Mathematics (NDA)

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

Q. If f(x) = x^2 + 3x + 2, what is the limit as x approaches -1?

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

Solution

lim x→-1 f(x) = (-1)^2 + 3(-1) + 2 = 1 - 3 + 2 = 0.

Correct Answer: C — 2

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Q. If f(x) = x^2 + 3x + 2, what is the value of f(-1) and is it continuous?

A. 0, Continuous
B. 0, Discontinuous
C. 4, Continuous
D. 4, Discontinuous

Solution

f(-1) = (-1)^2 + 3(-1) + 2 = 0. Since f(x) is a polynomial, it is continuous everywhere.

Correct Answer: C — 4, Continuous

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Q. If f(x) = x^2 + 3x + 5, what is f''(x)? (2020)

A. 2
B. 0
C. 3
D. 5

Solution

The first derivative f'(x) = 2x + 3, and the second derivative f''(x) = 2.

Correct Answer: A — 2

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Q. If f(x) = x^2 - 4, what is the continuity of f(x) at x = 2?

A. Continuous
B. Not Continuous
C. Only left continuous
D. Only right continuous

Solution

f(x) = x^2 - 4 is a polynomial function, which is continuous everywhere, including at x = 2.

Correct Answer: A — Continuous

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Q. If f(x) = x^2 for x < 1 and f(x) = 2x - 1 for x ≥ 1, is f(x) continuous at x = 1? (2019)

A. Yes
B. No
C. Only left continuous
D. Only right continuous

Solution

At x = 1, f(1) = 1^2 = 1 and the limit from the left is also 1, hence f(x) is continuous at x = 1.

Correct Answer: A — Yes

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Q. If f(x) = x^2 for x < 1 and f(x) = 3 for x ≥ 1, is f(x) continuous at x = 1?

A. Yes
B. No
C. Only left continuous
D. Only right continuous

Solution

At x = 1, f(1) = 3 and limit from left is 1^2 = 1. Since they are not equal, f(x) is discontinuous at x = 1.

Correct Answer: B — No

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Q. If f(x) = x^3 - 3x + 2, what is f(1)? Is f(x) continuous at x = 1? (2019)

A. 0, Yes
B. 0, No
C. 1, Yes
D. 1, No

Solution

f(1) = 1^3 - 3*1 + 2 = 0. The function is a polynomial and hence continuous everywhere, including at x = 1.

Correct Answer: C — 1, Yes

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Q. If f(x) = x^3 - 3x + 2, what is the value of f(1) and is it continuous?

A. 0, Continuous
B. 0, Not Continuous
C. 1, Continuous
D. 1, Not Continuous

Solution

f(1) = 1^3 - 3(1) + 2 = 0. Since f(x) is a polynomial, it is continuous everywhere.

Correct Answer: A — 0, Continuous

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Q. If f(x) = x^3 - 3x^2 + 4, what is f'(2)? (2020)

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

Solution

First, find f'(x) = 3x^2 - 6x. Then, f'(2) = 3(2^2) - 6(2) = 12 - 12 = 0.

Correct Answer: A — 0

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Q. If f(x) = x^3 - 4x + 1, what is f''(x)? (2023)

A. 6x - 4
B. 6x + 4
C. 3x^2 - 4
D. 3x^2 + 4

Solution

First derivative f'(x) = 3x^2 - 4, then f''(x) = 6x.

Correct Answer: A — 6x - 4

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Q. If f(x) = x^3 - 6x^2 + 9x, find the inflection point. (2023)

A. (1, 4)
B. (2, 0)
C. (3, 0)
D. (0, 0)

Solution

Find f''(x) = 6x - 12. Set f''(x) = 0 gives x = 2. The inflection point is (2, f(2)) = (2, 0).

Correct Answer: B — (2, 0)

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Q. If f(x) = x^4 - 2x^3 + x, what is f'(1)? (2023)

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

Solution

First, find f'(x) = 4x^3 - 6x^2 + 1. Then, f'(1) = 4(1)^3 - 6(1)^2 + 1 = 4 - 6 + 1 = -1.

Correct Answer: A — 2

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Q. If f(x) = x^4 - 4x^3 + 6x^2, what is f'(2)? (2019)

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

Solution

f'(x) = 4x^3 - 12x^2 + 12x; f'(2) = 4(2^3) - 12(2^2) + 12(2) = 32 - 48 + 24 = 8.

