**The Most Expected** Agniveer Mathematics Questions Types for 2024 Exam: To score maximum marks in the Mathematics section of the Agniveer Exam, students should have a clear idea about the types or level of questions that can be asked. As per the analysis of Agniveer last year papers, we have found some most repetitive types of questions that have a very high probability of being in this year too. So, must prepare these important types of questions before the exam to score full marks in the Mathematics section.

These question types are prepared by our expert faculties that have solid conceptual knowledge in this particular field of Indian Defence Exams such as NDA, CDS, AFCAT, CAPF, Agniveer, etc.

Here, you will get more than 10 types of Agniveer Mathematics expected Questions, mentioned one by one with example questions and answers.

**Most Expected Types of Maths Questions in Agniveer Exam 202**4 – Chapterwise

**Type 01: LCM and HCF**

**1. The ratio of 2 numbers is 4 ∶ 5. Their LCM is 700. Find their HCF.**

- (A) 35
**✔** - (B) 140
- (C) 175
- (D) 70

**2. Find the HCF of ^{8}/_{21} , ^{12}/_{35} , ^{32}/_{7}**

- (A) 4/105
**✔** - (B) 4/140
- (C) 4/175
- (D) 4/70

**3. If the ratio of two numbers is 2 : 7 and the product of their L.C.M and H.C.F is 686. Find the greatest number.**

- (A) 14
- (B) 49
**✔** - (C) 7
- (D) 21

**4. The LCM of two numbers is 48. The numbers are in the ratio 2:3. The sum of the numbers is –**

- (A) 28
- (B) 32
- (C) 40
**✔** - (D) 64

**5. Two numbers are in ratio 14 : 9, if HCF and LCM of both numbers are 3 and 378, then find the greater number.**

- (A) 21
- (B) 27
- (C) 28
- (D) 42
**✔**

**6. Six bells commence tolling together and toll at intervals of 2, 4, 6, 8 10 and 12 seconds respectively. In 30 minutes, how many times do they toll together ?**

- (A) 4
- (B) 10
- (C) 15
- (D) 16
**✔**

**Type 02: Ration and Proportion**

**7. If a sum of Rs. 3540 is divided in threeparts in a ratio of 2 : 6 : 7, then the largestpart will be:**

- (A) Rs. 1652
**✔** - (B) Rs. 1416
- (C) Rs. 944
- (D) Rs. 472

**8. Three numbers are in the ratio ^{1}/_{4} : ^{5}/_{9} : ^{7}/_{12} .The difference between the greatest and the smallest number is 180. Find the sum of all the three numbers.**

- (A) 500
- (B) 650
- (C) 750
**✔** - (D) 800

**9. Rs.10000 is divided among 3 persons. If ratio of amount between first and second person is 2 : 1 and between second and third person is 3 : 1, then find the amount get by third person.**

- 1. 3000
- 2. 1000
**✔** - 3. 6000
- 4. 2000

**10. In a bag, there are coins of 25 p, 10 p and 5 p in the ratio of 1 : 2 : 3. If there is Rs. 30 in all, how many 5 p coins are there?**

- a) 50
- b) 100
- c) 150
**✔** - d) 200

**11. A starts business with Rs. 3500 and after 5 months, B joins with A as his partner. After a year, the profit is divided in the ratio 2 : 3. What is B’s contribution in the capital?**

- a) 5000
- b) 1000
- c) 15000
- d) 9000
**✔**

**12. Three partners shared the profit in a business in the ratio 5:7:8. They had partnered for 14 months, 8 months and 7 months respectively. What was the ratio of their investments?**

- a) 20:49:64
**✔** - b) 20:49:28
- c) 20:64:49
- d) 49:20:64

**Type 03: Probability**

**13. A bag contains 5 black and 6 white balls; one balls are drawn at random. What is the probability that the balls drawn are black?**

- (A) 6/11
- (B) 5/6
- (C) 5/11
**✔** - (D) 2/5

**14. A bag contains 8 red ball and 12 orange ball. If a ball is drawn from the bag, then find the probability that the ball is red ball.**

