NDA MCQ & Objective Questions
The National Defence Academy (NDA) exam is a crucial stepping stone for students aspiring to join the Indian Armed Forces. It tests not only knowledge but also the ability to apply concepts effectively. Practicing NDA MCQs and objective questions is essential for enhancing your exam preparation, as it helps in identifying important questions and boosts confidence in tackling various subjects.
What You Will Practise Here
Mathematics: Key concepts, formulas, and problem-solving techniques.
General Knowledge: Current affairs, history, and geography relevant to NDA.
English: Grammar, comprehension, and vocabulary exercises.
Physics: Fundamental principles and application-based questions.
Chemistry: Important definitions, reactions, and theoretical concepts.
Logical Reasoning: Techniques for solving puzzles and analytical questions.
Military History: Significant events and figures in Indian military history.
Exam Relevance
The NDA exam is not only significant for aspiring defence candidates but also aligns with various school and competitive exams like CBSE, State Boards, NEET, and JEE. Questions often follow a pattern that includes multiple-choice formats, requiring students to apply their knowledge effectively. Understanding the common question types and formats will enhance your readiness for these exams.
Common Mistakes Students Make
Misinterpreting questions due to lack of careful reading.
Overlooking important formulas in Mathematics and Physics.
Confusing similar concepts in Chemistry and General Knowledge.
Neglecting to practice logical reasoning, leading to time management issues.
Failing to revise key definitions and terms in English and other subjects.
FAQs
Question: What are NDA MCQ questions?Answer: NDA MCQ questions are multiple-choice questions designed to test your knowledge and understanding of various subjects relevant to the NDA exam.
Question: How can I prepare for NDA objective questions with answers?Answer: Regular practice of NDA objective questions, along with reviewing answers and explanations, will help solidify your understanding and improve your performance.
Question: What are some important NDA questions for exams?Answer: Important NDA questions often cover key concepts in Mathematics, General Knowledge, English, and Science, focusing on application and analytical skills.
Start your journey towards success by solving NDA practice MCQs today! Testing your understanding through these objective questions will not only prepare you for the exam but also build your confidence to excel.
Q. If the roots of the equation x^2 + 5x + 6 = 0 are a and b, what is the value of ab? (2023)
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Solution
The product of the roots ab is given by c/a. Here, c = 6 and a = 1, so ab = 6.
Correct Answer:
A
— 6
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Q. If the roots of the equation x^2 + 5x + c = 0 are 2 and 3, what is the value of c? (2022)
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Solution
Using the product of the roots, c = 2 * 3 = 6.
Correct Answer:
A
— 6
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Q. If the roots of the equation x^2 + 5x + k = 0 are -2 and -3, what is the value of k?
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Solution
The product of the roots is (-2)(-3) = 6, so k = 6.
Correct Answer:
A
— 6
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Q. If the roots of the equation x^2 + 5x + k = 0 are real and distinct, what is the condition on k? (2023)
A.
k < 25
B.
k > 25
C.
k = 25
D.
k ≤ 25
Show solution
Solution
The discriminant must be greater than zero: 5^2 - 4(1)(k) > 0, leading to k < 25.
Correct Answer:
A
— k < 25
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Q. If the roots of the equation x^2 + 6x + k = 0 are real and distinct, what must be the condition on k? (2023)
A.
k < 9
B.
k > 9
C.
k = 9
D.
k ≤ 9
Show solution
Solution
For real and distinct roots, the discriminant must be greater than zero: 6^2 - 4*1*k > 0 leads to k < 9.
Correct Answer:
A
— k < 9
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Q. If the roots of the equation x^2 + mx + n = 0 are 3 and 4, what is the value of n? (2022)
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Solution
Using Vieta's formulas, n = 3 * 4 = 12.
Correct Answer:
A
— 12
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Q. If the roots of the equation x^2 - 2x + k = 0 are real and distinct, what is the condition for k?
