# NDA Paper I Mathematics for practice

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NDA Mathematics paper set 3
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Consider the following statements:
f(x) = e-|x| :
1) The function is continuous at x = 0.
2) The function is differentiable at x = 0.

2

What is the maximum value of sin x.cos x?

3

.What is  equal to?

4

What is the derivative of tan-1 x with respect to cot-1 x?

5

The function u(x, y) = c which satisfies the differential equation x(dx – dy) + y (dy – dx) = 0, is

6

What is the minimum value of  where A ∈ R?

7

Consider the following statements :

1)The function f(x) =  In xincreases in the interval (0, ∞).
2) The function f(x) =  increases in the interval  (-

π/2,
 π/2

)

Which of the above statements is/are correct?

8

.Which one of the following is correct in respect of the graph
of  ?

9

What is the solution of the differential equation  ?

10

Let l be the length and b be the breadth of a rectangle such that . What is the maximum area of the rectangle

11

.The numbers 4 and 9 have frequencies x and (x - 1) respectively. If their arithmetic mean is 6, then what is the value of x?

12

If three dice are rolled under the condition that no two dice show the same face, then what is the probability that one of the faces is having the number 6?

13

.If  and  then which one of the following is not correct

14

The sum of deviations of n number of observations measured from 2.5 is 50 . The sum of deviations of the same set of observations measured from 3.5 is -50 . What is the value of n?

15

A data set of n observations has mean 2M, while another data set of 2n observations has mean M. What is the mean of the combined data sets?