Correct Answer: B — 4

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Q. If f(x) = x^4 - 4x^3, find f'(2). (2023)

A. 0
B. 8
C. 16
D. 32

Solution

f'(x) = 4x^3 - 12x^2; thus, f'(2) = 4(2^3) - 12(2^2) = 32 - 48 = -16.

Correct Answer: C — 16

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Q. If f(x) = x^4 - 4x^3, what is f'(2)? (2019)

A. 0
B. 8
C. 16
D. 12

Solution

f'(x) = 4x^3 - 12x^2. f'(2) = 4(2^3) - 12(2^2) = 32 - 48 = -16.

Correct Answer: B — 8

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Q. If f(x) = x^4 - 8x^2 + 16, what is the minimum value of f(x)? (2023)

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

Solution

Finding the derivative f'(x) = 4x^3 - 16x. Setting it to zero gives x = 0, ±2. The minimum value occurs at x = 2, f(2) = 0.

Correct Answer: A — 0

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Q. If G = [[2, 3], [5, 7]], find the eigenvalues of G.

A. 1, 8
B. 2, 7
C. 3, 5
D. 4, 6

Solution

The eigenvalues are found by solving the characteristic equation det(G - λI) = 0. The eigenvalues are λ = 1, 8.

Correct Answer: A — 1, 8

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Q. If H = [[0, 1], [-1, 0]], what is the determinant of H? (2019)

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

Solution

The determinant of H is calculated as (0*-0) - (1*-1) = 0 + 1 = 1.

Correct Answer: C — -1

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Q. If H = [[1, 2, 3], [0, 1, 4], [5, 6, 0]], find the determinant of H. (2022)

A. -24
B. 24
C. 0
D. 12

Solution

Using the determinant formula for 3x3 matrices, det(H) = 1(1*0 - 4*6) - 2(0 - 4*5) + 3(0 - 1*5) = 0 - 40 - 15 = -55.

Correct Answer: A — -24

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Q. If H = [[1, 2], [2, 4]], what is the rank of H?

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

Solution

The rank of H is 1 because the second row is a multiple of the first row.

Correct Answer: A — 1

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Q. If H = [[2, 3], [5, 7]], find the eigenvalues of H. (2023)

A. 1, 8
B. 2, 7
C. 3, 5
D. 4, 5

Solution

The eigenvalues are found by solving the characteristic equation: det(H - λI) = 0, which gives λ^2 - 9λ + 1 = 0.

Correct Answer: A — 1, 8

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Q. If h(x) = e^(2x), what is h'(x)? (2019)

A. 2e^(2x)
B. e^(2x)
C. 2xe^(2x)
D. e^(x)

Solution

Using the chain rule, h'(x) = 2e^(2x).

Correct Answer: A — 2e^(2x)

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Q. If I = [[1, 1], [1, 1]], what is the rank of I? (2022)

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

Solution

The rank of I is 1 because all rows are linearly dependent.

Correct Answer: B — 1

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Q. If I = [[1, 2, 3], [0, 1, 4], [5, 6, 0]], find the determinant of I.

A. -24
B. 24
C. 0
D. 12

Solution

Using the determinant formula for 3x3 matrices, det(I) = 1(1*0 - 4*6) - 2(0 - 4*5) + 3(0 - 1*5) = 0 - 40 - 15 = -55.

Correct Answer: A — -24

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Q. If I = [[2, 1], [1, 2]], what is the trace of I?

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

Solution

The trace of a matrix is the sum of its diagonal elements. Thus, trace(I) = 2 + 2 = 4.

Correct Answer: C — 3

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Q. If J = [[1, 1], [1, 1]], what is the rank of J?

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

Solution

The rank of J is 1 because both rows are linearly dependent (they are identical).

Correct Answer: B — 1

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Q. If J = [[1, 2, 3], [4, 5, 6], [7, 8, 9]], what is det(J)?

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

Solution

The determinant of J is 0, as the rows are linearly dependent.

Correct Answer: A — 0

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Q. If log_10(0.01) = x, what is the value of x?

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

Solution

log_10(0.01) = log_10(10^-2) = -2, so x = -2.

Correct Answer: B — -2

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Q. If log_10(10^x) = 2, what is the value of x? (2023)

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

Solution

log_10(10^x) = x. Therefore, x = 2.

Correct Answer: B — 2

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Q. If log_10(2) = 0.301, what is log_10(20)? (2023)

A. 0.301
B. 0.699
C. 1.301
D. 1.699

Solution

log_10(20) = log_10(2) + log_10(10) = 0.301 + 1 = 1.301.

Correct Answer: C — 1.301

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Showing 541 to 570 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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