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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. If the roots of the equation x^2 + 5x + 6 = 0 are a and b, what is the value of ab? (2023)

A. 6
B. 5
C. 11
D. 1

Solution

The product of the roots ab is given by c/a. Here, c = 6 and a = 1, so ab = 6.

Correct Answer: A — 6

Q. If the roots of the equation x^2 + 5x + c = 0 are 2 and 3, what is the value of c? (2022)

A. 6
B. 5
C. 7
D. 8

Solution

Using the product of the roots, c = 2 * 3 = 6.

Correct Answer: A — 6

Q. If the roots of the equation x^2 + 5x + k = 0 are -2 and -3, what is the value of k?

A. 6
B. 5
C. 7
D. 8

Solution

The product of the roots is (-2)(-3) = 6, so k = 6.

Correct Answer: A — 6

Q. If the roots of the equation x^2 + 5x + k = 0 are real and distinct, what is the condition on k? (2023)

A. k < 25
B. k > 25
C. k = 25
D. k ≤ 25

Solution

The discriminant must be greater than zero: 5^2 - 4(1)(k) > 0, leading to k < 25.

Correct Answer: A — k < 25

Q. If the roots of the equation x^2 + 6x + k = 0 are real and distinct, what must be the condition on k? (2023)

A. k < 9
B. k > 9
C. k = 9
D. k ≤ 9

Solution

For real and distinct roots, the discriminant must be greater than zero: 6^2 - 4*1*k > 0 leads to k < 9.

Correct Answer: A — k < 9

Q. If the roots of the equation x^2 + mx + n = 0 are 3 and 4, what is the value of n? (2022)

A. 12
B. 7
C. 10
D. 15

Solution

Using Vieta's formulas, n = 3 * 4 = 12.

Correct Answer: A — 12

Q. If the roots of the equation x^2 - 2x + k = 0 are real and distinct, what is the condition for k?

A. k > 1
B. k < 1
C. k = 1
D. k ≥ 1

Solution

The discriminant must be positive for real and distinct roots: (-2)^2 - 4*1*k > 0, which simplifies to 4 - 4k > 0, or k < 1.

Correct Answer: A — k > 1

Q. If the roots of the equation x^2 - 4x + k = 0 are real and distinct, what is the condition for k? (2023)

A. k > 4
B. k < 4
C. k = 4
D. k ≤ 4

Solution

The discriminant must be greater than zero for real and distinct roots: (-4)^2 - 4*1*k > 0, which simplifies to 16 - 4k > 0, or k < 4.

Correct Answer: A — k > 4

Q. If the roots of the equation x^2 - 6x + k = 0 are 3 and 3, what is the value of k? (2020)

A. 6
B. 9
C. 12
D. 15

Solution

The equation can be expressed as (x - 3)^2 = 0, which expands to x^2 - 6x + 9 = 0. Thus, k = 9.

Correct Answer: B — 9

Q. If the roots of the equation x^2 - 6x + k = 0 are real and distinct, what is the range of k? (2020)

A. k < 9
B. k > 9
C. k = 9
D. k ≤ 9

Solution

For real and distinct roots, the discriminant must be greater than zero: (-6)^2 - 4*1*k > 0, leading to k < 9.

Correct Answer: A — k < 9

Q. If the roots of the equation x^2 - 7x + 10 = 0 are a and b, what is the value of ab? (2021)

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

Solution

By Vieta's formulas, ab = 10, which is the constant term of the polynomial.

Correct Answer: A — 10

Q. If the roots of the polynomial x^3 - 3x^2 + 3x - 1 = 0 are a, b, and c, what is the value of a + b + c?

A. 1
B. 3
C. 0
D. 2

Solution

By Vieta's formulas, the sum of the roots a + b + c = -(-3) = 3.

Correct Answer: B — 3

Q. If the roots of the quadratic equation ax^2 + bx + c = 0 are 4 and -1, what is the value of b if a = 1 and c = -4? (2023)

A. -3
B. 3
C. 5
D. -5

Solution

Using the sum of roots, b = - (4 + (-1)) = -3.

Correct Answer: A — -3

Q. If the roots of the quadratic equation ax^2 + bx + c = 0 are equal, which of the following must be true? (2019)

A. b^2 > 4ac
B. b^2 < 4ac
C. b^2 = 4ac
D. a + b + c = 0

Solution

For the roots to be equal, the discriminant must be zero, which means b^2 = 4ac.

Correct Answer: C — b^2 = 4ac

Q. If the roots of the quadratic equation x^2 + 2x + k = 0 are equal, what is the value of k? (2022)

A. 1
B. 2
C. 0
D. -1

Solution

For the roots to be equal, the discriminant must be zero. Thus, 2^2 - 4*1*k = 0 leads to k = 1.

