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Agniveer Army practice questions

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Question 1Mathematics

Simplify: 12 + 6 × 3 − 8 ÷ 4

  1. 26
  2. 30
  3. 28 Correct answer.
  4. 52

Explanation

Under BODMAS, multiplication and division are done before addition and subtraction. Here 6 × 3 = 18 and 8 ÷ 4 = 2, so the expression becomes 12 + 18 − 2 = 28.

Question 2Mathematics

What is 15% of 240?

  1. 40
  2. 24
  3. 16
  4. 36 Correct answer.

Explanation

15% means 15 per hundred, so multiply 240 by 15/100. That gives 3600/100 = 36.

Question 3Mathematics

Find the average of 12, 18, 24, 30 and 36.

  1. 20
  2. 22
  3. 24 Correct answer.
  4. 26

Explanation

The average equals the sum of the observations divided by their number. The sum is 12 + 18 + 24 + 30 + 36 = 120, and 120 ÷ 5 = 24.

Question 4Mathematics

Find the HCF of 36 and 48.

  1. 4
  2. 6
  3. 12 Correct answer.
  4. 24

Explanation

Factorising, 36 = 2² × 3² and 48 = 2⁴ × 3. The highest common factor takes the lowest power of each common prime: 2² × 3 = 12.

Question 5Mathematics

Find the simple interest on ₹5000 at 8% per annum for 3 years.

  1. ₹1500
  2. ₹1200 Correct answer.
  3. ₹1000
  4. ₹900

Explanation

Simple interest is P × R × T ÷ 100. Substituting, 5000 × 8 × 3 ÷ 100 = ₹1200.

Question 6Mathematics

₹720 is divided between two persons in the ratio 5 : 4. What is the larger share?

  1. ₹320
  2. ₹400 Correct answer.
  3. ₹480
  4. ₹360

Explanation

The total number of parts is 5 + 4 = 9, so each part is worth 720 ÷ 9 = ₹80. The larger share is 5 × 80 = ₹400.

Question 7Mathematics

Find the value of √1764.

  1. 38
  2. 44
  3. 42 Correct answer.
  4. 46

Explanation

Since 42 × 42 = 1764, the square root of 1764 is 42. Checking neighbours confirms that no other listed value squares to 1764.

Question 8Mathematics

An article bought for ₹400 is sold for ₹500. What is the profit percentage?

  1. 15%
  2. 30%
  3. 20%
  4. 25% Correct answer.

Explanation

Profit is ₹500 − ₹400 = ₹100, and profit percentage is always calculated on the cost price. Thus 100/400 × 100 = 25%.

Question 9Mathematics

Find the compound interest on ₹8000 at 10% per annum for 2 years, compounded annually.

  1. ₹1500
  2. ₹1720
  3. ₹1680 Correct answer.
  4. ₹1600

Explanation

The amount after 2 years is 8000 × (1.1)² = 8000 × 1.21 = ₹9680. Compound interest is the amount minus the principal, i.e. 9680 − 8000 = ₹1680.

Question 10Mathematics

A can complete a piece of work in 12 days and B in 18 days. Working together, in how many days will they finish it?

  1. 7.5 days
  2. 8 days
  3. 7.2 days Correct answer.
  4. 6.8 days

Explanation

A does 1/12 and B does 1/18 of the work per day, so together they do 1/12 + 1/18 = 5/36 per day. The time taken is the reciprocal, 36/5 = 7.2 days.

Question 11Mathematics

A train covers 360 km at a uniform speed. If the speed had been 5 km/h more, the journey would have taken 1 hour less. Find the speed of the train.

  1. 45 km/h
  2. 40 km/h Correct answer.
  3. 36 km/h
  4. 48 km/h

Explanation

Let the speed be x km/h. Then 360/x − 360/(x + 5) = 1, which simplifies to x² + 5x − 1800 = 0. Solving gives x = 40, so the speed is 40 km/h.

Question 12Mathematics

The circumference of a circle is 44 cm. Find its area.

  1. 144 cm²
  2. 77 cm²
  3. 616 cm²
  4. 154 cm² Correct answer.

Explanation

From 2πr = 44 with π = 22/7, the radius is 7 cm. The area is πr² = (22/7) × 49 = 154 cm².

Question 13Mathematics

A train 150 m long is running at 54 km/h. How long will it take to pass a pole?

  1. 9 s
  2. 12 s
  3. 15 s
  4. 10 s Correct answer.

Explanation

Convert the speed to metres per second: 54 × 5/18 = 15 m/s. To pass a pole the train covers its own length, so the time is 150 ÷ 15 = 10 seconds.

Question 14Mathematics

In what ratio must rice costing ₹30 per kg be mixed with rice costing ₹40 per kg so that the mixture costs ₹34 per kg?

