NDA Paper I Mathematics for practice

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NDA Mathematics paper set 2

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If p², q² and r² (where p, q, r > 0) are in GP, then which of the following is/are correct?

1) p, q and r are in GP.
2) ln p, ln q and ln r are in AP.

Select the correct answer using the code given below :

1 1 only

2 2 only

3 Both 1 and 2

4 Neither 1 nor 2

2

If A is a matrix of order 3 × 5 and B is a matrix of order 5 × 3, then the order of AB and BA will respectively be

1 3 × 3 and 3 × 3

2 3 × 5 and 5 × 3

3 3 × 3 and 5 × 5

4 5 × 3 and 3 × 5

3

If sin x + sin y = cos y – cos x, where

1 0

2 1/2

3 1

4 2

4

What is sin(α + 1o) + cos(β + 1o) equal to?

1

2

3

4

5

.What is the value of sin 7α - cos 7β?

1

2

3

4

6

What is the value of sin α + cos β?

1

2

3

4

7

.What is t₁²-t₂²equal to?

8

.What is t₁²-t₂²equal to?

1 cos 2θ

2 sin 2θ

3 2 cos θ

4 2 sin θ

9

What is equal to?

1

2

3

4

10

What is equal to?

1

2

3

4

11

.What is equal to?

1 sin2y

2 cos2 y

3 tan2 y

4 cot2 y

12

What is tan² x equal to?

1

2

3

4

13

.What is the equation of the plane which cuts an intercept 5 units on the z-axis and is parallel to xy-plane?

1 x + y = 5

2 z = 5

3 z = 0

4 x + y + z = 5

14

Into how many compartments do the coordinate planes divide the space?

1 2

2 4

3 8

4 16

15

If a line has direction ratios < a + b, b + c, c + a >, then what is the sum of the square of its direction cosines?

1 (a + b + c)2

2 2(a + b + c)

3 3

4 1

16

.What is the length of the diameter of the sphere whose centre is at (1, -2, 3) and which touches the plane 6x – 3y + 2z – 4 = 0?

1 1 unit

2 2 unit

3 3 unit

4 4 unit