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Defence Exams

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Defence Exams MCQ & Objective Questions

Defence Exams play a crucial role in shaping the future of aspiring candidates in India. These exams not only assess knowledge but also test the ability to apply concepts in real-world scenarios. Practicing MCQs and objective questions is essential for effective exam preparation, as it helps students identify important questions and enhances their understanding of key topics.

What You Will Practise Here

Fundamentals of Defence Studies
Key Historical Events and Their Impact
Important Defence Policies and Strategies
Current Affairs Related to National Security
Basic Concepts of Military Operations
Understanding Defence Technologies
Analysing Defence Budget and Expenditure

Exam Relevance

The topics covered in Defence Exams are highly relevant across various educational boards, including CBSE and State Boards, as well as competitive exams like NEET and JEE. Students can expect questions that focus on historical events, current affairs, and fundamental concepts related to defence. Common question patterns include multiple-choice questions that assess both theoretical knowledge and practical application.

Common Mistakes Students Make

Overlooking current affairs, which are often integrated into exam questions.
Confusing similar historical events or dates, leading to incorrect answers.
Neglecting the importance of definitions and key terms in objective questions.
Relying solely on rote memorization instead of understanding concepts.

FAQs

Question: What types of questions can I expect in Defence Exams?
Answer: You can expect a mix of MCQs covering historical events, current affairs, and fundamental concepts related to defence.

Question: How can I improve my performance in Defence Exams?
Answer: Regular practice of MCQs and understanding key concepts will significantly enhance your performance.

Start your journey towards success by solving practice MCQs today! Testing your understanding will not only boost your confidence but also prepare you for the important Defence Exams ahead.

NDA

Q. The scalar product of two unit vectors is 0.5. What is the angle between them?

A. 60°
B. 30°
C. 90°
D. 120°

Solution

cos(θ) = 0.5, θ = cos⁻¹(0.5) = 60°.

Correct Answer: A — 60°

Q. The scalar product of two vectors A and B is 12, and the angle between them is 60°. If |A| = 4, find |B|.

A. 6
B. 8
C. 10
D. 12

Solution

A · B = |A||B|cos(θ) => 12 = 4|B|(0.5) => |B| = 6.

Correct Answer: B — 8

Q. The scores of a class in a test are: 10, 12, 14, 16, 18. What is the variance? (2022)

A. 4
B. 6
C. 8
D. 10

Solution

Mean = 14. Variance = [(10-14)² + (12-14)² + (14-14)² + (16-14)² + (18-14)²] / 5 = 8.

Correct Answer: A — 4

Q. The scores of a test are: 20, 30, 40, 50. Calculate the variance. (2020)

A. 100
B. 200
C. 300
D. 400

Solution

Mean = (20 + 30 + 40 + 50) / 4 = 35. Variance = [(20-35)² + (30-35)² + (40-35)² + (50-35)²] / 4 = 250.

Correct Answer: B — 200

Q. The scores of a test are: 20, 30, 40, 50. What is the standard deviation? (2020)

A. 10
B. 15
C. 20
D. 25

Solution

Mean = (20 + 30 + 40 + 50) / 4 = 35. Variance = [(20-35)² + (30-35)² + (40-35)² + (50-35)²] / 4 = 125. SD = √125 = 11.18 (approx 10).

Correct Answer: B — 15

Q. The scores of five students are: 20, 22, 24, 26, 28. Calculate the variance. (2020)

A. 8
B. 10
C. 12
D. 14

Solution

Mean = (20 + 22 + 24 + 26 + 28) / 5 = 24. Variance = [(20-24)² + (22-24)² + (24-24)² + (26-24)² + (28-24)²] / 5 = 8.

Correct Answer: A — 8

Q. The scores of five students are: 20, 22, 24, 26, 28. What is the standard deviation? (2020)

A. 2
B. 3
C. 4
D. 5

Solution

Mean = (20 + 22 + 24 + 26 + 28) / 5 = 24. Variance = [(20-24)² + (22-24)² + (24-24)² + (26-24)² + (28-24)²] / 5 = 8. SD = √8 = 2.83 (approximately 3).

Correct Answer: A — 2

Q. The scores of five students are: 20, 22, 24, 26, 28. What is the variance? (2020)

A. 4
B. 6
C. 8
D. 10

Solution

Mean = (20 + 22 + 24 + 26 + 28) / 5 = 24. Variance = [(20-24)² + (22-24)² + (24-24)² + (26-24)² + (28-24)²] / 5 = 8.

Correct Answer: A — 4

Q. The slope of the tangent line to the curve y = x^2 at the point (2, 4) is: (2022)

A. 2
B. 4
C. 3
D. 1

Solution

The derivative y' = 2x. At x = 2, y' = 2(2) = 4.

Correct Answer: A — 2

Q. The soil of a riverbank is composed of 40% sand, 30% silt, and 30% clay. What is the percentage of silt in the soil? (2019)

A. 30%
B. 40%
C. 50%
D. 60%

Solution

The percentage of silt is given as 30%.

Correct Answer: A — 30%

Q. The soil of a riverbank is composed of 60% sand, 30% silt, and 10% clay. What is the percentage of silt in the soil? (2019)

A. 30%
B. 40%
C. 50%
D. 60%

Solution

The percentage of silt in the soil is given as 30%.

Correct Answer: A — 30%

Q. The standard deviation of a data set is 5. If all values are increased by 2, what will be the new standard deviation? (2020)

A. 3
B. 5
C. 7
D. 10

Solution

Standard deviation is unaffected by adding a constant. Therefore, new SD = 5.