  1. 1 : 2
  2. 3 : 4
  3. 2 : 3
  4. 3 : 2 Correct answer.

Explanation

By the rule of alligation, the ratio of cheaper to dearer is (40 − 34) : (34 − 30) = 6 : 4 = 3 : 2. Indeed, 3 kg at ₹30 and 2 kg at ₹40 give ₹170 for 5 kg, i.e. ₹34 per kg.

Question 15Mathematics

What is the smallest number that must be added to 1234 so that the result is divisible by 9?

  1. 2
  2. 8 Correct answer.
  3. 6
  4. 5

Explanation

A number is divisible by 9 when its digit sum is a multiple of 9. Here 1 + 2 + 3 + 4 = 10, and the next multiple of 9 is 18, so 8 must be added, giving 1242 whose digit sum is 9.

Question 16Mathematics

If 3x − 7 = 2x + 5, then x equals:

  1. −12
  2. 12 Correct answer.
  3. 6
  4. 2

Explanation

Subtract 2x from both sides to get x − 7 = 5, then add 7 to both sides to obtain x = 12. Substituting back confirms 29 = 29.

Question 17Mathematics

The radius of a cylinder is 7 cm and its height is 10 cm. Find its volume, taking π = 22/7.

  1. 154 cm³
  2. 1440 cm³
  3. 1540 cm³ Correct answer.
  4. 3080 cm³

Explanation

Volume of a cylinder is πr²h. Substituting gives (22/7) × 7 × 7 × 10 = 22 × 7 × 10 = 1540 cm³.

Question 18Mathematics

A invests ₹5000 for 12 months and B invests ₹8000 for 6 months in a business. What is the ratio of their shares of the profit?

  1. 5 : 6
  2. 4 : 5
  3. 5 : 4 Correct answer.
  4. 3 : 2

Explanation

Profit shares are proportional to capital multiplied by time. A's figure is 5000 × 12 = 60000 and B's is 8000 × 6 = 48000, so the ratio is 60000 : 48000 = 5 : 4.

Question 19Mathematics

Two successive discounts of 20% and 10% are given on an article. What single discount is equivalent to them?

  1. 30%
  2. 28% Correct answer.
  3. 32%
  4. 25%

Explanation

After a 20% discount the customer pays 80% of the price, and after a further 10% discount pays 90% of that, i.e. 0.8 × 0.9 = 0.72 of the marked price. The equivalent single discount is therefore 100% − 72% = 28%.

Question 20Mathematics

The population of a town increases by 10% in one year and then decreases by 10% in the next year. What is the net change over the two years?

  1. no change
  2. 1% decrease Correct answer.
  3. 1% increase
  4. 2% decrease

Explanation

If the original population is 100, it becomes 110 after the rise and then 110 × 0.9 = 99 after the fall. The net change is a decrease of 1%, because the 10% fall is taken on the larger value.

Question 21Mathematics

Pipe A alone can fill a tank in 12 hours, pipe B alone in 15 hours, and pipe C alone can empty it in 20 hours. If all three are opened together, in how many hours will the tank be filled?

  1. 15 hours
  2. 10 hours Correct answer.
  3. 8 hours
  4. 12 hours

Explanation

Net filling per hour is 1/12 + 1/15 − 1/20 = 5/60 + 4/60 − 3/60 = 6/60 = 1/10. The tank therefore fills in 10 hours.

Question 22Mathematics

The speed of a boat in still water is 10 km/h and the speed of the stream is 2 km/h. How long does the boat take to go 24 km downstream and return to the starting point?

  1. 4.8 hours
  2. 5 hours Correct answer.
  3. 6 hours
  4. 5.5 hours

Explanation

Downstream speed is 10 + 2 = 12 km/h and upstream speed is 10 − 2 = 8 km/h. The times are 24/12 = 2 hours and 24/8 = 3 hours, giving a total of 5 hours.

Question 23Mathematics

If x + 1/x = 3, what is the value of x² + 1/x²?

  1. 6
  2. 11
  3. 7 Correct answer.
  4. 9

Explanation

Squaring both sides gives (x + 1/x)² = x² + 2 + 1/x² = 9. Hence x² + 1/x² = 9 − 2 = 7.

Question 24Mathematics

The angles of a triangle are in the ratio 2 : 3 : 4. What is the largest angle?

  1. 60°
  2. 80° Correct answer.
  3. 90°
  4. 70°

Explanation

The angles total 180°, and the ratio has 2 + 3 + 4 = 9 parts, so each part is 20°. The angles are 40°, 60° and 80°, of which the largest is 80°.

Question 25Mathematics

A and B together can do a piece of work in 12 days, B and C together in 15 days, and A and C together in 20 days. In how many days can A alone do the work?

