) $\quad x + 3 $, b) $\quad x - 3$, c) $\quad \sqrt{x^2 - 9}$, d) $\quad x - 9$

The Correct Answer is $\quad x - 3$.

Q: 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. Student Maths (150) Chemistry (130) Physics (120) Geography (100) History (60) Computer Science (40) Ayush 90 50 90 60 70 80 Aman 100 80 80 40 80 70 Sajal 90 60 70 70 90 80 Rohit 80 65 80 80 60 60 Tanvi 70 75 65 85 40 70 Tarun 65 35 50 77 80 80 Muskan 80 65 85 95 50 90 If 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?, Options are a) $91 \frac{1}{6}\% $, b) 95.16%, c) 91%, d) $90 \frac{5}{6}\% $

The Correct Answer is $91 \frac{1}{6}\% $.

Q: If cosecθ = 5/3, then evaluate (sec²θ - 1) × cot²θ × (1 + cot²θ)., Options are a) $\frac {25}{16}$, b) $\frac {9}{16}$, c) $\frac {25}{9}$, d) $\frac {4}{5}$

The Correct Answer is $\frac {25}{9}$.

Question 1

The radii of the two cones are in the ratio of 2 : 5 and their volumes are in the ratio of 3 : 5. What is the ratio of their heights?, Options are a) 15 : 4, b) 11 : 15, c) 13 : 11, d) 4 : 11

Accepted Answer

The Correct Answer is 15 : 4.

Question 2

Rajesh, in his printing press, got an order to print some books, out of which he completed $\frac{17}{27}$ of the order in 34 days. In how many days did he complete the entire order of printing?, Options are a) 60, b) 20, c) 54, d) 56

Accepted Answer

The Correct Answer is 54.

Question 3

A grocer professes to sell rice at the cost price, but uses a fake weight of 870 g for 1 kg. Find his profit percentage (correct to two decimal places)., Options are a) 15.11%, b) 14.94%, c) 18.21%, d) 11.11%

Accepted Answer

The Correct Answer is 14.94%.

Question 4

In a circular race of 840 m, A and B start running in the same direction at the same time from the same point at the speeds of 6 m/s and 12 m/s, respectively. After how much time will they meet next?, Options are a) 140 s, b) 20 s, c) 40 s, d) 70 s

Accepted Answer

The Correct Answer is 140 s.

Question 5

The distance between the centres of two circles of radii 22 cm and 10 cm is 37 cm. If the points of contact of a direct common tangent to these circles are M and Q, then find the length of the line segment MQ., Options are a) 35 cm, b) 39 cm, c) 29 cm, d) 25 cm

Accepted Answer

The Correct Answer is 35 cm.

Question 6

Which of the following can be the value of k, if $\frac{(88 \div 8 \times k - 3 \times 3)}{(6^2 - 7 \times 5 + k^2)} = 1? $, Options are a) 1,10, b) 4,7, c) 3,10, d) 2,7

Accepted Answer

The Correct Answer is 1,10.

Question 7

Fill pipe P is 21 times faster than fill pipe Q. If Q can fill a cistern in 110 minutes, find the time it takes to fill the cistern when both fill pipes are open., Options are a) 5 minutes, b) 4 minutes, c) 3 minutes, d) 6 minutes

Accepted Answer

The Correct Answer is 5 minutes.

Question 8

Simplify:
$\frac{(x^2 - 9)}{x + 3} $, Options are a) $\quad x + 3 $, b) $\quad x - 3$, c) $\quad \sqrt{x^2 - 9}$, d) $\quad x - 9$

Accepted Answer

The Correct Answer is $\quad x - 3$.

Question 9

The given table shows the percentage of marks obtained by three students in three different subjects in an institute.
(maximum marks are given in brackets)

Student
			History (175) 
			Geography (200) 
			Botany (125)

Ram
			54 %
			87 %
			71 %

Mohan 
			51 %
			79 %
			78 %

Shyam
			75 %
			49 %
			76%

If in order to pass the exam, a minimum of 105 marks are needed in History, how many students pass in the exam?, Options are a) 3, b) 1, c) 0, d) 2

Accepted Answer

The Correct Answer is 1.

Question 10

Let O be the centre of the circle and AB and CD are two parallel chords on the same side of the radius. OP is perpendicular to AB and OQ is perpendicular to CD. If AB = 10 cm, CD = 24 cm and PQ = 7 cm, then the diameter (in cm) of the circle is equal to:, Options are a) 26, b) 13, c) 12, d) 24

Accepted Answer

The Correct Answer is 26.

