Q. What is the distance between the points (3, 7) and (3, 1)?
Show solution
Solution
Using the distance formula: d = √[(3 - 3)² + (1 - 7)²] = √[0 + 36] = √36 = 6.
Correct Answer:
A
— 6
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Q. What is the distance between the points (5, 5) and (1, 1)?
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Solution
Using the distance formula: d = √[(1 - 5)² + (1 - 5)²] = √[16 + 16] = √32 = 4√2.
Correct Answer:
A
— 4√2
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Q. What is the distance between the points (6, 8) and (6, 2)?
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Solution
Using the distance formula: d = √[(6 - 6)² + (2 - 8)²] = √[0 + 36] = √36 = 6.
Correct Answer:
A
— 6
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Q. What is the equation of a circle with center at (2, -3) and radius 4? (2022)
A.
(x-2)² + (y+3)² = 16
B.
(x+2)² + (y-3)² = 16
C.
(x-2)² + (y-3)² = 16
D.
(x+2)² + (y+3)² = 16
Show solution
Solution
The standard form of a circle's equation is (x-h)² + (y-k)² = r². Here, h=2, k=-3, r=4. Thus, (x-2)² + (y+3)² = 16.
Correct Answer:
A
— (x-2)² + (y+3)² = 16
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Q. What is the equation of a circle with center at (3, -2) and radius 4? (2023)
A.
(x-3)² + (y+2)² = 16
B.
(x+3)² + (y-2)² = 16
C.
(x-3)² + (y-2)² = 16
D.
(x+3)² + (y+2)² = 16
Show solution
Solution
The standard equation of a circle is (x-h)² + (y-k)² = r². Here, h=3, k=-2, r=4. Thus, (x-3)² + (y+2)² = 16.
Correct Answer:
A
— (x-3)² + (y+2)² = 16
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Q. What is the equation of a circle with center at (3, -2) and radius 5? (2022)
A.
(x-3)² + (y+2)² = 25
B.
(x+3)² + (y-2)² = 25
C.
(x-3)² + (y-2)² = 25
D.
(x+3)² + (y+2)² = 25
Show solution
Solution
The standard form of a circle's equation is (x-h)² + (y-k)² = r². Here, h=3, k=-2, r=5, so (x-3)² + (y+2)² = 25.
Correct Answer:
A
— (x-3)² + (y+2)² = 25
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Q. What is the equation of the circle with center at (2, -3) and radius 5?
A.
(x-2)² + (y+3)² = 25
B.
(x+2)² + (y-3)² = 25
C.
(x-2)² + (y-3)² = 25
D.
(x+2)² + (y+3)² = 25
Show solution
Solution
Standard form of a circle: (x-h)² + (y-k)² = r². Here, h=2, k=-3, r=5.
Correct Answer:
A
— (x-2)² + (y+3)² = 25
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Q. What is the equation of the directrix of the parabola x^2 = 12y?
A.
y = 3
B.
y = -3
C.
y = 6
D.
y = -6
Show solution
Solution
The directrix of the parabola x^2 = 4py is given by y = -p. Here, p = 3, so the directrix is y = -3.
Correct Answer:
B
— y = -3
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Q. What is the equation of the line parallel to y = 3x + 2 that passes through the point (4, 1)? (2020)
A.
y = 3x - 11
B.
y = 3x + 1
C.
y = 3x + 2
D.
y = 3x - 2
Show solution
Solution
Since parallel lines have the same slope, the equation is y - 1 = 3(x - 4) which simplifies to y = 3x - 11.
Correct Answer:
A
— y = 3x - 11
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Q. What is the equation of the line parallel to y = 3x + 4 that passes through the point (1, 2)? (2020)
A.
y = 3x - 1
B.
y = 3x + 1
C.
y = 3x + 2
D.
y = 3x - 2
Show solution
Solution
Parallel lines have the same slope. Using point-slope form: y - 2 = 3(x - 1) gives y = 3x - 1.
Correct Answer:
A
— y = 3x - 1
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Q. What is the equation of the line parallel to y = 3x - 4 that passes through the point (2, 1)? (2020)
A.
y = 3x - 5
B.
y = 3x + 1
C.
y = 3x - 1
D.
y = 3x + 4
Show solution
Solution
Since parallel lines have the same slope, the equation is y - 1 = 3(x - 2) which simplifies to y = 3x - 5.
Correct Answer:
C
— y = 3x - 1
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Q. What is the equation of the line that is perpendicular to y = 3x + 2 and passes through the point (1, 1)? (2022)
A.
y = -1/3x + 4/3
B.
y = 3x - 2
C.
y = -3x + 4
D.
y = 1/3x + 2/3
Show solution
Solution
The slope of the perpendicular line is -1/3. Using point-slope form: y - 1 = -1/3(x - 1) gives y = -1/3x + 4/3.
Correct Answer:
A
— y = -1/3x + 4/3
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Q. What is the equation of the line that is perpendicular to y = 3x + 4 and passes through the point (1, 1)? (2022)
A.
y - 1 = -1/3(x - 1)
B.
y - 1 = 3(x - 1)
C.
y - 1 = 3/1(x - 1)
D.
y - 1 = -3(x - 1)
Show solution
Solution
The slope of the perpendicular line is -1/3. Using point-slope form: y - 1 = -1/3(x - 1).
Correct Answer:
A
— y - 1 = -1/3(x - 1)
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Q. What is the equation of the line that passes through the origin and has a slope of -4? (2023)
A.
y = -4x
B.
y = 4x
C.
y = -x/4
D.
y = 1/4x
Show solution
Solution
Using the slope-intercept form y = mx + b, with m = -4 and b = 0, the equation is y = -4x.