  1. 36 days
  2. 24 days
  3. 30 days Correct answer.
  4. 20 days

Explanation

Adding the three pair rates gives 1/12 + 1/15 + 1/20 = 1/5, so 2(1/A + 1/B + 1/C) = 1/5 and 1/A + 1/B + 1/C = 1/10. Subtracting B and C's combined rate gives 1/A = 1/10 − 1/15 = 1/30, so A alone needs 30 days.

Question 26Mathematics

What is the HCF of 36 and 84?

  1. 24
  2. 12 Correct answer.
  3. 6
  4. 18

Explanation

Write each number as a product of prime factors: 36 = 2² × 3² and 84 = 2² × 3 × 7. The HCF is the product of the common prime factors taken with the lowest powers, i.e. 2² × 3 = 12.

Question 27Mathematics

What is the average of the numbers 4, 8, 10 and 14?

  1. 10
  2. 7
  3. 9 Correct answer.
  4. 12

Explanation

The average of a set of numbers is their sum divided by the count of numbers. Here the sum is 4 + 8 + 10 + 14 = 36 and there are 4 numbers, so the average is 36 ÷ 4 = 9.

Question 28Mathematics

What is the simple interest on ₹5000 at 8% per annum for 3 years?

  1. ₹1000
  2. ₹1500
  3. ₹1200 Correct answer.
  4. ₹1150

Explanation

Simple interest is calculated as SI = (P × R × T) / 100. Substituting P = 5000, R = 8 and T = 3 gives (5000 × 8 × 3) / 100 = ₹1200.

Question 29Mathematics

A triangle has a base of 12 cm and a height of 9 cm. What is its area?

  1. 27 cm²
  2. 54 cm² Correct answer.
  3. 96 cm²
  4. 108 cm²

Explanation

The area of a triangle is half the product of its base and height. So the area is ½ × 12 × 9 = 54 cm².

Question 30Mathematics

What is the value of (a + b)² − (a − b)²?

  1. a² − b²
  2. 4ab Correct answer.
  3. 2(a² + b²)
  4. 2ab

Explanation

Expand both squares using the standard identities: (a + b)² = a² + 2ab + b² and (a − b)² = a² − 2ab + b². Subtracting gives 2ab − (−2ab) = 4ab.

Question 31Mathematics

What is the sum of the interior angles of a regular hexagon?

  1. 900°
  2. 720° Correct answer.
  3. 540°
  4. 1080°

Explanation

For a polygon with n sides, the interior angles add up to (n − 2) × 180°. A hexagon has 6 sides, so the sum is 4 × 180° = 720°.

Question 32Mathematics

Expressed as a fraction in its lowest terms, 0.75 is equal to:

  1. 3/4 Correct answer.
  2. 3/5
  3. 4/5
  4. 7/10

Explanation

The decimal 0.75 means 75 hundredths, that is 75/100. Dividing both numerator and denominator by their HCF 25 gives 3/4, which cannot be reduced further.

Question 33Mathematics

What is the median of the data 3, 7, 9, 11, 15?

  1. 7
  2. 9 Correct answer.
  3. 15
  4. 11

Explanation

The median is the middle observation once the data are arranged in order. The values are already in ascending order, and the third of the five values is 9.

Question 34Mathematics

What is the LCM of 12, 15 and 20?

  1. 120
  2. 30
  3. 60 Correct answer.
  4. 180

Explanation

Write prime factorisations: 12 = 2² × 3, 15 = 3 × 5 and 20 = 2² × 5. The LCM takes each prime with its highest power, giving 2² × 3 × 5 = 60.

Question 35Mathematics

A fair die is rolled once. What is the probability of getting a prime number?

  1. 1/3
  2. 2/3
  3. 1/2 Correct answer.
  4. 1/6

Explanation

Probability equals favourable outcomes divided by total outcomes. The prime numbers on a die are 2, 3 and 5, giving 3 favourable outcomes out of 6, so the probability is 3/6 = 1/2.

Question 36Mathematics

What are the roots of the equation x² − 5x + 6 = 0?

  1. 2 and 3 Correct answer.
  2. −1 and −6
  3. −2 and −3
  4. 1 and 6

Explanation

Factorise by finding two numbers whose product is the constant term 6 and whose sum is 5. Those numbers are 2 and 3, so x² − 5x + 6 = (x − 2)(x − 3) and the roots are 2 and 3.

Question 37Mathematics

If a : b = 3 : 4 and b : c = 8 : 9, then a : c equals:

  1. 2 : 3 Correct answer.
  2. 9 : 4
  3. 3 : 2
  4. 4 : 9

Explanation

Multiply the two ratios after making the common term b equal: a/c = (a/b) × (b/c) = (3/4) × (8/9) = 24/36 = 2/3. Hence a : c = 2 : 3.