- (A) 1/5
- (B) 3/5
- (C) 2/5
**✔** - (D) 4/5

**15. A bag contains 15 red balls and some green balls. If the probability of drawing a green ball is 1/6, then the number of green balls is**

- (A) 5
- (B) 4
- (C) 3
**✔** - (D) 2

**16. A bag contains 2 black, 3 yellow and 2 purple balls. Two balls are drawn at random. What is the probability that none of the balls drawn is purple?**

- a) 10/21
**✔** - b) 11/21
- c) 4/3
- d) 6/5

**17. What is the probability of drawing a Red Numbered Card from a deck of Cards ?**

- (A) 10/52
**✔** - (B) 27/52
- (C) 26/52
- (D) 25/52

**18. Two dice are thrown simultaneously. Find the probability of getting a sum of more than 7.**

- (A) 7/12
- (B) 1/3
- (C) 5/12
- (D) 19/36
**✔**

**19. What is the probability of getting atleast 2 Heads when a 3 coins are tossed simultaneously.**

- (A) 1/2
**✔** - (B) 1/4
- (C) 1/8
- (D) None

**Also Check Out:-**

**Type 04: Trigonometry **

**20. Find the value of cot1°.cot2°.cot3° _______ cot89°.**

- 1. 0
- 2. 1
**✔** - 3. 2
- 4. 1/2

**21. What is the value of –**

**sin ^{2}60° + tan^{2}45 ° + sec^{2}45 ° – cosec^{2}30 °?**

- (A) 4
- (B) 1/4
- (C) -1/4
**✔** - (D) -4

**22. Find the value of tan135°?**

- (A) 1
- (B) -√3
- (C) -1
**✔** - (D) √3

**23. If **

**then **k =?

- a) cos𝜽
- b) sec𝜽
**✔** - c) sin𝜽
- d) cosec𝜽

**24. Find the value of**

**cot25° × cot35° × cot45° × cot55° × cot65°**

- (A) √3
- (B) 2
- (C) 1
**✔** - (D) 0

**25. Find the value**

- (a) 2
- (b) 1
- (c) 0
- (d) -1
**✔**

**26. If Cot A = 12/5, then the value of** **(SinA + CosA) × Cosec A** **is-**

- (a) 13/5
- (b) 17/5
**✔** - (c) 14/5
- (d) 1

**27. Find the value of x if **

- 1. 1
- 2. 1/2
- 3. √𝟑/𝟐
**✔** - 4. 0

**28. An observer 1.6 m tall is 203 away from a tower. The angle of elevation from his eye to the top of the tower is 30°. The height of the tower is:**

- a) 21.6 m
**✔** - b) 23.2 m
- c) 24.72 m
- d) None of these

**Type 05: Mensuration**

**29. The area of a square is 144 cm ^{2} . What is the perimeter of the square formed with the diagonal of the original square as its side?**

- (A) 48 √𝟐 cm
**✔** - (B) 24 √𝟐 cm
- (C) 48 cm
- (D) 24 cm

**30. If the side of the square is increased by 5 cm, then the area increases by 175 cm2. The side of the square is:**

- (A) 15 cm
**✔** - (B) 20 cm
- (C) 18 cm
- (D) 17 cm

**31. Area of square is 3/5th of area of rectangle. If sides of rectangle are 9 cm and 15 cm, then find the perimeter of the square.**

- 1. 9 cm
- 2. 18 cm
- 3. 36 cm
**✔** - 4. 81 cm

**32. The diagonal of the rectangle is 17 cm and the length is 15 cm. find the area of the rectangle.**

- (A) 160 cm
^{2} - (B) 240 cm
^{2} - (C) 108 cm
^{2} - (D) 120 cm
^{2}**✔**

**33. A rectangular grassy plot is 112 m long and 78 m broad. It has a travel path 2.5 m wide all around it on the sides. Find the area of the path.**

