Q. What is the area of a sector of a circle with radius 10 cm and angle 90 degrees? (2022)
A.
25π cm²
B.
50π cm²
C.
100π cm²
D.
75π cm²
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Solution
Area of sector = (θ/360) × πr² = (90/360) × π × 10² = (1/4) × 100π = 25π cm².
Correct Answer:
A
— 25π cm²
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Q. What is the area of a sector of a circle with radius 6 cm and a central angle of 90 degrees? (2023)
A.
9π cm²
B.
12π cm²
C.
18π cm²
D.
6π cm²
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Solution
Area of sector = (θ/360) × πr² = (90/360) × π × 6² = (1/4) × 36π = 9π cm².
Correct Answer:
A
— 9π cm²
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Q. What is the area of a sector of a circle with radius 6 cm and angle 90 degrees? (2021)
A.
9π cm²
B.
12π cm²
C.
18π cm²
D.
6π cm²
Show solution
Solution
Area of sector = (θ/360) × πr² = (90/360) × π(6)² = (1/4) × 36π = 9π cm².
Correct Answer:
A
— 9π cm²
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Q. What is the area of a square with a side length of 8 cm? (2023)
A.
64 cm²
B.
32 cm²
C.
16 cm²
D.
48 cm²
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Solution
Area = side² = 8² = 64 cm²
Correct Answer:
A
— 64 cm²
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Q. What is the area of a trapezium with bases 5 cm and 7 cm, and height 4 cm? (2023)
A.
24 cm²
B.
20 cm²
C.
30 cm²
D.
28 cm²
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Solution
Area = 1/2 * (base1 + base2) * height = 1/2 * (5 + 7) * 4 = 24 cm²
Correct Answer:
A
— 24 cm²
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Q. What is the area of a triangle with a base of 8 cm and a height of 5 cm? (2020)
A.
20 cm²
B.
30 cm²
C.
40 cm²
D.
10 cm²
Show solution
Solution
The area of a triangle is given by A = 1/2 * base * height. Here, A = 1/2 * 8 * 5 = 20 cm².
Correct Answer:
A
— 20 cm²
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Q. What is the area of an equilateral triangle with a side length of 6 cm? (2022)
A.
9√3 cm²
B.
12√3 cm²
C.
18√3 cm²
D.
24√3 cm²
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Solution
Area = (√3/4) * side² = (√3/4) * 6² = (√3/4) * 36 = 9√3 cm².
Correct Answer:
A
— 9√3 cm²
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Q. What is the area under the curve y = 1/x from x = 1 to x = 4?
A.
ln(4)
B.
ln(3)
C.
ln(2)
D.
ln(1)
Show solution
Solution
The area under the curve is given by ∫(from 1 to 4) (1/x) dx = [ln(x)] from 1 to 4 = ln(4) - ln(1) = ln(4).
Correct Answer:
A
— ln(4)
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Q. What is the area under the curve y = 2x^2 + 3 from x = 0 to x = 2?
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Solution
The area under the curve is given by ∫(from 0 to 2) (2x^2 + 3) dx = [(2/3)x^3 + 3x] from 0 to 2 = (16/3 + 6) = 10.
Correct Answer:
B
— 12
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Q. What is the axis of symmetry for the parabola given by the equation y = -3(x - 2)^2 + 5?
A.
x = 2
B.
y = 5
C.
y = -3
D.
x = -2
Show solution
Solution
The axis of symmetry for a parabola in vertex form y = a(x - h)^2 + k is x = h. Here, h = 2.
Correct Answer:
A
— x = 2
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Q. What is the axis of symmetry for the parabola given by the equation y^2 = 6x?
A.
x-axis
B.
y-axis
C.
y = x
D.
x = 0
Show solution
Solution
The axis of symmetry for the parabola y^2 = 4px is the x-axis.
Correct Answer:
B
— y-axis
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Q. What is the characteristic polynomial of the matrix E = [[2, 1], [1, 2]]? (2021)
A.
λ^2 - 3λ + 1
B.
λ^2 - 5λ + 4
C.
λ^2 - 4λ + 3
D.
λ^2 - 2λ + 1
Show solution
Solution
The characteristic polynomial is det(E - λI) = det([[2-λ, 1], [1, 2-λ]]) = (2-λ)(2-λ) - 1 = λ^2 - 3λ + 1.
Correct Answer:
A
— λ^2 - 3λ + 1
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Q. What is the characteristic polynomial of the matrix G = [[2, 1], [1, 2]]? (2020)
A.
λ^2 - 3λ + 1
B.
λ^2 - 5λ + 4
C.
λ^2 - 2λ + 1
D.
λ^2 - 4λ + 4
Show solution
Solution
The characteristic polynomial is given by det(G - λI) = det([[2-λ, 1], [1, 2-λ]]) = (2-λ)(2-λ) - 1 = λ^2 - 3λ + 3.
Correct Answer:
A
— λ^2 - 3λ + 1
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Q. What is the circumference of a circle with a diameter of 14 cm? (2023)
A.
22 cm
B.
28 cm
C.
44 cm
D.
