Mathematics (NDA)

Algebra Coordinate Geometry Differential Calculus Geometry Integral Calculus & Differential Equations Matrices & Determinants Statistics & Probability Trigonometry Vector Algebra

Q. What is the value of k if the equation x^2 - kx + 9 = 0 has roots that are both positive?

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

Solution

For both roots to be positive, k must be greater than 6 (sum of roots) and k^2 - 36 > 0 (discriminant). Thus, k > 6 and k < 12.

Correct Answer: C — 10

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Q. What is the value of k if the quadratic equation x^2 + kx + 16 = 0 has roots that are both negative? (2019)

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

Solution

For both roots to be negative, k must be negative and |k| > 8. Thus, k = -8.

Correct Answer: A — -8

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Q. What is the value of k if the quadratic equation x^2 + kx + 16 = 0 has roots that are both real and distinct? (2019)

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

Solution

For real and distinct roots, the discriminant must be positive: k^2 - 4(1)(16) > 0. Thus, k^2 > 64, leading to k < -8 or k > 8.

Correct Answer: D — -5

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Q. What is the value of k if the quadratic equation x^2 + kx + 16 = 0 has roots that are real and distinct? (2019)

A. -8
B. -4
C. 4
D. 8

Solution

For real and distinct roots, the discriminant must be positive: k^2 - 4(1)(16) > 0. Thus, k^2 > 64, leading to k < -8 or k > 8.

Correct Answer: B — -4

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Q. What is the value of k if the quadratic equation x^2 + kx + 9 = 0 has roots 3 and -3? (2022)

A. 0
B. 6
C. 9
D. 12

Solution

Using Vieta's formulas, the sum of the roots is 0, so k = -0 = 0. The product of the roots is 9, confirming k = 6.

Correct Answer: B — 6

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Q. What is the value of k if the quadratic equation x^2 + kx + 9 = 0 has roots that are both positive? (2023)

A. -6
B. -4
C. -2
D. 0

Solution

For both roots to be positive, k must be negative and k^2 > 36. Thus, k < -6.

Correct Answer: A — -6

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Q. What is the value of k if the quadratic equation x^2 + kx + 9 = 0 has roots that are both negative? (2023)

A. -6
B. -4
C. -2
D. 0

Solution

For both roots to be negative, k must be positive and k^2 > 4(1)(9). Thus, k > 6.

Correct Answer: A — -6

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Q. What is the value of k if the roots of the equation x^2 + kx + 4 = 0 are -2 and -2?

A. 4
B. 8
C. 6
D. 0

Solution

The sum of the roots is -2 + -2 = -4, so k = 4.

Correct Answer: C — 6

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Q. What is the value of k if the roots of the equation x^2 + kx + 9 = 0 are imaginary?

A. k < 0
B. k > 0
C. k = 0
D. k ≤ 0

Solution

The discriminant must be less than zero: k^2 - 4*1*9 < 0 leads to k^2 < 36, hence k < 0 or k > 0.

Correct Answer: A — k < 0

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Q. What is the value of k if the roots of the equation x^2 - 5x + k = 0 are equal? (2020)

A. 6.25
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. Solving gives k = 6.25.

Correct Answer: A — 6.25

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Q. What is the value of k if the roots of the equation x^2 - kx + 16 = 0 are real and distinct?

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

Solution

For the roots to be real and distinct, the discriminant must be positive: k^2 - 64 > 0, leading to k > 8 or k < -8.

Correct Answer: C — 12

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Q. What is the value of k if the roots of the equation x^2 - kx + 8 = 0 are 2 and 4? (2023)

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

Solution

The sum of the roots is 2 + 4 = 6, so k = 6.

Correct Answer: A — 6

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Q. What is the value of k if the roots of the equation x^2 - kx + 9 = 0 are 3 and 3?

A. 6
B. 9
C. 3
D. 12

Solution

The sum of the roots is 3 + 3 = 6, so k = 6.

Correct Answer: A — 6

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Q. What is the value of k if the roots of the equation x^2 - kx + 9 = 0 are real and distinct?

A. k > 18
B. k < 18
C. k = 18
D. k = 9

Solution

For the roots to be real and distinct, the discriminant must be greater than zero: k^2 - 4(1)(9) > 0, which simplifies to k^2 > 36, hence k < -6 or k > 6.

Correct Answer: B — k < 18

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Q. What is the value of log_10(0.01)?

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

Solution

log_10(0.01) = log_10(10^-2) = -2.

Correct Answer: B — -2

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Q. What is the value of log_2(1/8)? (2023)

A. -3
B. -2
C. 2
D. 3

Solution

log_2(1/8) = log_2(2^-3) = -3.

Correct Answer: A — -3

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Q. What is the value of log_4(16)?

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

Solution

log_4(16) = log_4(4^2) = 2.

Correct Answer: B — 2

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Q. What is the value of log_5(1)?

A. 0
B. 1
C. 5
D. undefined

Solution

log_5(1) = 0 because 5^0 = 1.

Correct Answer: A — 0

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Q. What is the value of log_5(25) + log_5(4)? (2021)

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

Solution

log_5(25) = 2, so log_5(25) + log_5(4) = 2 + log_5(4).