A.
k > 1
B.
k < 1
C.
k = 1
D.
k ≥ 1
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Solution
The discriminant must be positive for real and distinct roots: (-2)^2 - 4*1*k > 0, which simplifies to 4 - 4k > 0, or k < 1.
Correct Answer:
A
— k > 1
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Q. If the roots of the equation x^2 - 4x + k = 0 are real and distinct, what is the condition for k? (2023)
A.
k > 4
B.
k < 4
C.
k = 4
D.
k ≤ 4
Show solution
Solution
The discriminant must be greater than zero for real and distinct roots: (-4)^2 - 4*1*k > 0, which simplifies to 16 - 4k > 0, or k < 4.
Correct Answer:
A
— k > 4
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Q. If the roots of the equation x^2 - 6x + k = 0 are 3 and 3, what is the value of k? (2020)
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Solution
The equation can be expressed as (x - 3)^2 = 0, which expands to x^2 - 6x + 9 = 0. Thus, k = 9.
Correct Answer:
B
— 9
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Q. If the roots of the equation x^2 - 6x + k = 0 are real and distinct, what is the range of k? (2020)
A.
k < 9
B.
k > 9
C.
k = 9
D.
k ≤ 9
Show solution
Solution
For real and distinct roots, the discriminant must be greater than zero: (-6)^2 - 4*1*k > 0, leading to k < 9.
Correct Answer:
A
— k < 9
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Q. If the roots of the equation x^2 - 7x + 10 = 0 are a and b, what is the value of ab? (2021)
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Solution
By Vieta's formulas, ab = 10, which is the constant term of the polynomial.
Correct Answer:
A
— 10
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Q. If the roots of the polynomial x^3 - 3x^2 + 3x - 1 = 0 are a, b, and c, what is the value of a + b + c?
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Solution
By Vieta's formulas, the sum of the roots a + b + c = -(-3) = 3.
Correct Answer:
B
— 3
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Q. If the roots of the quadratic equation ax^2 + bx + c = 0 are 4 and -1, what is the value of b if a = 1 and c = -4? (2023)
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Solution
Using the sum of roots, b = - (4 + (-1)) = -3.
Correct Answer:
A
— -3
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Q. If the roots of the quadratic equation ax^2 + bx + c = 0 are equal, which of the following must be true? (2019)
A.
b^2 > 4ac
B.
b^2 < 4ac
C.
b^2 = 4ac
D.
a + b + c = 0
Show solution
Solution
For the roots to be equal, the discriminant must be zero, which means b^2 = 4ac.
Correct Answer:
C
— b^2 = 4ac
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Q. If the roots of the quadratic equation x^2 + 2x + k = 0 are equal, what is the value of k? (2022)
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Solution
For the roots to be equal, the discriminant must be zero. Thus, 2^2 - 4*1*k = 0 leads to k = 1.
Correct Answer:
D
— -1
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Q. If the roots of the quadratic equation x^2 + 4x + k = 0 are equal, what is the value of k?
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Solution
For the roots to be equal, the discriminant must be zero. Thus, 4^2 - 4(1)(k) = 0 leads to k = 4.
Correct Answer:
B
— 8
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Q. If the roots of the quadratic equation x^2 + px + q = 0 are -2 and -3, what is the value of p + q? (2019)
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Solution
Using Vieta's formulas, p = -(-2 - 3) = 5 and q = (-2)(-3) = 6. Therefore, p + q = 5 + 6 = 11.
Correct Answer:
B
— -6
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Q. If the roots of the quadratic equation x^2 + px + q = 0 are -2 and -3, what is the value of p? (2019)
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Solution
The sum of the roots is -(-2) + -(-3) = 5, hence p = 5.
Correct Answer:
A
— 5
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Q. If the roots of the quadratic equation x² - 5x + k = 0 are equal, what is the value of k? (2023)
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Solution
For the roots to be equal, the discriminant must be zero. Thus, (-5)² - 4(1)(k) = 0, giving k = 25/4 = 6.25.