Correct Answer: D — -1

Q. If the roots of the quadratic equation x^2 + 4x + k = 0 are equal, what is the value of k?

A. 4
B. 8
C. 16
D. 0

Solution

For the roots to be equal, the discriminant must be zero. Thus, 4^2 - 4(1)(k) = 0 leads to k = 4.

Correct Answer: B — 8

Q. If the roots of the quadratic equation x^2 + px + q = 0 are -2 and -3, what is the value of p? (2019)

A. 5
B. 6
C. 7
D. 8

Solution

The sum of the roots is -(-2) + -(-3) = 5, hence p = 5.

Correct Answer: A — 5

Q. If the roots of the quadratic equation x^2 + px + q = 0 are -2 and -3, what is the value of p + q? (2019)

A. -5
B. -6
C. -7
D. -8

Solution

Using Vieta's formulas, p = -(-2 - 3) = 5 and q = (-2)(-3) = 6. Therefore, p + q = 5 + 6 = 11.

Correct Answer: B — -6

Q. If the roots of the quadratic equation x² - 5x + k = 0 are equal, what is the value of k? (2023)

A. 6
B. 5
C. 4
D. 3

Solution

For the roots to be equal, the discriminant must be zero. Thus, (-5)² - 4(1)(k) = 0, giving k = 25/4 = 6.25.

Correct Answer: A — 6

Q. If the scalar product of two vectors A and B is 0, what can be inferred about the vectors?

A. They are equal
B. They are parallel
C. They are orthogonal
D. They are collinear

Solution

If A · B = 0, then A and B are orthogonal (perpendicular) to each other.

Correct Answer: C — They are orthogonal

Q. If the scalar product of two vectors A and B is 15 and the magnitudes are |A| = 5 and |B| = 3, find the angle between them.

A. 60°
B. 45°
C. 30°
D. 90°

Solution

A · B = |A||B|cos(θ) => 15 = 5*3*cos(θ) => cos(θ) = 1, θ = 0°.

Correct Answer: B — 45°

Q. If the scalar product of two vectors A and B is equal to the product of their magnitudes, what can be inferred?

A. They are perpendicular
B. They are parallel
C. They are equal
D. They are opposite

Solution

If A · B = |A||B|, then the angle between them is 0°, meaning they are parallel.

Correct Answer: B — They are parallel

Q. If the scalar product of vectors A and B is equal to the product of their magnitudes, what can be said about the angle between them?

A. 0°
B. 90°
C. 180°
D. 45°

Solution

If A · B = |A||B|, then cos(θ) = 1, which means θ = 0°.

Correct Answer: A — 0°

Q. If the sediment load of a river increases, what is the most likely effect on the river's flow?

A. Increased velocity
B. Decreased velocity
C. No effect
D. Increased depth

Solution

Increased sediment load generally decreases the velocity of the river due to increased friction.

Correct Answer: B — Decreased velocity

Q. If the sides of a triangle are in the ratio 3:4:5, what type of triangle is it? (2022)

A. Equilateral
B. Isosceles
C. Scalene
D. Right-angled

Solution

A triangle with sides in the ratio 3:4:5 satisfies the Pythagorean theorem, hence it is a right-angled triangle.

Correct Answer: D — Right-angled

Q. If the sides of triangle DEF are in the ratio 3:4:5, what type of triangle is it? (2021)

A. Acute
B. Obtuse
C. Right
D. Equilateral

Solution

A triangle with sides in the ratio 3:4:5 is a right triangle, as it satisfies the Pythagorean theorem.

Correct Answer: C — Right

Q. If the sides of triangle XYZ are in the ratio 3:4:5, what type of triangle is it? (2021)

A. Acute
B. Obtuse
C. Right
D. Equilateral

Solution

A triangle with sides in the ratio 3:4:5 is a right triangle, as it satisfies the Pythagorean theorem.

Correct Answer: C — Right

Q. If the slope of a riverbed is 1:1000, what is the vertical drop over a distance of 2 km? (2000)

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

Solution

Vertical drop = Distance × Slope = 2000 m × (1/1000) = 2 m.

Correct Answer: A — 2 m

Q. If the soil erosion rate in a river basin is 2 tons per hectare per year, how much soil will be eroded from a 50-hectare area in 5 years? (2023)

A. 500 tons
B. 1000 tons
C. 2000 tons
D. 2500 tons

Solution

Soil eroded = 2 tons/hectare/year × 50 hectares × 5 years = 500 tons.

Correct Answer: C — 2000 tons

Q. If the soil erosion rate is 2 tons per hectare per year, how much soil will be eroded from 50 hectares in 5 years?

A. 500 tons
B. 1000 tons
C. 200 tons
D. 100 tons

Solution

Soil eroded = Erosion rate × Area × Time = 2 tons/hectare/year × 50 hectares × 5 years = 500 tons.

Correct Answer: B — 1000 tons

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