- a) 825 m
- b) 725 m
- c) 925 m
**✔** - d) 900 m

**34. The perimeter of a rectangle and a square are 160 m each. The area of the rectangle is less than that of the square by 100 sq. m. The length of the larger side of the rectangle is :**

- a) 70 m
- b) 60 m
- c) 40 m
- d) 50 m

**35. The perimeter and the area of a rectangular sheet are 42 m and 108 m2, respectively. The length of the diagonal is:**

- a) 12 m
- b) 15 m
- c) 10 m
- d) 14 m

**36. Find the area of the right-angle triangle, if its base is 8 cm and hypotenuse is 17 cm.**

- (A) 52 cm2
- (B) 24 cm2
- (C) 60 cm2
- (D) 30 cm2

**37. If diagonal of cube is 𝟏𝟐 cm, then its volume in cm3**

- a) 18
- b) 9
- c) 6
- d) 8
**✔**

**38. How many 3 metre cubes can be cut from a cuboid measuring 18m×12m×9m ?**

- a) 18
- b) 90
- c) 60
- d) 72
**✔**

**39. If the radius of a sphere is doubled, what is the ratio of the volume of original sphere to that of new sphere**

- a) 1:8
**✔** - b) 8:1
- c) 1:2
- d) 2:1

**40. The slant height of a cone is 13cm. the diameter of the base is 10cm. Find the total surface area of the cone.**

- a) 80π
- b) 10π
- c) 90π
**✔** - d) 70π

**41. The floor of a room is to be paved with tiles of length 60 cm and breadth 40 cm. If the floor of the room is 72 m × 48 m, find the number of tiles required.**

- 1. 10000
- 2. 8000
- 3. 6400
- 4. 14400
**✔**

**42. Area of a circle is equal to the area of a rectangle. Perimeter of rectangle is 150 cm. If length is 9 cm more than the breadth, then what will be the radius of circle?**

- (A) 21 cm
**✔** - (B) 10.5 cm
- (C) 42 cm
- (D) 28 cm

**43. Find the perimeter of the following figure- (All lengths are in cm.)**

- a) 50 cm
- b) 52 cm
- c) 54 cm
- d) 5.4 cm

**Type 06: Speed, Distance and Time **

**44. A man walks at the rate of 5 km/hr for 6 hours and at 4 km/hr for 12 hours. The average speed of the man is:**

- a) 4
- b) 4
^{𝟏}/_{𝟐} - c) 4
^{𝟏}/_{𝟑}**✔** - d) 4
^{𝟐}/_{𝟑}

**45. A car traveling at 40 km/hr completes a journey in 5 hours. At what speed will it have to cover the same distance in 8 hours?**

- (A) 30 km/hr
- (B) 40 km/hr
- (C) 35 km/hr
- (D) 25 km/hr
**✔**

**46. A man travelled from a point A to B at the rate of 25 Kmph and walked back at the rate of 4 Kmph. If the whole journey took 5 hrs 48 minutes, the distance between A and B is**

- a) 30 km
- b) 24 km
- c) 20 km
**✔** - d) 51.6 km

**47. A 900 meter long train crosses a platform with the speed of 90 km/hr. It takes 1 minutes to cross the platform. Find the length of platform.**

- (A) 800 meter
- (B) 1000 meter
- (C) 600 meter
**✔** - (D) 900 meter

**48. The speeds of two trains A and B are in the ratio 3 : 4. If train B takes 2 hours less than train A to travel 480 km then find the speed of train A.**

- 1. 45 km/h
- 2. 80 km/h
- 3. 30 km/h
- 4. 60 km/h
**✔**

**49. Ram has to cover a certain distance in a specified time. If he moves at the speed of 24 kmph, he will get late by 1 hour and if he moves at the speed of 30 kmph, he will reach 1 hour early. Find the distance.**

- (A) 160
- (B) 240
**✔** - (C) 380
- (D) 480

**50. How much time taken to cross a 1600 meter long platform by a 500 meter long train which is running at the speed of 60 km/hr?**