Question 11

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.

Student
			Maths (150)
			Chemistry (130)
			Physics (120)
			Geography (100)
			History (60)
			Computer Science (40)

Ayush
			90
			50
			90
			60
			70
			80

Aman
			100
			80
			80
			40
			80
			70

Sajal
			90
			60
			70
			70
			90
			80

Rohit
			80
			65
			80
			80
			60
			60

Tanvi
			70
			75
			65
			85
			40
			70

Tarun
			65
			35
			50
			77
			80
			80

Muskan
			80
			65
			85
			95
			50
			90

If 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?, Options are a) $91 \frac{1}{6}\% $, b) 95.16%, c) 91%, d) $90 \frac{5}{6}\% $

Accepted Answer

The Correct Answer is $91 \frac{1}{6}\% $.

Question 12

Which of the following statements is sufficient to conclude that two triangles are congruent?, Options are a) These have two equal sides and the same perimeter., b) These have the same area and the same base., c) One side and one angle of both triangles are equal., d) These have the same base and the same height.

Accepted Answer

The Correct Answer is These have two equal sides and the same perimeter..

Question 13

The average marks (out of 100) of boys and girls in an examination are 75 and 80, respectively. If the average marks of all the students in that examination are 78. Find the ratio of the number of boys to the number of girls., Options are a) 2 : 3, b) 3 : 4, c) 1 : 3, d) 1 : 2

Accepted Answer

The Correct Answer is 2 : 3.

Question 14

R pays ₹100 to P with ₹5, ₹2 and ₹1 coins. The total number of coins used for paying are 40. What is the number of coins of denomination ₹5 in the payment?, Options are a) 16, b) 17, c) 18, d) 13

Accepted Answer

The Correct Answer is 13.

Question 15

The following table shows the marks (out of 100) obtained by five students in five different subjects.

Who obtained 79% marks in all the subjects taken together?

Student/Subject 
			Maths
			Physics
			Chemistry
			English
			Physical Education

Tarun
			65
			80
			75
			85
			90

Rohit
			69
			76
			80
			88
			94

Mohit
			73
			84
			77
			90
			95

Shobhit
			76
			85
			76
			86
			78

Sumit
			90
			88
			78
			82
			68

, Options are a) Sumit, b) Mohit, c) Rohit, d) Tarun

Accepted Answer

The Correct Answer is Tarun.

Question 16

If cosecθ = 5/3, then evaluate (sec²θ - 1) × cot²θ × (1 + cot²θ)., Options are a) $\frac {25}{16}$, b) $\frac {9}{16}$, c) $\frac {25}{9}$, d) $\frac {4}{5}$

Accepted Answer

The Correct Answer is $\frac {25}{9}$.

Question 17

Simplify:

$\frac{x^3 + 15x^2 + 75x + 125}{x^2 - 25} (x - 5). $, Options are a) x2 + 25, b) x2 + 5x + 25, c) x2 + 10x + 25, d) x2 - 25

Accepted Answer

The Correct Answer is x2 + 10x + 25.

Question 18

The value of$cos^2 29^{\circ} + cos^2 61^{\circ}$is:, Options are a) (√(3))/(2), b) 2, c) 1, d) 0

Accepted Answer

The Correct Answer is 1.

Question 19

If the sum of two sides of an equilateral triangle is 16 cm, then find the third side., Options are a) 4 cm, b) 16 cm, c) Cannot be found, d) 8 cm

Accepted Answer

The Correct Answer is 8 cm.

Question 20

The following table shows the total candidates appeared and number of candidates present, in different exam centres – P, Q and R.
Study the table and answer the question that follows.

"Total' denotes total candidates applied for the centre, 'Present' denotes the candidates appeared.
In which year was the number of absentees the second highest in total of all centres?, Options are a) 2018, b) 2017, c) 2020, d) 2019

Accepted Answer

The Correct Answer is 2019.

Question 21

Mohan borrows a sum of ₹4,22,092 at the rate of 20% per annum simple interest. At the end of the first year, he repays ₹21,679 towards return of principal amount borrowed. If Mohan clears all pending dues at the end of the second year, including interest payment that accrued during the first year, how much does he pay (in ₹) at the end of the second year?, Options are a) 556367, b) 558380, c) 561347, d) 564914

Accepted Answer

The Correct Answer is 564914.

Question 22

In an election between two candidates, y% of the voters did not vote. 10% of the votes cast were declared invalid, while all the valid votes were cast in favour of either of the two candidates. The candidate who got 59.375% of the valid votes cast was declared elected by 2484 votes. If the number of people eligible to vote in that election was 16,000, what is the value of y?, Options are a) 7.2, b) 8.4, c) 8, d) 7.5

Accepted Answer

The Correct Answer is 8.

