Q. Which of the following is the correct expansion of (x - y)³?
A.
x³ - 3x²y + 3xy² - y³
B.
x³ - y³
C.
x³ - 3xy² + 3x²y - y³
D.
3x²y - 3xy²
Show solution
Solution
(x - y)³ = x³ - 3x²y + 3xy² - y³ by the binomial theorem.
Correct Answer:
A
— x³ - 3x²y + 3xy² - y³
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Q. Which of the following is the correct factorization of a² - b²?
A.
(a + b)(a - b)
B.
(a - b)(a - b)
C.
(a + b)(a + b)
D.
a² - 2ab + b²
Show solution
Solution
a² - b² = (a + b)(a - b) by the difference of squares identity.
Correct Answer:
A
— (a + b)(a - b)
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Q. Which of the following is the correct identity for (a - b)(a + b)? (2019)
A.
a² + b²
B.
a² - b²
C.
ab
D.
a - b
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Solution
(a - b)(a + b) = a² - b² by the difference of squares formula.
Correct Answer:
B
— a² - b²
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Q. Which of the following is the correct identity for (a - b)²?
A.
a² - 2ab + b²
B.
a² + 2ab + b²
C.
a² - b²
D.
2a² - 2b²
Show solution
Solution
(a - b)² = a² - 2ab + b² by the expansion of the square of a binomial.
Correct Answer:
A
— a² - 2ab + b²
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Q. Which of the following is the correct identity for (x + y + z)³?
A.
x³ + y³ + z³ + 3(x + y)(y + z)(z + x)
B.
x³ + y³ + z³ + 3xyz
C.
x³ + y³ + z³ + 3xy + 3yz + 3zx
D.
x³ + y³ + z³ - 3xyz
Show solution
Solution
(x + y + z)³ = x³ + y³ + z³ + 3xyz.
Correct Answer:
B
— x³ + y³ + z³ + 3xyz
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Q. Which of the following is the correct identity for (x + y)³?
A.
x³ + y³ + 3xy(x + y)
B.
x³ + y³ - 3xy(x + y)
C.
x³ + y³ + 3xy²
D.
x³ - y³
Show solution
Solution
(x + y)³ = x³ + y³ + 3xy(x + y) by the binomial expansion.
Correct Answer:
A
— x³ + y³ + 3xy(x + y)
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Q. Which of the following is the expanded form of (x + 2)²?
A.
x² + 4
B.
x² + 4x + 4
C.
x² + 2x + 2
D.
x² + 2
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Solution
(x + 2)² = x² + 2*2*x + 2² = x² + 4x + 4.
Correct Answer:
B
— x² + 4x + 4
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Q. Which of the following is the smallest positive integer? (2023)
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Solution
The smallest positive integer is 1.
Correct Answer:
B
— 1
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Q. Which of the following is true for log_10(0.1)?
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Solution
log_10(0.1) = log_10(10^-1) = -1.
Correct Answer:
A
— -1
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Q. Which of the following is true for log_a(b) + log_a(c)?
A.
log_a(bc)
B.
log_a(b/c)
C.
log_a(b-c)
D.
log_a(b+c)
Show solution
Solution
log_a(b) + log_a(c) = log_a(bc) by the product property of logarithms.
Correct Answer:
A
— log_a(bc)
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Q. Which of the following is true for log_a(b) and log_a(c) if b < c? (2019)
A.
log_a(b) < log_a(c)
B.
log_a(b) > log_a(c)
C.
log_a(b) = log_a(c)
D.
None of the above
Show solution
Solution
If a > 1, then log_a(b) < log_a(c) when b < c.
Correct Answer:
A
— log_a(b) < log_a(c)
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Q. Which of the following is true for log_a(bc)?
A.
log_a(b) + log_a(c)
B.
log_a(b) - log_a(c)
C.
log_a(bc) = log_a(b) * log_a(c)
D.
None of the above
Show solution
Solution
log_a(bc) = log_a(b) + log_a(c) by the product rule of logarithms.
Correct Answer:
A
— log_a(b) + log_a(c)
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Q. Which of the following is true for the identity (a + b)³?
A.
a³ + b³
B.
a³ + 3a²b + 3ab² + b³
C.
a² + b²
D.
3ab
Show solution
Solution
(a + b)³ = a³ + 3a²b + 3ab² + b³.
Correct Answer:
B
— a³ + 3a²b + 3ab² + b³
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Q. Which of the following is true for the identity (x + y)²?
A.
x² + y²
B.
x² + 2xy + y²
C.
x² - 2xy + y²
D.
2xy
Show solution
Solution
(x + y)² = x² + 2xy + y².
Correct Answer:
B
— x² + 2xy + y²
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Q. Which of the following lines is parallel to the line 3x - 4y + 5 = 0?
A.
6x - 8y + 10 = 0
B.
4x + 3y - 7 = 0
C.
3x + 4y - 5 = 0
D.
2x - 3y + 1 = 0
Show solution
Solution
Parallel lines have the same slope. The slope of the given line is 3/4, and the line 6x - 8y + 10 = 0 also has the same slope.
Correct Answer:
A
— 6x - 8y + 10 = 0
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Q. Which of the following matrices is a diagonal matrix? (2023)
A.
[[1, 0], [0, 2]]
B.
[[1, 2], [3, 4]]
C.
[[0, 1], [1, 0]]
D.
[[1, 1], [1, 1]]
Show solution
Solution
A diagonal matrix is one where all off-diagonal elements are zero. The matrix [[1, 0], [0, 2]] is a diagonal matrix.
