Q. In triangle DEF, if DE = 12 cm, EF = 16 cm, and DF = 20 cm, what is the semi-perimeter? (2021)
A.
24 cm
B.
28 cm
C.
30 cm
D.
20 cm
Show solution
Solution
Semi-perimeter s = (12 + 16 + 20) / 2 = 48 / 2 = 24 cm.
Correct Answer:
B
— 28 cm
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Q. In triangle DEF, if DE = 5 cm, EF = 12 cm, and DF = 13 cm, is triangle DEF a right triangle? (2019)
A.
Yes
B.
No
C.
Cannot be determined
D.
Only if angle D is 90 degrees
Show solution
Solution
Using the Pythagorean theorem, 5^2 + 12^2 = 25 + 144 = 169 = 13^2. Thus, triangle DEF is a right triangle.
Correct Answer:
A
— Yes
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Q. In triangle GHI, if angle G = 30 degrees and side GH = 10 cm, what is the length of side HI if angle H = 60 degrees? (2023)
A.
5 cm
B.
10 cm
C.
15 cm
D.
20 cm
Show solution
Solution
Using the sine rule, HI/sin(60) = GH/sin(30). Therefore, HI = (10 * sin(60)) / sin(30) = 10 * (√3/2) / (1/2) = 10√3 cm.
Correct Answer:
C
— 15 cm
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Q. In triangle GHI, if angle G = 90 degrees and GH = 9 cm, HI = 12 cm, what is the length of side GI? (2022)
A.
15 cm
B.
10 cm
C.
12 cm
D.
9 cm
Show solution
Solution
Using the Pythagorean theorem, GI = √(HI² - GH²) = √(12² - 9²) = √(144 - 81) = √63 = 15 cm.
Correct Answer:
A
— 15 cm
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Q. In triangle GHI, if GH = 10 cm, HI = 24 cm, and GI = 26 cm, what is the area of the triangle? (2019)
A.
120 cm²
B.
130 cm²
C.
140 cm²
D.
150 cm²
Show solution
Solution
Using Heron's formula, semi-perimeter s = (10 + 24 + 26) / 2 = 30. Area = √(s(s-a)(s-b)(s-c)) = √(30*20*6*4) = 120 cm².
Correct Answer:
A
— 120 cm²
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Q. In triangle GHI, if GH = 10 cm, HI = 24 cm, and GI = 26 cm, what is the length of the longest side? (2022)
A.
10 cm
B.
24 cm
C.
26 cm
D.
Cannot be determined
Show solution
Solution
The longest side of triangle GHI is GI, which measures 26 cm.
Correct Answer:
C
— 26 cm
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Q. In triangle GHI, if GH = 10 cm, HI = 24 cm, and GI = 26 cm, what is the perimeter? (2019)
A.
50 cm
B.
60 cm
C.
70 cm
D.
80 cm
Show solution
Solution
Perimeter = GH + HI + GI = 10 + 24 + 26 = 60 cm.
Correct Answer:
A
— 50 cm
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Q. In triangle GHI, if the lengths of sides GH, HI, and GI are in the ratio 3:4:5, what type of triangle is it? (2019)
A.
Equilateral
B.
Isosceles
C.
Scalene
D.
Right-angled
Show solution
Solution
Since the sides are in the ratio 3:4:5, it follows the Pythagorean theorem, indicating it is a right-angled triangle.
Correct Answer:
D
— Right-angled
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Q. In triangle JKL, if angle J = 90 degrees and JK = 15 cm, KL = 20 cm, what is the length of side JL? (2023)
A.
10 cm
B.
12 cm
C.
15 cm
D.
25 cm
Show solution
Solution
Using Pythagoras theorem: JL = √(KL² - JK²) = √(20² - 15²) = √(400 - 225) = √175 = 12 cm.
Correct Answer:
B
— 12 cm
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Q. In triangle JKL, if angle J = 90 degrees and JK = 15 cm, KL = 20 cm, what is the length of JL? (2022)
A.
10 cm
B.
12 cm
C.