Correct Answer: C — 4

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Q. What is the value of p for the parabola defined by the equation y^2 = 20x?

A. 5
B. 10
C. 20
D. 4

Solution

In the equation y^2 = 4px, we have 4p = 20, thus p = 5.

Correct Answer: A — 5

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Q. What is the value of sin(180° - θ)?

A. sin θ
B. cos θ
C. tan θ
D. sec θ

Solution

Using the identity, sin(180° - θ) = sin θ.

Correct Answer: A — sin θ

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Q. What is the value of sin² θ + cos² θ? (2021)

A. 0
B. 1
C. 2
D. sin² θ

Solution

According to the Pythagorean identity, sin² θ + cos² θ = 1 for any angle θ.

Correct Answer: B — 1

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Q. What is the value of tan(60°)?

A. 1
B. √3
C. √2
D. 0

Solution

tan(60°) = √3.

Correct Answer: B — √3

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Q. What is the value of the 3rd term in the expansion of (a + b)^6?

A. 15ab^4
B. 20ab^4
C. 30ab^4
D. 35ab^4

Solution

The 3rd term in the expansion of (a + b)^6 is given by C(6, 2) * a^4 * b^2 = 15 * a^4 * b^2.

Correct Answer: B — 20ab^4

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Q. What is the value of the 3rd term in the expansion of (x + 2)^5?

A. 40
B. 80
C. 60
D. 100

Solution

The 3rd term in the expansion of (x + 2)^5 is C(5, 2)(x)^2(2)^3 = 10 * x^2 * 8 = 80.

Correct Answer: A — 40

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Q. What is the value of the 5th term in the expansion of (x + 2)^7?

A. 672
B. 672x^4
C. 672x^3
D. 672x^2

Solution

The 5th term is C(7,4) * (2)^4 * x^3 = 35 * 16 * x^3 = 560x^3.

Correct Answer: C — 672x^3

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Q. What is the value of the coefficient of x^0 in the expansion of (x + 5)^3?

A. 0
B. 5
C. 15
D. 125

Solution

The coefficient of x^0 in (x + 5)^3 is given by 3C0 * (5)^3 = 1 * 125 = 125.

Correct Answer: D — 125

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Q. What is the value of the coefficient of x^4 in the expansion of (2x - 5)^6?

A. -600
B. -720
C. 720
D. 600

Solution

The coefficient of x^4 in (2x - 5)^6 is given by 6C2 * (2)^4 * (-5)^2 = 15 * 16 * 25 = 600. The coefficient is -720.

Correct Answer: B — -720

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Q. What is the value of the coefficient of x^4 in the expansion of (x + 5)^6?

A. 150
B. 300
C. 600
D. 750

Solution

The coefficient of x^4 in (x + 5)^6 is given by 6C4 * 5^2 = 15 * 25 = 375.

Correct Answer: B — 300

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Q. What is the value of the coefficient of x^5 in the expansion of (x + 1)^8?

A. 56
B. 70
C. 80
D. 90

Solution

The coefficient of x^5 is given by C(8, 5) = 56.

Correct Answer: B — 70

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Mathematics (NDA) MCQ & Objective Questions

Mathematics plays a crucial role in the NDA exam, as it tests your analytical and problem-solving skills. Practicing Mathematics (NDA) MCQ and objective questions is essential for scoring better in this competitive environment. By focusing on practice questions, you can identify important questions and enhance your exam preparation effectively.

What You Will Practise Here

Algebra: Understanding equations, inequalities, and functions.
Geometry: Key concepts of shapes, angles, and theorems.
Trigonometry: Important ratios, identities, and applications.
Statistics: Basics of mean, median, mode, and standard deviation.
Probability: Fundamental principles and problem-solving techniques.
Calculus: Introduction to limits, derivatives, and integrals.
Mensuration: Formulas for areas and volumes of various shapes.

Exam Relevance

The Mathematics (NDA) syllabus is relevant not only for the NDA exam but also for various other competitive exams like CBSE, State Boards, NEET, and JEE. In these exams, you will often encounter multiple-choice questions that test your understanding of mathematical concepts. Common question patterns include direct application of formulas, problem-solving scenarios, and conceptual understanding, making it essential to practice regularly.

Common Mistakes Students Make

Misinterpreting the question: Students often overlook key details in the problem statement.
Formula errors: Forgetting or misapplying mathematical formulas can lead to incorrect answers.
Calculation mistakes: Simple arithmetic errors can cost valuable marks.
Neglecting units: Failing to consider units in problems involving measurements.
Rushing through questions: Students may skip steps or fail to double-check their work under time pressure.

FAQs

Question: What are the best ways to prepare for Mathematics (NDA) MCQs?
Answer: Regular practice with objective questions, understanding key concepts, and solving previous years' papers are effective strategies.

Question: How can I improve my speed in solving Mathematics (NDA) questions?
Answer: Time yourself while practicing and focus on solving simpler problems quickly to build speed and confidence.

Start solving Mathematics (NDA) MCQs today to test your understanding and boost your confidence for the exams. Remember, consistent practice is the key to success!

Mathematics (NDA)

Mathematics (NDA) MCQ & Objective Questions

What You Will Practise Here

Exam Relevance

Common Mistakes Students Make

FAQs

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