Correct Answer: B — 5

Q. The standard deviation of a data set is 5. What is the variance? (2023)

A. 20
B. 25
C. 30
D. 35

Solution

Variance is the square of the standard deviation. Therefore, variance = 5² = 25.

Correct Answer: B — 25

Q. The sum of the angles in a triangle is equal to how many degrees? (2021)

A. 90
B. 180
C. 270
D. 360

Solution

The sum of the angles in any triangle is always 180 degrees.

Correct Answer: B — 180

Q. The sum of the roots of the equation x^2 - 7x + k = 0 is 7. What is the value of k if the product of the roots is 10? (2023)

A. 10
B. 15
C. 20
D. 25

Solution

Using Vieta's formulas, the sum of the roots is 7 and the product is k = 10.

Correct Answer: A — 10

Q. The sum of the roots of the quadratic equation 2x^2 - 8x + 6 = 0 is equal to what? (2020)

A. 2
B. 4
C. 6
D. 8

Solution

The sum of the roots is given by -b/a = 8/2 = 4.

Correct Answer: B — 4

Q. The sum of the roots of the quadratic equation 3x^2 + 12x + 12 = 0 is equal to what? (2022)

A. -4
B. -3
C. 3
D. 4

Solution

Using Vieta's formulas, the sum of the roots is -b/a = -12/3 = -4.

Correct Answer: A — -4

Q. The Thar Desert is located in which Indian state? (2023)

A. Rajasthan
B. Gujarat
C. Punjab
D. Haryana

Solution

The Thar Desert is primarily located in Rajasthan.

Correct Answer: A — Rajasthan

Q. The total number of seats in the Lok Sabha is 543. If 20% of the seats are reserved for women, how many seats are reserved? (2022)

A. 100
B. 110
C. 120
D. 130

Solution

Reserved seats = 20% of 543 = 0.2 * 543 = 108.6, rounded to 110.

Correct Answer: B — 110

Q. The total number of states in India is 28. If each state has an average of 5 representatives in the Lok Sabha, how many representatives are there in total from the states?

A. 120
B. 140
C. 150
D. 160

Solution

Total representatives = 28 states * 5 representatives/state = 140 representatives.

Correct Answer: B — 140

Q. The unit vector in the direction of vector A = 6i - 8j is:

A. 3/5 i - 4/5 j
B. 6/10 i - 8/10 j
C. 1/5 i - 4/5 j
D. 2/5 i - 3/5 j

Solution

Unit vector = A/|A| = (6i - 8j)/√(6^2 + (-8)^2) = (6i - 8j)/10 = 3/5 i - 4/5 j.

Correct Answer: A — 3/5 i - 4/5 j

Q. The variance of a sample is calculated as 25. What is the standard deviation?

A. 5
B. 10
C. 15
D. 20

Solution

Standard Deviation = √Variance = √25 = 5.

Correct Answer: A — 5

Q. The vertex of the parabola given by the equation y = 2x^2 - 4x + 1 is located at which point?

A. (1, -1)
B. (2, 0)
C. (1, 0)
D. (0, 1)

Solution

To find the vertex, use the formula x = -b/(2a). Here, a = 2, b = -4, so x = 1. Plugging x = 1 into the equation gives y = -1.

Correct Answer: A — (1, -1)

Q. The World Health Organization (WHO) was established in which year? (1948)

A. 1948
B. 1950
C. 1965
D. 1975

Solution

The World Health Organization (WHO) was established on April 7, 1948.

Correct Answer: A — 1948

Q. Two circles have radii of 3 cm and 4 cm. What is the distance between their centers if they are externally tangent? (2022)

A. 7 cm
B. 1 cm
C. 12 cm
D. 5 cm

Solution

The distance between the centers of two externally tangent circles is the sum of their radii: 3 + 4 = 7 cm.

Correct Answer: A — 7 cm

Q. Two circles touch each other externally. If the radius of the first circle is 3 cm and the second is 5 cm, what is the distance between their centers? (2023)

A. 8 cm
B. 2 cm
C. 15 cm
D. 10 cm

Solution

Distance between centers = r1 + r2 = 3 cm + 5 cm = 8 cm.

Correct Answer: A — 8 cm

Q. Two circles with radii 3 cm and 4 cm are externally tangent. What is the distance between their centers? (2022)

A. 7 cm
B. 1 cm
C. 12 cm
D. 5 cm

Solution

The distance between the centers of two externally tangent circles is the sum of their radii: 3 + 4 = 7 cm.

Correct Answer: A — 7 cm

Q. Two circles with radii 5 cm and 3 cm are externally tangent. What is the distance between their centers? (2023)

A. 8 cm
B. 10 cm
C. 6 cm
D. 5 cm

Solution

Distance between centers = r1 + r2 = 5 cm + 3 cm = 8 cm.

Correct Answer: A — 8 cm

Q. Two dice are thrown simultaneously. What is the probability that the sum of the numbers on the dice is 7?

A. 1/6
B. 1/12
C. 1/36
D. 1/3

Solution

Possible outcomes for sum = 7 are (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) = 6 outcomes. Total outcomes = 6 * 6 = 36. Probability = 6/36 = 1/6.

Correct Answer: A — 1/6

Q. Two lines are perpendicular to each other. If one line makes an angle of 30 degrees with the horizontal, what is the angle made by the other line with the horizontal? (2022)

A. 30 degrees
B. 60 degrees
C. 90 degrees
D. 120 degrees

Solution

If two lines are perpendicular, the sum of their angles is 90 degrees. Therefore, if one line makes an angle of 30 degrees with the horizontal, the other line must make an angle of 90 - 30 = 60 degrees with the horizontal.

Correct Answer: C — 90 degrees

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