15 cm
D.
25 cm
Show solution
Solution
Using the Pythagorean theorem, JL = √(KL² - JK²) = √(20² - 15²) = √(400 - 225) = √175 = 12.25 cm.
Correct Answer:
B
— 12 cm
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Q. In triangle JKL, if JK = 15 cm, KL = 20 cm, and JL = 25 cm, what is the semi-perimeter of the triangle? (2022)
A.
30 cm
B.
25 cm
C.
20 cm
D.
35 cm
Show solution
Solution
Semi-perimeter = (JK + KL + JL) / 2 = (15 + 20 + 25) / 2 = 30 cm.
Correct Answer:
A
— 30 cm
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Q. In triangle JKL, if JK = 15 cm, KL = 20 cm, and JL = 25 cm, what is the semi-perimeter? (2022)
A.
30 cm
B.
25 cm
C.
20 cm
D.
15 cm
Show solution
Solution
Semi-perimeter = (JK + KL + JL) / 2 = (15 + 20 + 25) / 2 = 30 cm.
Correct Answer:
A
— 30 cm
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Q. In triangle JKL, if JK = 15 cm, KL = 20 cm, and JL = 25 cm, what is the type of triangle? (2023)
A.
Equilateral
B.
Isosceles
C.
Scalene
D.
Right-angled
Show solution
Solution
Since 15² + 20² = 25² (225 + 400 = 625), triangle JKL is a right-angled triangle.
Correct Answer:
D
— Right-angled
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Q. In triangle JKL, if JK = 5 cm, KL = 12 cm, and JL = 13 cm, what is the type of triangle? (2023)
A.
Equilateral
B.
Isosceles
C.
Scalene
D.
Right-angled
Show solution
Solution
Since 5² + 12² = 13² (25 + 144 = 169), triangle JKL is a right-angled triangle.
Correct Answer:
D
— Right-angled
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Q. In triangle MNO, if MN = 8 cm, NO = 15 cm, and MO = 17 cm, what is the type of triangle? (2023)
A.
Equilateral
B.
Isosceles
C.
Scalene
D.
Right-angled
Show solution
Solution
Using the Pythagorean theorem, 8² + 15² = 64 + 225 = 289 = 17². Hence, it is a right-angled triangle.
Correct Answer:
D
— Right-angled
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Q. In triangle PQR, if PQ = 10 cm, PR = 24 cm, and QR = 26 cm, what is the area of the triangle? (2019)
A.
120 cm²
B.
240 cm²
C.
60 cm²
D.
80 cm²
Show solution
Solution
Using Heron's formula, s = (10 + 24 + 26) / 2 = 30. Area = √(30(30-10)(30-24)(30-26)) = √(30*20*6*4) = √(4800) = 120 cm².
Correct Answer:
A
— 120 cm²
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Q. In triangle PQR, if PQ = 8 cm, QR = 6 cm, and PR = 10 cm, what is the perimeter of the triangle? (2022)
A.
24 cm
B.
26 cm
C.
22 cm
D.
20 cm
Show solution
Solution
Perimeter = PQ + QR + PR = 8 + 6 + 10 = 24 cm.
Correct Answer:
A
— 24 cm
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Q. In triangle PQR, if PQ = 8 cm, QR = 6 cm, and PR = 10 cm, what is the semi-perimeter of the triangle? (2022)
A.
12 cm
B.
14 cm
C.
16 cm
D.
18 cm
Show solution
Solution
Semi-perimeter = (PQ + QR + PR) / 2 = (8 + 6 + 10) / 2 = 12 cm.
Correct Answer:
B
— 14 cm
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Q. In triangle PQR, if PQ = 8 cm, QR = 6 cm, and PR = 10 cm, what is the semi-perimeter? (2022)
A.
12 cm
B.
14 cm
C.
16 cm
D.
18 cm
Show solution
Solution
Semi-perimeter = (PQ + QR + PR) / 2 = (8 + 6 + 10) / 2 = 12 cm.
