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NDA Hard Maths 25 Questions

The document contains a series of hard-level practice questions for NDA Maths, covering various topics such as Algebra, Trigonometry, Probability & Statistics, Mensuration, Geometry, Arithmetic, Matrices, Differentiation & Integration, and Vector Algebra. Each question is multiple-choice with four answer options. The questions are designed to test advanced mathematical concepts and problem-solving skills.

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rajkumarkuttyma
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150 views2 pages

NDA Hard Maths 25 Questions

The document contains a series of hard-level practice questions for NDA Maths, covering various topics such as Algebra, Trigonometry, Probability & Statistics, Mensuration, Geometry, Arithmetic, Matrices, Differentiation & Integration, and Vector Algebra. Each question is multiple-choice with four answer options. The questions are designed to test advanced mathematical concepts and problem-solving skills.

Uploaded by

rajkumarkuttyma
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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NDA Maths Hard Level - Practice Questions

Algebra

1. If x + 1/x = 3, find x^5 + 1/x^5.

A) 243 B) 126 C) 121 D) 123

2. Solve: x^3 - 3x^2 + 4x - 12 = 0

A) 2, 2, 3 B) 1, 2, 3 C) 2, 2, 2 D) 1, 1, 3

3. If x^2 + y^2 = 1, what is the maximum value of x + y?

A) sqrt2 B) 1 C) 2 D) 3/2

Trigonometry

4. If tan A + cot A = 2, find tan^2 A + cot^2 A.

A) 4 B) 6 C) 8 D) 10

5. If sin theta = 3/5, find tan theta + cot theta.

A) 13/6 B) 10/3 C) 5/3 + 3/5 D) 34/15

6. If sin^4 x + cos^4 x = 5/8, find sin 2x.

A) 1 B) sqrt2/2 C) 3/4 D) sqrt3/2

Probability & Statistics

7. Box has 5 red, 4 green, 3 blue balls. Probability both drawn are green?

A) 2/11 B) 2/33 C) 1/11 D) 1/3

8. Mean of 5 numbers is 20. One number is 0. Mean of remaining 4?

A) 24 B) 25 C) 20 D) 16

9. Two dice are thrown. Probability that sum is prime?

A) 5/18 B) 15/36 C) 11/36 D) 1/2

Mensuration

10. Cylinder: height 10 cm, radius 3 cm. Total surface area?

A) 60pi B) 90pi C) 120pi D) 180pi

11. Cone and hemisphere have same radius and height. Volume ratio?

A) 2:1 B) 1:2 C) 1:1 D) 3:2

12. Sphere has volume = surface area. Find radius.

A) 1 B) 3 C) 2 D) 6

Geometry
NDA Maths Hard Level - Practice Questions

13. Triangle ABC: AB = AC, angle BAC = 40 degrees. Find angle ABC.

A) 70 degrees B) 40 degrees C) 30 degrees D) 20 degrees

14. Diagonal of cube = 12sqrt3 cm. Volume?

A) 1728 cm^3 B) 1000 cm^3 C) 144 cm^3 D) 1200 cm^3

15. ABC: AB=6, AC=8, angle BAC=60 degrees, D is midpoint of BC. Find AD.

A) 5 B) 6 C) 7 D) 8

Arithmetic

16. A in 12 days, B in 15. Together for 4 days. Work left?

A) 2/5 B) 1/5 C) 3/5 D) 7/15

17. Train 72 km/hr, platform 120 m, crosses in 10 s. Train length?

A) 280 m B) 220 m C) 180 m D) 320 m

18. Age ratio A:B = 4:5. After 6 years -> 5:6. As age?

A) 24 B) 30 C) 36 D) 40

Matrices

19. If A = [[2,3],[1,4]], find A^2.

A) [[7,18],[6,19]] B) [[10,17],[8,19]] C) [[13,18],[6,17]] D) [[16,21],[7,22]]

20. Find x for determinant |1 x 3; 2 5 x; x 1 4| = 0

A) 1 B) 2 C) 3 D) 4

Differentiation & Integration

21. y = sin(x^2), dy/dx = ?

A) 2x cos(x^2) B) cos(x^2) C) 2x sin(x^2) D) x cos(x^2)

22. y = tan^-1(2x / (1 - x^2)) => y = ?

A) tan^-1(x) B) 2tan^-1(x) C) cot^-1(x) D) sec^-1(x)

23. Integral of xe^x dx = ?

A) x e^x - e^x + C B) x e^x + e^x + C C) e^x(x - 1) + C D) e^x(x + 1) + C

24. Integral of 1/sqrt(1 - x^2) dx = ?

A) cos^-1x + C B) tan^-1x + C C) sin^-1x + C D) ln|x| + C

Vector Algebra

25. a = i + j, b = i - j. Find |a + b|.

A) sqrt2 B) 2 C) sqrt5 D) sqrt3

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