Question 23

An article is marked at ₹550. If it is sold at a discount of 40%, then the selling price becomes 10% more than its cost price. What is the cost price (in ₹)?, Options are a) 220, b) 330, c) 300, d) 200

Accepted Answer

The Correct Answer is 300.

Question 24

Which of the following can be the value of 'k' so that the number 217924k is divisible by 6?, Options are a) 4, b) 6, c) 2, d) 0

Accepted Answer

The Correct Answer is 2.

Question 25

The value of sin2 30 – sin2 40 + sin2 45 – sin2 55 – sin2 35 + sin2 45 – sin2 50 + sin2 60 is:, Options are a) 1, b) 2, c) 4, d) 0

Accepted Answer

The Correct Answer is 0.

SSC CGL 2024 Math PYQ 9Sept, 1st Shift

CGL 2024 Math PYQ 9Sept, 1st Shift

The radii of the two cones are in the ratio of 2 : 5 and their volumes are in the ratio of 3 : 5. What is the ratio of their heights?

Rajesh, in his printing press, got an order to print some books, out of which he completed \(\frac{17}{27}\) of the order in 34 days. In how many days did he complete the entire order of printing?

A grocer professes to sell rice at the cost price, but uses a fake weight of 870 g for 1 kg. Find his profit percentage (correct to two decimal places).

In a circular race of 840 m, A and B start running in the same direction at the same time from the same point at the speeds of 6 m/s and 12 m/s, respectively. After how much time will they meet next?

The distance between the centres of two circles of radii 22 cm and 10 cm is 37 cm. If the points of contact of a direct common tangent to these circles are M and Q, then find the length of the line segment MQ.

Which of the following can be the value of k, if \(\frac{(88 \div 8 \times k - 3 \times 3)}{(6^2 - 7 \times 5 + k^2)} = 1? \)

Fill pipe P is 21 times faster than fill pipe Q. If Q can fill a cistern in 110 minutes, find the time it takes to fill the cistern when both fill pipes are open.

Simplify:
\(\frac{(x^2 - 9)}{x + 3} \)

Let O be the centre of the circle and AB and CD are two parallel chords on the same side of the radius. OP is perpendicular to AB and OQ is perpendicular to CD. If AB = 10 cm, CD = 24 cm and PQ = 7 cm, then the diameter (in cm) of the circle is equal to:

Which of the following statements is sufficient to conclude that two triangles are congruent?

The average marks (out of 100) of boys and girls in an examination are 75 and 80, respectively. If the average marks of all the students in that examination are 78. Find the ratio of the number of boys to the number of girls.

R pays ₹100 to P with ₹5, ₹2 and ₹1 coins. The total number of coins used for paying are 40. What is the number of coins of denomination ₹5 in the payment?

If cosecθ = 5/3, then evaluate (sec²θ - 1) × cot²θ × (1 + cot²θ).

Simplify:

\(\frac{x^3 + 15x^2 + 75x + 125}{x^2 - 25} (x - 5). \)

The value of\(cos^2 29^{\circ} + cos^2 61^{\circ}\)is:

If the sum of two sides of an equilateral triangle is 16 cm, then find the third side.

An article is marked at ₹550. If it is sold at a discount of 40%, then the selling price becomes 10% more than its cost price. What is the cost price (in ₹)?

Which of the following can be the value of 'k' so that the number 217924k is divisible by 6?

The value of sin² 30 – sin² 40 + sin² 45 – sin² 55 – sin² 35 + sin² 45 – sin² 50 + sin² 60 is:

Student	History (175)	Geography (200)	Botany (125)
Ram	54 %	87 %	71 %
Mohan	51 %	79 %	78 %
Shyam	75 %	49 %	76%

Student	Maths (150)	Chemistry (130)	Physics (120)	Geography (100)	History (60)	Computer Science (40)
Ayush	90	50	90	60	70	80
Aman	100	80	80	40	80	70
Sajal	90	60	70	70	90	80
Rohit	80	65	80	80	60	60
Tanvi	70	75	65	85	40	70
Tarun	65	35	50	77	80	80
Muskan	80	65	85	95	50	90

Student/Subject	Maths	Physics	Chemistry	English	Physical Education
Tarun	65	80	75	85	90
Rohit	69	76	80	88	94
Mohit	73	84	77	90	95
Shobhit	76	85	76	86	78
Sumit	90	88	78	82	68