Mathematics (NDA)

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

Q. For the quadratic equation x^2 + 2x + k = 0 to have real roots, what must be the condition on k? (2023)

A. k < 1
B. k > 1
C. k >= 1
D. k <= 1

Solution

The discriminant must be non-negative: 2^2 - 4*1*k >= 0 leads to k <= 1.

Correct Answer: D — k <= 1

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Q. For the quadratic equation x^2 + 6x + 9 = 0, what type of roots does it have? (2019)

A. Real and distinct
B. Real and equal
C. Complex
D. None of the above

Solution

The discriminant D = 6^2 - 4*1*9 = 0, indicating real and equal roots.

Correct Answer: B — Real and equal

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Q. For the quadratic equation x^2 + 6x + k = 0 to have distinct roots, what must be the condition on k? (2020)

A. k < 9
B. k = 9
C. k > 9
D. k ≤ 9

Solution

The discriminant must be positive: 6^2 - 4*1*k > 0, which simplifies to k < 9.

Correct Answer: A — k < 9

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Q. For the quadratic equation x^2 + 6x + k = 0 to have real roots, what must be the condition on k? (2020)

A. k < 9
B. k = 9
C. k > 9
D. k ≤ 9

Solution

The discriminant must be non-negative: 6^2 - 4(1)(k) ≥ 0, which gives k ≤ 9.

Correct Answer: D — k ≤ 9

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Q. For the quadratic equation x^2 + px + q = 0, if the roots are -2 and -3, what is the value of p? (2020)

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

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Q. For the quadratic equation x^2 - 4x + 4 = 0, what type of roots does it have? (2019)

A. Real and distinct
B. Real and equal
C. Complex
D. None of the above

Solution

The discriminant is 0, indicating that the roots are real and equal.

Correct Answer: B — Real and equal

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Q. For the quadratic equation x^2 - 6x + k = 0 to have one root equal to 3, what is the value of k? (2023)

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

Solution

If one root is 3, then substituting x = 3 gives 3^2 - 6*3 + k = 0, leading to k = 9.

Correct Answer: C — 9

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Q. For the quadratic equation x^2 - 8x + 15 = 0, what are the roots? (2023)

A. 3 and 5
B. 2 and 6
C. 1 and 7
D. 4 and 4

Solution

The roots can be found by factorization: (x - 3)(x - 5) = 0, hence the roots are 3 and 5.

Correct Answer: A — 3 and 5

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Q. For vectors A = 2i + 3j and B = 5i + 6j, what is A · B?

A. 28
B. 30
C. 32
D. 26

Solution

A · B = (2)(5) + (3)(6) = 10 + 18 = 28.

Correct Answer: A — 28

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Q. For vectors A = 2i + j and B = 3i + 4j, what is the scalar product A · B?

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

Solution

A · B = (2)(3) + (1)(4) = 6 + 4 = 10.

Correct Answer: A — 14

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Q. For vectors A = 4i + 3j and B = 3i - 4j, find A · B.

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

Solution

A · B = (4)(3) + (3)(-4) = 12 - 12 = 0.

Correct Answer: A — -6

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Q. For vectors A = 6i + 8j and B = 2i + 3j, find A · B.

A. 42
B. 48
C. 36
D. 30

Solution

A · B = (6)(2) + (8)(3) = 12 + 24 = 36.

Correct Answer: A — 42

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Q. For which value of c is the function f(x) = { x^2, x < 1; c, x = 1; 2x, x > 1 } continuous at x = 1? (2022)

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

Solution

To make f(x) continuous at x = 1, we need c = 1^2 = 1. Thus, c must be 1.

Correct Answer: B — 2

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Q. For which value of k does the equation x^2 + kx + 16 = 0 have equal roots? (2019)

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

Solution

For equal roots, the discriminant must be zero: k^2 - 4*1*16 = 0. Solving gives k = -8.

Correct Answer: B — -4

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Q. For which value of k is the function f(x) = kx + 2 continuous at x = 3? (2023)

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

Solution

The function f(x) = kx + 2 is a linear function and is continuous for all k at x = 3.

Correct Answer: B — k = 1

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Q. For which value of k is the function f(x) = { kx + 1, x < 2; 3, x >= 2 } continuous at x = 2?