Correct Answer:
A
— 6
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Q. If the scalar product of two vectors A and B is 0, what can be inferred about the vectors?
A.
They are equal
B.
They are parallel
C.
They are orthogonal
D.
They are collinear
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Solution
If A · B = 0, then A and B are orthogonal (perpendicular) to each other.
Correct Answer:
C
— They are orthogonal
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Q. If the scalar product of two vectors A and B is 15 and the magnitudes are |A| = 5 and |B| = 3, find the angle between them.
A.
60°
B.
45°
C.
30°
D.
90°
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Solution
A · B = |A||B|cos(θ) => 15 = 5*3*cos(θ) => cos(θ) = 1, θ = 0°.
Correct Answer:
B
— 45°
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Q. If the scalar product of two vectors A and B is equal to the product of their magnitudes, what can be inferred?
A.
They are perpendicular
B.
They are parallel
C.
They are equal
D.
They are opposite
Show solution
Solution
If A · B = |A||B|, then the angle between them is 0°, meaning they are parallel.
Correct Answer:
B
— They are parallel
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Q. If the scalar product of vectors A and B is equal to the product of their magnitudes, what can be said about the angle between them?
A.
0°
B.
90°
C.
180°
D.
45°
Show solution
Solution
If A · B = |A||B|, then cos(θ) = 1, which means θ = 0°.
Correct Answer:
A
— 0°
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Q. If the sediment load of a river increases, what is the most likely effect on the river's flow?
A.
Increased velocity
B.
Decreased velocity
C.
No effect
D.
Increased depth
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Solution
Increased sediment load generally decreases the velocity of the river due to increased friction.
Correct Answer:
B
— Decreased velocity
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Q. If the sides of a triangle are in the ratio 3:4:5, what type of triangle is it? (2022)
A.
Equilateral
B.
Isosceles
C.
Scalene
D.
Right-angled
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Solution
A triangle with sides in the ratio 3:4:5 satisfies the Pythagorean theorem, hence it is a right-angled triangle.
Correct Answer:
D
— Right-angled
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Q. If the sides of triangle DEF are in the ratio 3:4:5, what type of triangle is it? (2021)
A.
Acute
B.
Obtuse
C.
Right
D.
Equilateral
Show solution
Solution
A triangle with sides in the ratio 3:4:5 is a right triangle, as it satisfies the Pythagorean theorem.
Correct Answer:
C
— Right
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Q. If the sides of triangle XYZ are in the ratio 3:4:5, what type of triangle is it? (2021)
A.
Acute
B.
Obtuse
C.
Right
D.
Equilateral
Show solution
Solution
A triangle with sides in the ratio 3:4:5 is a right triangle, as it satisfies the Pythagorean theorem.
Correct Answer:
C
— Right
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Q. If the slope of a riverbed is 1:1000, what is the vertical drop over a distance of 2 km? (2000)
A.
2 m
B.
1 m
C.
3 m
D.
4 m
Show solution
Solution
Vertical drop = Distance × Slope = 2000 m × (1/1000) = 2 m.
Correct Answer:
A
— 2 m
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Q. If the soil erosion rate in a river basin is 2 tons per hectare per year, how much soil will be eroded from a 50-hectare area in 5 years? (2023)
A.
500 tons
B.
1000 tons
C.
2000 tons
D.
2500 tons
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Solution
Soil eroded = 2 tons/hectare/year × 50 hectares × 5 years = 500 tons.
Correct Answer:
C
— 2000 tons
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Q. If the soil erosion rate is 2 tons per hectare per year, how much soil will be eroded from 50 hectares in 5 years?
A.
500 tons
B.
1000 tons
C.
200 tons
D.
100 tons
Show solution
Solution
Soil eroded = Erosion rate × Area × Time = 2 tons/hectare/year × 50 hectares × 5 years = 500 tons.
Correct Answer:
B
— 1000 tons
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