Correct Answer:
A
— y = -4x
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Q. What is the equation of the line that passes through the origin and has a slope of -3? (2022)
A.
y = -3x
B.
y = 3x
C.
y = -x/3
D.
y = 1/3x
Show solution
Solution
The equation of a line through the origin with slope m is y = mx. Thus, y = -3x.
Correct Answer:
A
— y = -3x
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Q. What is the expansion of (2x - 3)²? (2022)
A.
4x² - 9
B.
4x² - 12x + 9
C.
4x² + 12x + 9
D.
4x² - 6x
Show solution
Solution
(2x - 3)² = 4x² - 12x + 9 by the square of a binomial.
Correct Answer:
B
— 4x² - 12x + 9
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Q. What is the expansion of (2x - 3y)²?
A.
4x² - 9y²
B.
4x² - 12xy + 9y²
C.
4x² + 9y²
D.
4x² + 12xy + 9y²
Show solution
Solution
(2x - 3y)² = 4x² - 12xy + 9y² by applying the square of a binomial.
Correct Answer:
B
— 4x² - 12xy + 9y²
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Q. What is the expansion of (x + 2)(x - 2)?
A.
x² - 4
B.
x² + 4
C.
2x² - 4
D.
x² - 2
Show solution
Solution
(x + 2)(x - 2) = x² - 2² = x² - 4 by the difference of squares.
Correct Answer:
A
— x² - 4
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Q. What is the first derivative of f(x) = ln(x)? (2019)
A.
1/x
B.
x
C.
ln(x)
D.
e^x
Show solution
Solution
The derivative f'(x) = 1/x.
Correct Answer:
A
— 1/x
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Q. What is the first derivative of f(x) = tan(x)? (2021)
A.
sec^2(x)
B.
cos^2(x)
C.
sin^2(x)
D.
csc^2(x)
Show solution
Solution
The derivative of f(x) = tan(x) is f'(x) = sec^2(x).
Correct Answer:
A
— sec^2(x)
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Q. What is the focus of the parabola defined by the equation y^2 = 20x?
A.
(5, 0)
B.
(0, 5)
C.
(0, 10)
D.
(10, 0)
Show solution
Solution
In the equation y^2 = 4px, we have 4p = 20, thus p = 5. The focus is at (5, 0).
Correct Answer:
A
— (5, 0)
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Q. What is the focus of the parabola given by the equation y^2 = 20x?
A.
(5, 0)
B.
(0, 5)
C.
(0, -5)
D.
(10, 0)
Show solution
Solution
For the parabola y^2 = 4px, here 4p = 20, so p = 5. The focus is at (5, 0).
Correct Answer:
A
— (5, 0)
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Q. What is the general solution of the differential equation dy/dx = 3x^2?
A.
y = x^3 + C
B.
y = 3x^3 + C
C.
y = x^2 + C
D.
y = 3x^2 + C
Show solution
Solution
Integrating both sides gives y = ∫3x^2 dx = x^3 + C.
Correct Answer:
A
— y = x^3 + C
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Q. What is the general solution of the differential equation dy/dx = 4y? (2019)
A.
y = Ce^(4x)
B.
y = Ce^(x/4)
C.
y = 4Ce^x
D.
y = 4Ce^(4x)
Show solution
Solution
The differential equation dy/dx = 4y can be solved using separation of variables, leading to y = Ce^(4x).
Correct Answer:
A
— y = Ce^(4x)
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Q. What is the indefinite integral of e^x? (2020)
A.
e^x + C
B.
e^x
C.
x e^x + C
D.
x^2 e^x + C
Show solution
Solution
The indefinite integral of e^x is e^x + C.
Correct Answer:
A
— e^x + C
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Q. What is the integral of cos(3x) dx?
A.
(1/3)sin(3x) + C
B.
3sin(3x) + C
C.
(1/3)cos(3x) + C
D.
sin(3x) + C
Show solution
Solution
The integral of cos(3x) is (1/3)sin(3x) + C, where C is the constant of integration.
Correct Answer:
A
— (1/3)sin(3x) + C
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Q. What is the integral of e^(2x) dx?
A.
(1/2)e^(2x) + C
B.
2e^(2x) + C
C.
e^(2x) + C
D.
(1/2)e^(x) + C
Show solution
Solution
The integral of e^(2x) is (1/2)e^(2x) + C, where C is the constant of integration.
Correct Answer:
A
— (1/2)e^(2x) + C
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Q. What is the integral of e^(2x)? (2023)
A.
(1/2)e^(2x) + C
B.
2e^(2x) + C
C.
e^(2x) + C
D.
(1/2)e^(x) + C
Show solution
Solution
The integral of e^(2x) is (1/2)e^(2x) + C.
Correct Answer:
A
— (1/2)e^(2x) + C
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Q. What is the integral of e^x dx?
A.
e^x + C
B.
e^x
C.
x e^x + C
D.
x e^x
Show solution
Solution
The integral of e^x is e^x + C, where C is the constant of integration.
Correct Answer:
A
— e^x + C
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Q. What is the integral of f(x) = 1/x? (2023)
A.
ln
B.
x
C.
+ C
D.
1/x + C
.
x + C
.
e^x + C
Show solution
Solution
The integral of 1/x is ln|x| + C.
Correct Answer:
A
— ln
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Showing 1261 to 1290 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!