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

Solution

To be continuous at x = 2, k(2) + 1 must equal 3. Thus, 2k + 1 = 3, leading to k = 1.

Correct Answer: B — 2

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Q. For which value of k is the function f(x) = { kx + 1, x < 2; 3, x = 2; 2x - 1, x > 2 } continuous at x = 2?

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

Solution

To ensure continuity at x = 2, k(2) + 1 must equal 3. Thus, k = 1.

Correct Answer: B — 2

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Q. For which value of k is the function f(x) = { kx + 1, x < 2; 3, x ≥ 2 } continuous at x = 2? (2019)

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

Solution

To be continuous at x = 2, k(2) + 1 must equal 3. Thus, 2k + 1 = 3, giving k = 1.

Correct Answer: B — 2

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Q. From a deck of 52 cards, how many ways can you choose 5 cards?

A. 2598960
B. 1001
C. 3125
D. 1024

Solution

The number of ways to choose 5 cards from 52 is 52C5 = 2598960.

Correct Answer: A — 2598960

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Q. From a group of 8 people, how many ways can a team of 3 be selected? (2022)

A. 56
B. 24
C. 36
D. 48

Solution

The number of ways to choose 3 people from 8 is given by 8C3 = 56.

Correct Answer: A — 56

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Q. From a point on the ground, the angle of elevation to the top of a hill is 30 degrees. If the height of the hill is 100 m, how far is the point from the base of the hill? (2022)

A. 173.21 m
B. 100 m
C. 200 m
D. 150 m

Solution

Distance = height / tan(30) = 100 / (1/√3) = 100√3 ≈ 173.21 m.

Correct Answer: A — 173.21 m

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Q. From the top of a 100 m high building, the angle of depression to a point on the ground is 45 degrees. How far is the point from the base of the building? (2020)

A. 50 m
B. 100 m
C. 150 m
D. 200 m

Solution

Distance = height / tan(angle) = 100 / tan(45) = 100 / 1 = 100 m.

Correct Answer: B — 100 m

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Q. From the top of a 50 m high tower, the angle of depression to a point on the ground is 30 degrees. How far is the point from the base of the tower? (2022)

A. 50 m
B. 100 m
C. 75 m
D. 25 m

Solution

Using tan(30) = 1/√3, distance = height * √3 = 50 * √3 ≈ 86.60 m, which rounds to 100 m.

Correct Answer: B — 100 m

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Q. From the top of a tower, the angle of depression to a point on the ground is 45 degrees. If the height of the tower is 100 meters, how far is the point from the base of the tower? (2020)

A. 100 m
B. 50 m
C. 70 m
D. 80 m

Solution

Using tan(45) = 1, Distance = Height = 100 m.

Correct Answer: A — 100 m

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Q. Given A = 1i + 1j and B = 1i + 1j, what is A · B?

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

Solution

A · B = (1)(1) + (1)(1) = 1 + 1 = 2.

Correct Answer: A — 2

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Q. Given A = 2i + 2j and B = 3i + 3j, what is the scalar product A · B?

A. 12
B. 18
C. 10
D. 14

Solution

A · B = (2)(3) + (2)(3) = 6 + 6 = 12.

Correct Answer: A — 12

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Q. Given the data set 8, 8, 9, 10, 10, 10, 11, 12, what is the mode?

A. 8
B. 9
C. 10
D. 11

Solution

The mode is 10, as it appears 3 times, which is more than any other number.

Correct Answer: C — 10

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Q. Given the data set: 1, 1, 2, 3, 4, 4, 4, 5, 5, what is the mode?

A. 1
B. 2
C. 4
D. 5

Solution

The mode is 4, as it appears three times, more than any other number.

Correct Answer: C — 4

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Q. Given vectors A = 2i + 2j and B = 3i + 4j, what is the value of A · B?

A. 14
B. 10
C. 12
D. 16

Solution

A · B = (2)(3) + (2)(4) = 6 + 8 = 14.

Correct Answer: A — 14

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Q. Given vectors A = 4i + 2j and B = -i + 3j, calculate A · B.

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

Solution

A · B = (4)(-1) + (2)(3) = -4 + 6 = 2.

Correct Answer: C — 8

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Showing 331 to 360 of 1593 (54 Pages)

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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