- 1. 156 sec
- 2. 126 sec
- 3. 115 sec
- 4. 220 sec

**51. A boat goes 18 km upstream and comes back to its starting point in 2 h and 24 min. If the speed of the current is 4 km/h, what will be the speed of the boat in still water?**

- a) 18
- b) 14
- c) 16
**✔** - d) 20

**52. A thief is noticed by a policeman from a distance of 500 m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 10 km and 12 km per hour respectively. What is the distance between them after 12 minutes?**

- 1.150m
- 2. 180m
- 3. 100m
**✔** - 4. 130m

**53. A 130 meter long train running at a speed of 45 km/h crosses a platform in 30 seconds. What is the length of the platform?**

- (A) 245 m
- (B) 375 m
- (C) 275 m
- (D) 345 m

**54. A 152.5 meter long train running at a speed of 57 km/h crosses a platform in 39 seconds. What is the length of the platform?**

- (A) 378 m
- (B) 278 m
- (C) 356.5 m
- (D) 465 m

**Type 07: Average **

**55. Find the average of numbers between 8 and 74, which is divided by 7.**

- (A) 49
- (B) 42
**✔** - (C) 56
- (D) 35

**56. The average of three numbers is 45. First number is twice the second number and second number is thrice the third number. Then find the smallest number?**

- (A) 13.50
**✔** - (B) 14.75
- (C) 15
- (D) 17.50

**57. The average marks scored by boys in a class is 72. The average marks of class is 77 and there are total 40 students in the class. If number of girls in class is 25 then find the average marks of girls in class.**

- 1. 78
- 2. 80
**✔** - 3. 82
- 4. 84

**58. Mira scored some runs in her continuous 9 innings. She scored 50 runs in her 10 ^{th} innings and thus her average decreased by 4 runs. What was the average runs at the end of the 10th innings?**

- (A) 80
- (B) 94
- (C) 90
- (D) 86
**✔**

**59. 10 years ago the average age of 4 members of a family was 24 years. The present average age of 6 members after the birth of two children is 24 years. If the difference between the ages of the two children is 2 years, then find the age of the younger child.**

