Math – Anvi Classes

Quantitative Aptitude (SSC CGL)

Simplify $\frac{(x^2 – 9)}{x + 3}$

$x – 9$
$x + 3$
$x – 3$
$\sqrt{x^2 – 9}$

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

Cannot be found
16 cm
4 cm
8 cm

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 ₹)?

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?

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

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?

13:11
4:11
11:15
15:4

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?

561347
564914
558380
556367

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?

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	70
Rohit	80	65	80	80	60	60
Mrakian	80	65	85	95	50	50
Tanvi	70	75	65	85	40	60
Taran	65	35	50	77	80	80

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?

$90 \frac{5}{6}\%$
$91 \frac{1}{6}\%$
$95.16\%$
$91\%$

10.

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

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

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

Rohit
Tarun
Mohit
Sumit

11.

Which of the following can be the value of $k$, if $\frac{(88 + 8 \times k – 3 \times 3)}{(6^2 – 7 \times 5 + k^2)} = 17$

2, 7
4, 7
3, 10
1, 10

12.

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 opened together.

3 minutes
5 minutes
4 minutes
6 minutes

13.

If $\cscθ = \frac{5}{3}$, then evaluate $(\sec^2θ – 1) \times \cot^2θ \times (1 + \cot^2θ)$.

$\frac{9}{16}$
$\frac{25}{9}$
$\frac{25}{16}$
$\frac{4}{5}$

14.

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)

Subject	History (175)	Geography (200)	Botany (125)
Ram	54	87	71
Motian	51	79	78
Sliyam	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?

15.

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

$x^2 + 5x + 25$
$x^2 – 25$
$x^2 + 10x + 25$
$x^2 + 25$

16.

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

One side and one angle of both triangles are equal.
These have two equal sides and the same perimeter.
These have the same area and the same base.
These have the same base and the same height.

17.

Rajesh, in his priming 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?

18.

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:

19.

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.

20.

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?

140 s
40 s
70 s
20 s

21.

The value of $\sin^2 30 – \sin^2 40 + \sin^2 45 – \sin^2 55 – \sin^2 35 + \sin^2 45 – \sin^2 50 + \sin^2 60$ is:

22.

The value of $ \cos^2 29^\circ + \cos^2 61^\circ $ is:

$\frac{\sqrt{3}}{2}$
2
0
1

23.

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.

39 cm
29 cm
35 cm
25 cm

24.

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).

11.11%
14.94%
15.11%
18.21%

25.

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

Year	P		Q		R
	Total	Present	Total	Present	Total	Present
2016	45	42	56	45	55	50
2017	50	45	75	55	45	40
2018	64	60	65	45	65	55
2019	80	69	84	72	70	62
2020	55	44	80	66	90	85

In which year was the number of absentees the second highest in total of all centres?

2018
2019
2020
2017