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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 z = -3 + 4i, what is the real part of z?

A. -3
B. 4
C. 0
D. 3

Solution

The real part of a complex number z = a + bi is a. Here, the real part is -3.

Correct Answer: A — -3

Q. If z = 1 + i, find |z|².

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

Solution

|z|² = (1)² + (1)² = 1 + 1 = 2.

Correct Answer: B — 2

Q. If z = 1 + i, what is the argument of z?

A. π/4
B. π/2
C. 0
D. π

Solution

The argument of a complex number z = a + bi is given by θ = tan⁻¹(b/a). Here, θ = tan⁻¹(1/1) = π/4.

Correct Answer: A — π/4

Q. If z = 1 + i, what is the value of z^3? (2023)

A. -2 + 2i
B. 2i
C. 0
D. 2 + 2i

Solution

z^3 = (1 + i)^3 = 1 + 3i + 3i^2 + i^3 = 1 + 3i - 3 - i = -2 + 2i.

Correct Answer: A — -2 + 2i

Q. If z = 1 + i√3, find the conjugate of z.

A. 1 - i√3
B. 1 + i√3
C. 1 + √3i
D. 1 - √3i

Solution

The conjugate of a complex number z = a + bi is given by z* = a - bi. Thus, the conjugate of z = 1 + i√3 is 1 - i√3.

Correct Answer: A — 1 - i√3

Q. If z = 1 + i√3, what is the value of z^2? (2023)

A. -2 + 2i√3
B. 4
C. 1 - 2i√3
D. 1 + 2i√3

Solution

z^2 = (1 + i√3)^2 = 1^2 + 2(1)(i√3) + (i√3)^2 = 1 + 2i√3 - 3 = -2 + 2i√3.

Correct Answer: A — -2 + 2i√3

Q. If z = 1 + √3i, what is the square of the modulus of z?

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

Solution

The modulus of z = 1 + √3i is |z| = √(1² + (√3)²) = √(1 + 3) = √4 = 2. The square of the modulus is 2² = 4.

Correct Answer: A — 4

Q. If z = 2 + 2i, find z².

A. 0
B. 8i
C. 8
D. 4 + 8i

Solution

z² = (2 + 2i)² = 4 + 8i - 4 = 8i.

Correct Answer: C — 8

Q. If z = 2 + 2i, what is the argument of z? (2023)

A. π/4
B. π/2
C. 3π/4
D. 0

Solution

The argument of z is given by tan^(-1)(2/2) = tan^(-1)(1) = π/4.

Correct Answer: A — π/4

Q. If z = 2 + 2i, what is the value of z^3? (2022)

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

Solution

z^3 = (2 + 2i)^3 = 8 + 12i - 12 - 8i = 8.

Correct Answer: C — 8

Q. If z = 2(cos(π/3) + i sin(π/3)), what is z in rectangular form? (2022)

A. 1 + √3i
B. 2 + √3i
C. 1 + 2i
D. 2 + 2i

Solution

Using Euler's formula, z = 2(cos(π/3) + i sin(π/3)) = 2(1/2 + i√3/2) = 1 + √3i.

Correct Answer: A — 1 + √3i

Q. If z = 3 + 4i, what is the modulus of z? (2021)

A. 5
B. 7
C. 25
D. 12

Solution

The modulus of z is given by |z| = √(3^2 + 4^2) = √(9 + 16) = √25 = 5.

Correct Answer: A — 5

Q. If z = 4 - 3i, find the conjugate of z. (2023)

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

Solution

The conjugate of z = 4 - 3i is z* = 4 + 3i.

Correct Answer: A — 4 + 3i

Q. If z = 4e^(iπ/3), find the rectangular form of z.

A. 2 + 2√3i
B. 4 + 0i
C. 0 + 4i
D. 4 + 4i

Solution

z = 4(cos(π/3) + i sin(π/3)) = 4(1/2 + i√3/2) = 2 + 2√3i.

Correct Answer: A — 2 + 2√3i

Q. If z = 5 + 12i, find the argument of z. (2020)

A. arctan(12/5)
B. arctan(5/12)
C. π/2
D. 0

Solution

The argument of z = 5 + 12i is θ = arctan(12/5).