- 1. 3 years
**✔** - 2. 5 years
- 3. 6 years
- 4. 4 years

**Type 08: Simplification**

**60. If [(216) ^{4}÷ 36^{4}] × 6^{5}= 6^{m}, then m = ?**

- a) 13
- b) 11
- c) 10
- d) 9
**✔**

**61. If 𝐱 − ^{𝟏}/_{x}= 𝟓, 𝒕𝒉𝒆𝒏 𝒇𝒊𝒏𝒅 𝒕𝒉𝒆 𝒗𝒂𝒍𝒖𝒆 𝒐𝒇 **

- a) 125
- b) 140
**✔** - c) 135
- d) 150

**62. Find the value of –**

- (A) 115
- (B) 770
- (C) 885
- (D) 1000
**✔**

**63. The value of **

- a) 31/40
- b) 1/8
**✔** - c) 40/9
- d) 40/31

**64. If 𝟑 ^{𝟒𝒙−𝟐} = 𝟕𝟐𝟗, then find the value of x.**

- (A) 4
- (B) 3
- (C) 2
**✔** - (D) 5

**65. Find the value of –**

- (A) 3√12
- (B) 5√2
- (C) 5
**✔** - (D) 2

**66. What will come in place of question mark‘?’ in the following question?**

**4 of 8 + [(6 × 3) + (2 – 5 × 3)] – 2 = ?**

- 1. 20
- 2. 24
- 3. 30
- 4. 35
**✔**

**67. If 3x = 4y, then find the value of (x + y)/(x – y).**

- 1. 7
**✔** - 2. 1/7
- 3. 4
- 4. 1/4

**68. Find the value of ‘?’ in the following question.**

**2 of 3 ÷ 9 × 18 + 1 (6 + 3 ) = ?**

- 1. 20
- 2. 21
- 3. 22
- 4. 24

**69. Find the value of ‘?’ in the following question.**

- a) 94
- b) 115
- c) 168
- d) 84

**70. **Find the value

- 1. 2.5
- 2. 5
**✔** - 3. 25
- 4. 1

**71. If 0.25x = 0.75y, then find the value of ^{(x + y)}/_{(x – y)}.**

- 1. 0
- 2. 1
- 3. 2
- 4. 4

**72. Simplify the following:**

- (A) 4/5
- (B) 16/25
**✔** - (C) 8/25
- (D) 13/8

**Type 09: Time and Work **

**73. X and Y together can complete a piece of work in 12 days, Y and Z can do it 18 days and X and Z can complete the same work in 15 days. If X, Y and Z can together complete the work, approximately how many days will be required to complete the work?**

- (A) 12
- (B) 18
- (C) 14
- (D) 10
**✔**

**74. To complete a certain work, A and B together take 10 days; B and C together take 14 days, and C and A together take 20 days. All the three worked together for 8 days, then A and B left. C alone will complete the remaining work in:**

- (A) 10.66 days
**✔** - (B) 11.5 days
- (C) 13 days
- (D) 20 days

**75. A and B alone can complete work in 9 days and 18 days respectively. They worked together; however 3 days before the completion of the work A left. In how many days was the work completed?**

- 1. 5
- 2. 6
- 3. 7
- 4. 8

**76. P and Q can do a piece of work in 15 days and 20 days respectively. They work for 5 days and P left then in how many days Q alone can finish the remaining work?**

- (A) 𝟖
^{𝟏}/_{𝟑}Days - (B) 7
^{𝟏}/_{𝟑}Days - (C) 𝟖
^{𝟏}/_{𝟐}Days - (D) 8 Days

**77. 6 men or 8 boys can do a piece of work in 18 days, then how many days will 3 men and 5 boys take to do the same work?**

- (A) 16 days
**✔** - (B) 20 days
- (C) 18 days
- (D) 22 days

**78. A can do a piece of work in 6 days. ‘B’ destroy it in 4 days. A does work for 4 days, During the last 2 days of which B has been destroying A’s work. How many more days must A work alone to complete the work?**

- 1. 4
- 2. 7
- 3. 5.5
- 4. 5
**✔**

**79. 6 men and 8 women can complete a piece of work in 10 days while 13 men and 24 women can complete the same piece of work in 4 days. Find the ratio of work efficiency of a man and a woman?**

- (A) 1 : 2
- (B) 2 : 1
**✔** - (C) 2 : 3
- (D) 3 : 2

**Also Check Out:-**

**Type 10: Percentage and Profit-Loss **

**80. If 9 books are purchased at Rs.18 and sold at Rs 20, then the profit % is**

- (A) 11
- (B) 11
^{𝟏}/_{𝟗}**✔** - (C) 12
- (D) 𝟏𝟐
^{𝟏}/_{𝟗}

**81. In an election between two candidates, one got 56% of the total valid votes, 14% of the votes are invalid. If the total number of votes was 90000, what was the number of valid votes the other candidate got?**

- a) 42990
- b) 43344
- c) 52345
- d) 34056
**✔**

**82. Amit’s salary first increased by 5% and then decreased by 5%. What is the percentage change in his salary?**

- (A) 25%
- (B) 0.25%
**✔** - (C) 2.5%
- (D) 1.25%

**83. The cost price of an article is 75% of the marked price. If a discount of 15% is allowed, then the profit or loss percentage is:**

- (A) 12.44% loss
- (B) 15% profit
- (C) 15.55% loss
- (D) 13.33% profit
**✔**

**84. The cost price of 14 articles is equal to the selling price of 10 articles. Find the gain per cent.**

- (A) 20%
- (B) 40%
**✔** - (C) 30%
- (D) 10%

**85. A trader sells his goods at a discount of 8%. He still makes a profit of 15%. In order to make a profit of20%, how much percent discount should he allow?**