Question 38Mathematics

What is the difference between the compound interest and the simple interest on ₹10000 at 10% per annum for 2 years, compounded annually?

  1. ₹200
  2. ₹50
  3. ₹110
  4. ₹100 Correct answer.

Explanation

For two years the difference is P × (R/100)². Substituting P = 10000 and R = 10 gives 10000 × (0.1)² = ₹100, which is the interest earned in the second year on the first year's interest.

Question 39Mathematics

Simplify: 2³ × 2⁴ ÷ 2⁵

  1. 4 Correct answer.
  2. 8
  3. 16
  4. 2

Explanation

For the same base, multiplying adds the indices and dividing subtracts them. So the expression equals 2^(3 + 4 − 5) = 2² = 4.

Question 40Mathematics

The diagonal of a square is 10 cm. What is the area of the square?

  1. 25 cm²
  2. 50 cm² Correct answer.
  3. 75 cm²
  4. 100 cm²

Explanation

A square of side s has diagonal s√2, so s = 10/√2. The area is s² = (10/√2)² = 100/2 = 50 cm², which is also given directly by the rule area = d²/2.

Question 41Mathematics

The radius of a cylinder is 7 cm and its height is 5 cm. Taking π = 22/7, what is its curved surface area?

  1. 110 cm²
  2. 154 cm²
  3. 220 cm² Correct answer.
  4. 440 cm²

Explanation

The curved surface area of a cylinder is 2πrh. Substituting r = 7, h = 5 and π = 22/7 gives 2 × (22/7) × 7 × 5 = 220 cm².

Question 42Mathematics

The average of five numbers is 27. When one of the numbers, 35, is removed, what is the average of the remaining four numbers?

  1. 20
  2. 24
  3. 26
  4. 25 Correct answer.

Explanation

The total of the five numbers is 5 × 27 = 135. Removing 35 leaves 100 to be shared among four numbers, so the new average is 100 ÷ 4 = 25.

Question 43Mathematics

What is the value of sin 30° + cos 60°?

  1. √3/2
  2. 1/2
  3. 2
  4. 1 Correct answer.

Explanation

From the standard trigonometric table, sin 30° = 1/2 and cos 60° = 1/2. Adding them gives 1/2 + 1/2 = 1.

Question 44Mathematics

Factorise x² − 5x + 6.

  1. (x − 2)(x − 3) Correct answer.
  2. (x + 2)(x + 3)
  3. (x + 1)(x + 6)
  4. (x − 1)(x − 6)

Explanation

We need two numbers whose product is +6 and whose sum is −5. The numbers −2 and −3 satisfy both conditions, so the factorisation is (x − 2)(x − 3).

Question 45Mathematics

If 25% of a number is 30, what is the number?

  1. 120 Correct answer.
  2. 100
  3. 90
  4. 110

Explanation

Let the number be N. Then (25/100) × N = 30, so N = 30 × 100/25 = 120.

Question 46Mathematics

A shopkeeper marks an article 40% above its cost price and then allows a discount of 25% on the marked price. What is his profit percentage?

  1. 15% loss
  2. 5% Correct answer.
  3. 15%
  4. 10%

Explanation

Take the cost price as ₹100. The marked price is ₹140, and after a 25% discount the selling price is 140 × 0.75 = ₹105, so the profit is ₹5 on ₹100, that is 5%.

Question 47Mathematics

The sum of three consecutive odd numbers is 87. What is the largest of the three numbers?

  1. 29
  2. 31 Correct answer.
  3. 35
  4. 33

Explanation

Let the numbers be n, n + 2 and n + 4. Their sum is 3n + 6 = 87, so 3n = 81 and n = 27. The largest number is 27 + 4 = 31.

Question 48Mathematics

Twelve men can complete a piece of work in 15 days. How many men are needed to complete the same work in 9 days?

  1. 24
  2. 20 Correct answer.
  3. 18
  4. 16

Explanation

The total work equals 12 × 15 = 180 man-days. To finish the same work in 9 days, the number of men required is 180 ÷ 9 = 20.

Question 49Mathematics

What is the total surface area of a sphere of radius 7 cm, taking π = 22/7?

  1. 308 cm²
  2. 616 cm² Correct answer.
  3. 154 cm²
  4. 1232 cm²

Explanation

The surface area of a sphere is 4πr². Substituting r = 7 and π = 22/7 gives 4 × (22/7) × 49 = 616 cm².

Question 50Mathematics

If x + y = 10 and xy = 21, what is the value of x² + y²?

  1. 42
  2. 58 Correct answer.
  3. 79
  4. 100

Explanation

Use the identity x² + y² = (x + y)² − 2xy. Substituting the given values gives 10² − 2 × 21 = 100 − 42 = 58.