Correct Answer: A — arctan(12/5)

Q. If z = 5(cos(θ) + i sin(θ)), what is the value of z when θ = π/3? (2023)

A. 5 + 5i
B. 5 + 2.5i
C. 2.5 + 5i
D. 2.5 + 2.5i

Solution

z = 5(cos(π/3) + i sin(π/3)) = 5(1/2 + i√3/2) = 2.5 + 5i√3/2.

Correct Answer: B — 5 + 2.5i

Q. If z1 = 2 + 2i and z2 = 1 - i, find z1 + z2.

A. 3 + i
B. 1 + i
C. 3 - i
D. 1 - i

Solution

z1 + z2 = (2 + 2i) + (1 - i) = 3 + i.

Correct Answer: A — 3 + i

Q. If z1 = 2 + 2i and z2 = 2 - 2i, what is the value of z1 * z2? (2019)

A. 8
B. 0
C. 4
D. 4 + 0i

Solution

z1 * z2 = (2 + 2i)(2 - 2i) = 4 - 4i^2 = 4 + 4 = 8.

Correct Answer: A — 8

Q. If z1 = 2 + 2i and z2 = 3 - i, find z1 + z2. (2023)

A. 5 + i
B. 5 + 3i
C. 1 + i
D. 1 - i

Solution

z1 + z2 = (2 + 2i) + (3 - i) = 5 + i.

Correct Answer: A — 5 + i

Q. If \( C = \begin{pmatrix} 1 & 0 & 2 \\ 0 & 1 & 3 \\ 0 & 0 & 1 \end{pmatrix} \), what is the determinant of C? (2022)

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

Solution

The determinant of an upper triangular matrix is the product of its diagonal elements: 1 * 1 * 1 = 1.

Correct Answer: B — 1

Q. If \( G = \begin{pmatrix} 0 & 2 & 1 \\ 1 & 0 & 3 \\ 4 & 1 & 0 \end{pmatrix} \), what is the determinant of G? (2020)

A. -10
B. 10
C. 0
D. 5

Solution

Det(G) = 0 because the first column has a zero entry, leading to a linear dependence.

Correct Answer: A — -10

Q. In 2023, which country announced a plan to phase out coal by 2030? (2023)

A. India
B. Germany
C. Australia
D. South Africa

Solution

Germany announced a plan to phase out coal by 2030 in 2023.

Correct Answer: B — Germany

Q. In 2023, which country became the first to achieve 100% renewable energy? (2023)

A. Germany
B. Denmark
C. Costa Rica
D. Iceland

Solution

Costa Rica became the first country to achieve 100% renewable energy in 2023.

Correct Answer: C — Costa Rica

Q. In 2023, which country hosted the G20 summit? (2023)

A. India
B. Italy
C. Indonesia
D. Germany

Solution

India hosted the G20 summit in 2023, focusing on global economic recovery.

Correct Answer: A — India

Q. In 2023, which country was the first to achieve 100% renewable energy for a full day? (2023)

A. Germany
B. Denmark
C. Costa Rica
D. Iceland

Solution

Denmark achieved 100% renewable energy for a full day in 2023.

Correct Answer: B — Denmark

Q. In 2023, which country was the largest producer of solar energy? (2023)

A. USA
B. Germany
C. China
D. India

Solution

China remains the largest producer of solar energy in 2023.

Correct Answer: C — China

Q. In 2023, which Indian city was ranked as the most polluted city in the world? (2023)

A. Delhi
B. Mumbai
C. Kolkata
D. Bengaluru

Solution

Delhi was ranked as the most polluted city in the world in 2023.

Correct Answer: A — Delhi

Q. In 2023, which Indian company became the first to reach a market capitalization of $200 billion? (2023)

A. Reliance Industries
B. Tata Consultancy Services
C. Infosys
D. HDFC Bank

Solution

Reliance Industries became the first Indian company to reach a market capitalization of $200 billion in 2023.

Correct Answer: A — Reliance Industries

Q. In 2023, which Indian sportsperson won a gold medal at the World Athletics Championships? (2023)

A. Neeraj Chopra
B. P.V. Sindhu
C. Mary Kom
D. Saina Nehwal

Solution

Neeraj Chopra won a gold medal at the World Athletics Championships in 2023.

Correct Answer: A — Neeraj Chopra

Q. In 2023, which organization announced a new climate change initiative? (2023)

A. UNESCO
B. WHO
C. UNEP
D. IMF

Solution

The United Nations Environment Programme (UNEP) announced a new climate change initiative in 2023.

Correct Answer: C — UNEP

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