Correct Answer:
A
— [[1, 0], [0, 2]]
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Q. Which of the following matrices is a zero matrix? (2022)
A.
[[0, 0], [0, 0]]
B.
[[1, 0], [0, 1]]
C.
[[1, 2], [3, 4]]
D.
[[0, 1], [1, 0]]
Show solution
Solution
A zero matrix is one where all elements are zero. The matrix [[0, 0], [0, 0]] meets this criterion.
Correct Answer:
A
— [[0, 0], [0, 0]]
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Q. Which of the following matrices is an identity matrix? (2023)
A.
[[1, 0], [0, 1]]
B.
[[0, 1], [1, 0]]
C.
[[1, 1], [1, 1]]
D.
[[0, 0], [0, 0]]
Show solution
Solution
An identity matrix has 1s on the diagonal and 0s elsewhere. The matrix [[1, 0], [0, 1]] fits this definition.
Correct Answer:
A
— [[1, 0], [0, 1]]
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Q. Which of the following matrices is an orthogonal matrix? (2021)
A.
A matrix whose transpose is equal to its inverse
B.
A matrix with all elements equal
C.
A matrix with only one row
D.
A matrix with all diagonal elements equal
Show solution
Solution
An orthogonal matrix is defined as a matrix whose transpose is equal to its inverse.
Correct Answer:
A
— A matrix whose transpose is equal to its inverse
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Q. Which of the following matrices is not invertible? (2019)
A.
[[1, 2], [3, 4]]
B.
[[0, 1], [0, 0]]
C.
[[5, 6], [7, 8]]
D.
[[9, 10], [11, 12]]
Show solution
Solution
A matrix is not invertible if its determinant is zero. The matrix [[0, 1], [0, 0]] has a determinant of 0.
Correct Answer:
B
— [[0, 1], [0, 0]]
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Q. Which of the following matrices is symmetric? (2023)
A.
A = [[1, 2], [3, 4]]
B.
B = [[1, 2], [2, 1]]
C.
C = [[1, 0], [0, 1]]
D.
D = [[1, 2, 3], [4, 5, 6]]
Show solution
Solution
A symmetric matrix is one that is equal to its transpose. Matrix B is symmetric because B = B^T.
Correct Answer:
B
— B = [[1, 2], [2, 1]]
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Q. Which of the following numbers is a perfect square?
Show solution
Solution
25 is a perfect square (5^2).
Correct Answer:
C
— 25
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Q. Which of the following points lies on the parabola y = x^2 - 4?
A.
(2, 0)
B.
(0, -4)
C.
(1, -3)
D.
(3, 5)
Show solution
Solution
Substituting x = 1 into the equation gives y = 1^2 - 4 = -3, so the point (1, -3) lies on the parabola.
Correct Answer:
C
— (1, -3)
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Q. Which of the following points lies on the parabola y^2 = 8x?
A.
(2, 4)
B.
(1, 2)
C.
(4, 4)
D.
(2, 2)
Show solution
Solution
To check if a point lies on the parabola, substitute the x-coordinate into the equation. For (2, 4), 4^2 = 16 and 8*2 = 16, so it lies on the parabola.
Correct Answer:
A
— (2, 4)
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Q. Which of the following represents the complex number 4 in polar form?
A.
4(cos 0 + i sin 0)
B.
4(cos π/2 + i sin π/2)
C.
4(cos π + i sin π)
D.
4(cos π/4 + i sin π/4)
Show solution
Solution
The polar form of a complex number r(cos θ + i sin θ) where r is the modulus and θ is the argument. Here, 4 = 4(cos 0 + i sin 0).
Correct Answer:
A
— 4(cos 0 + i sin 0)
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Q. Which of the following represents the identity for (a + b + c)²?
A.
a² + b² + c² + 2ab + 2bc + 2ca
B.
a² + b² + c² + 3abc
C.
a² + b² + c²
D.
a² + b² + c² + ab + ac + bc
Show solution
Solution
(a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca.
Correct Answer:
A
— a² + b² + c² + 2ab + 2bc + 2ca
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Q. Which of the following statements is true about the function f(x) = 1/(x-1)? (2022)
A.
Continuous at x = 1
B.
Continuous everywhere
C.
Not continuous at x = 1
D.
Continuous at x = 0
Show solution
Solution
The function f(x) = 1/(x-1) is not continuous at x = 1 because it is undefined there.
Correct Answer:
C
— Not continuous at x = 1
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Q. Which of the following statements is true about the function f(x) = 1/(x-3)?
A.
Continuous at x = 3
B.
Continuous everywhere
C.
Not continuous at x = 3
D.
Continuous at x = 0
Show solution
Solution
The function f(x) = 1/(x-3) is not defined at x = 3, hence it is not continuous at that point.
Correct Answer:
C
— Not continuous at x = 3
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Q. Which of the following statements is true about the function f(x) = |x|?
A.
Continuous everywhere
B.
Discontinuous at x = 0
C.
Continuous only at x = 1
D.
Discontinuous everywhere
Show solution
Solution
The function f(x) = |x| is continuous everywhere, including at x = 0.
Correct Answer:
A
— Continuous everywhere
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Q. Which of the following statements is true about variance? (2020)
A.
It can be negative
B.
It is always positive
C.
It is the average of the data
D.
It is the sum of the data
Show solution
Solution
Variance is always non-negative as it is calculated as the average of squared deviations from the mean.
Correct Answer:
B
— It is always positive
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Showing 1561 to 1590 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!