56 cm
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Solution
The circumference C of a circle is given by C = π * diameter. Here, C = π * 14 cm ≈ 3.14 * 14 ≈ 44 cm.
Correct Answer:
B
— 28 cm
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Q. What is the circumference of a circle with a radius of 7 cm? (2019)
A.
14π cm
B.
21π cm
C.
7π cm
D.
28π cm
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Solution
Circumference = 2 * π * radius = 2 * π * 7 = 14π cm
Correct Answer:
A
— 14π cm
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Q. What is the coefficient of x^0 in the expansion of (x - 1)^5?
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Solution
The coefficient of x^0 in (x - 1)^5 is given by 5C5 * (-1)^5 = -1.
Correct Answer:
C
— -5
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Q. What is the coefficient of x^2 in the expansion of (2x + 5)^4?
A.
60
B.
80
C.
100
D.
120
Show solution
Solution
Using the binomial theorem, the coefficient of x^2 in (2x + 5)^4 is given by 4C2 * (2)^2 * (5)^2 = 6 * 4 * 25 = 600.
Correct Answer:
A
— 60
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Q. What is the coefficient of x^2 in the expansion of (2x - 5)^5? (2019)
A.
-300
B.
-600
C.
600
D.
300
Show solution
Solution
The coefficient of x^2 in (2x - 5)^5 is given by 5C2 * (2)^2 * (-5)^3 = 10 * 4 * (-125) = -5000.
Correct Answer:
B
— -600
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Q. What is the coefficient of x^2 in the expansion of (3x + 4)^5?
A.
60
B.
80
C.
100
D.
120
Show solution
Solution
The coefficient of x^2 in (3x + 4)^5 is C(5, 2) * (3)^2 * (4)^3 = 10 * 9 * 64 = 5760.
Correct Answer:
B
— 80
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Q. What is the coefficient of x^3 in the expansion of (3x + 2)^5? (2023)
A.
90
B.
180
C.
270
D.
360
Show solution
Solution
The coefficient of x^3 in (3x + 2)^5 is given by 5C3 * (3)^3 * (2)^2 = 10 * 27 * 4 = 1080.
Correct Answer:
B
— 180
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Q. What is the coefficient of x^3 in the expansion of (x + 5)^6?
A.
150
B.
300
C.
450
D.
600
Show solution
Solution
The coefficient of x^3 in (x + 5)^6 is C(6, 3) * (5)^3 = 20 * 125 = 2500.
Correct Answer:
B
— 300
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Q. What is the coefficient of x^4 in the expansion of (x + 3)^6?
A.
81
B.
162
C.
243
D.
324
Show solution
Solution
The coefficient of x^4 in (x + 3)^6 is C(6, 4) * 3^2 = 15 * 9 = 135.
Correct Answer:
C
— 243
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Q. What is the conjugate of the complex number z = 7 - 4i? (2021)
A.
7 + 4i
B.
7 - 4i
C.
-7 + 4i
D.
-7 - 4i
Show solution
Solution
The conjugate of z is given by z* = 7 + 4i.
Correct Answer:
A
— 7 + 4i
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Q. What is the continuity of the function f(x) = sqrt(x) at x = 0? (2022)
A.
Continuous
B.
Not continuous
C.
Only left continuous
D.
Only right continuous
Show solution
Solution
The function f(x) = sqrt(x) is continuous at x = 0 as it is defined and the limit exists.
Correct Answer:
A
— Continuous
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Q. What is the critical point of f(x) = x^2 - 4x + 4? (2022)
Show solution
Solution
Set f'(x) = 2x - 4 = 0; solving gives x = 2.
Correct Answer:
B
— 2
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Q. What is the critical point of the function f(x) = x^2 - 4x + 4? (2022)
Show solution
Solution
Find f'(x) = 2x - 4. Set f'(x) = 0, giving 2x - 4 = 0, hence x = 2.
Correct Answer:
B
— 2
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Q. What is the critical point of the function f(x) = x^4 - 4x^3 + 6? (2023)
Show solution
Solution
First derivative f'(x) = 4x^3 - 12x^2. Setting f'(x) = 0 gives x = 0, 1, 3.
Correct Answer:
B
— 1
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Q. What is the cross product of vectors A = i + 2j + 3k and B = 4i + 5j + 6k?
A.
-3i + 6j - 3k
B.
-3i + 6j + 3k
C.
3i - 6j + 3k
D.
3i + 6j - 3k
Show solution
Solution
A × B = |i j k| |1 2 3| |4 5 6| = -3i + 6j - 3k.
Correct Answer:
A
— -3i + 6j - 3k
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Q. What is the cross product of vectors A = i + 2j and B = 3i + 4j? (2021)
Show solution
Solution
A × B = |i j k| |1 2 0| |3 4 0| = (0 - 0)i - (0 - 0)j + (4 - 6)k = -2k.
Correct Answer:
A
— -2k
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Q. What is the cross product of vectors E = i + 2j and F = 3i + 4j?
Show solution
Solution
E × F = |i j k| |1 2 0| |3 4 0| = (0 - 0)i - (0 - 0)j + (1*4 - 2*3)k = -2k.
Correct Answer:
A
— -2k
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Showing 1201 to 1230 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!