Correct Answer:
B
— 14 cm
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Q. In triangle XYZ, if angle X = 45 degrees and angle Y = 45 degrees, what is the length of side XY if side XZ = 10 cm? (2020)
A.
5√2 cm
B.
10 cm
C.
10√2 cm
D.
20 cm
Show solution
Solution
In an isosceles right triangle, the sides opposite the 45-degree angles are equal. Therefore, XY = XZ / √2 = 10 / √2 = 5√2 cm.
Correct Answer:
A
— 5√2 cm
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Q. In triangle XYZ, if angle X = 45 degrees and angle Y = 45 degrees, what is the ratio of the lengths of sides opposite to these angles? (2021)
A.
1:1
B.
1:√2
C.
√2:1
D.
2:1
Show solution
Solution
In an isosceles triangle with angles 45 degrees, the sides opposite these angles are equal, hence the ratio is 1:1.
Correct Answer:
A
— 1:1
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Q. In triangle XYZ, if angle X = 45 degrees and angle Y = 45 degrees, what is the ratio of the sides opposite to these angles? (2021)
A.
1:1
B.
1:√2
C.
√2:1
D.
2:1
Show solution
Solution
In an isosceles triangle with angles 45-45-90, the sides opposite the equal angles are equal, hence the ratio is 1:1.
Correct Answer:
A
— 1:1
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Q. In triangle XYZ, if XY = 12 cm, YZ = 16 cm, and XZ = 20 cm, what is the semi-perimeter? (2020)
A.
24 cm
B.
28 cm
C.
30 cm
D.
32 cm
Show solution
Solution
Semi-perimeter s = (XY + YZ + XZ)/2 = (12 + 16 + 20)/2 = 24 cm.
Correct Answer:
A
— 24 cm
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Q. In triangle XYZ, if XY = 8 cm, YZ = 15 cm, and XZ = 17 cm, what is the length of the longest side? (2020)
A.
8 cm
B.
15 cm
C.
17 cm
D.
Not determinable
Show solution
Solution
The longest side in triangle XYZ is XZ, which measures 17 cm.
Correct Answer:
C
— 17 cm
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Q. Is the function f(x) = 1/(x-1) continuous at x = 1?
A.
Yes
B.
No
C.
Only left continuous
D.
Only right continuous
Show solution
Solution
The function f(x) = 1/(x-1) is not defined at x = 1, hence it is discontinuous at that point.
Correct Answer:
B
— No
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Q. Is the function f(x) = sqrt(x) continuous at x = 0?
A.
Yes
B.
No
C.
Only from the right
D.
Only from the left
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
— Yes
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Q. Is the function f(x) = |x| continuous at x = 0?
A.
Yes
B.
No
C.
Only left continuous
D.
Only right continuous
Show solution
Solution
The function f(x) = |x| is continuous at x = 0 because the left limit, right limit, and f(0) all equal 0.
Correct Answer:
A
— Yes
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Q. Solve for x: 3x - 7 = 2x + 5. (2021)
Show solution
Solution
Subtract 2x from both sides: x - 7 = 5. Then add 7: x = 12.
Correct Answer:
A
— 12
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Q. Solve the differential equation dy/dx = 2y.
A.
y = Ce^(2x)
B.
y = 2Ce^x
C.
y = Ce^(x/2)
D.
y = 2x + C
Show solution
Solution
This is a separable equation. Separating variables and integrating gives ln|y| = 2x + C, hence y = Ce^(2x).
Correct Answer:
A
— y = Ce^(2x)
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Q. Solve the differential equation dy/dx = 5 - 2y.
A.
y = 5/2 + Ce^(-2x)
B.
y = 5/2 - Ce^(-2x)
C.
y = 2.5 + Ce^(2x)
D.
y = 2.5 - Ce^(2x)
Show solution
Solution
Rearranging gives dy/(5 - 2y) = dx. Integrating both sides leads to y = 5/2 + Ce^(-2x).
Correct Answer:
A
— y = 5/2 + Ce^(-2x)
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Showing 991 to 1020 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!
