NDA Paper I Mathematics for practice

Free

NDA Mathematics paper set 3

Time left =

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

1 1 only

2 2 only

3 Both 1 and 2

4 Neither 1 nor 2

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

1 2

2 1

3 1/2

4 2√2

.What is equal to?

1 0

2 -1

3 1

4 Limit does not exist

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

1 1

2 -1

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

1 x2 + y2 = xy + c

2 x2 + y2 = 2xy + c

3 x2 - y2 = xy + c

4 x2 - y2 = 2xy + c

What is the minimum value of where A ∈ R?

1 -3

2 -1

3 0

4 3

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?

1 1 only

2 2 only

3 Both 1 and 2

4 Neither 1 nor 2

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

1 The domain is {x ∈ R | X ≠ 1} and the range is the set of reals.

2 The domain is {x ∈ R | X ≠ 1}, the range is {y ∈ R | y ≠ 0} and the graph intersects y-axis at (0, -1).

3 The domain is the set of reals and the range is the singleton set {0}.

4 The domain is {x ∈ R | X ≠ 1} and the range is the set of points on the y-axis

What is the solution of the differential equation ?

1 y = ex + c

2 y = e-x + c

3 y = ln x + c

4 y = 2 ln x + c

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

1 2k2

2 k2

3 k2/2

4 k2/4

.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?

1 2

2 3

3 4

4 5

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?

1 5/6

2 5/9

3 1/2

4 5/12

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

2 P(A ∩ B) = P(A) P(B)

3 P(A ∪ B) > P(A) + P(B)

4 P(not A and not B) = P(not A) P(not B)

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?

1 50

2 60

3 80

4 100

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?

1 M