- (A) 3
- (B) 4
**✔** - (C) 3.5
- (D) 5

**86. An article is sold for Rs 950 after a loss of 5%. If it was sold for Rs.1040, find the profit percent.**

- 1. 2%
- 2. 4%
**✔** - 3. 6%
- 4. 8%

**87. Two successive discounts of 10% and 20% are equivalent to a single discount of?**

- 1. 28%
**✔** - 2. 27%
- 3. 25%
- 4. 30%

**88. In an exam the ratio of girls and boys is 7 : 5. If 40% of the girls and 60% of the boys passed, then what is the ratio of failed girls to failed boys?**

- 1. 12 : 13
- 2. 16 : 11
- 3. 41 : 11
- 4. 21 : 10
**✔**

**89. If a product is sold at Rs. 564 then a loss of 6% occurs. Find the selling price if the same product is sold at 6% profit.**

- (A) Rs 600
- (B) Rs 636
**✔** - (C) Rs 672
- (D) Rs 650

**90. The population of a town increases every year by 4%. If its present population is 50,000, then after 2 years it will be.**

- (A) 54000
- (B) 54060
- (C) 54080
**✔** - (D) 54800

**91. In a town there are two schools A and B. In school A there are 75% of total students out of which 20% students are failed in exam. If 10% students of school B are failed in exam then find the overall passing percentage of the town.**

- (A) 75%
- (B) 87.5%
- (C) 82.5%
**✔** - (D) 77.5%

**92. Profit earned by selling at Rs. 1540 is same as the loss incurred by selling the article for Rs. 1140. What is the selling price of the article if it sold at 25% profit?**

- (A) Rs. 1600
- (B) Rs. 1680
- (C) Rs. 1520
- (D) Rs. 1675

**93. In an election, The winner gets 60% of the total votes and wins the election by 1200 votes then find the number of total voters in the election.**

- (A) 6000
**✔** - (B) 8000
- (C) 10000
- (D) 12000

**94. There are 55 kg of apples in a box. If 3 kg of these are rotten. The price of the apple box is Rs. 2750. If he sell at Rs. 55 per kg. What is the profit after selling all the apples?**

- (A) Rs. 110
**✔** - (B) Rs. 120
- (C) Rs. 105
- (D) Rs. 95

**95. In an examination, 40% of students failed in English, 20% failed in math. If 10% of the students failed in both these subjects, then what percentage of students passed in both the subject?**

- (A) 50%
- (B) 40%
- (C) 30%
- (D) None of these

**96. A dealer sold a camera for 20% profit on the selling price. Find the selling price if the cost price is Rs. 28,800.**

- (A) Rs. 18,000
- (B) Rs. 36,000
- (C) Rs. 54,000
- (D) Rs. 72,000

**97. 5 kg honey contains 60% sugar. If 3 kg more sugar is added to it then find new sugar percentage.**

- (A) 70%
- (A) 75%
**✔** - (A) 80%
- (A) 90%

**98. Ravi sold two television sets, one at a profit of 10%, and the other at a loss of 10%. Find the overall loss or gain percentage in the overall transaction.**

- (A) Profit, 1%
- (B) Loss, 1%
**✔** - (C) Profit, 2%
- (D) No profit, no loss

**99. By selling an article for Rs 480 a person lost 20%. For what should he sell it to make a profit of 20%?**

- (A) Rs. 675
- (B) Rs. 720
- (C) Rs. 700
- (D) Rs. 750

**100. If the cost of production of an article is 2/5 of its marked retail price. If it is sold at 10% discount then what will be profit?**

- (A) 25%
- (B) 40%
- (C) 50%
- (D) 125%
**✔**

**101. A person bought some apples at the rate of Rs.3 per apple. He again bought the same number of apples at the rate of Rs.4 per apple. If he sold all the apples at the rate of Rs.3 per apple, then find his loss percent.**

- (A) 16.67%
- (B) 12.5%
- (C) 14.28%
**✔** - (D) 10%

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