NDA PYSP Practice Mini Mock - Mathematics for NDA Exams

Question 1

It is given that the roots of the equation

are real. For this, the minimum value of

is

Question 2

If

, then what is

equal to?

Question 3

Consider the following statements :

1) If 3θ is an acute angle such that sin 3θ = cos 2θ, then the measurement of θ in radian equals to .

2) One radian is the angle subtended at the centre of a circle by an arc of the same circle whose length is equal to the diameter of that circle.

Which of the above statements is/are correct?

Question 4

The vector

is equal to

Question 5

A force

is applied at the point (1, -1, 2). What is the moment of the force about the point (2, -1, 3)?

Question 6

The probability that a ship safely reaches a port is

The probability that out of 5 ships, at least 4 ships would arrive safely is

Question 7

The distance of the point (1, 3) from the line

measured parallel to the line

is

Question 8

The order and degree of the differential equation

Are respectively

Question 9

Three independent events,

and

occur with probabilities

. What is the probability that at least one of the three events occurs?

Question 10

Consider the following statements:

Statement 1: Range is not a good measure of dispersion.

Statement 2: Range is highly affected by the existence of extreme values.

Which one of the following is correct in respect of the above statements?

Question 11

if

and

then

is equal to

Question 12

is true if

Question 13

The function f(x) = tan^-1(sinx + cosx) is an increasing function in

Question 14

Every quadratic equation ax² + bx + c = 0 where a, b, c ∈ R , a ≠ 0 has

Question 15

The mean of a group of 100 observations was found to be 20.Later it was found that four observations were incorrect, which were recorded as 21, 21, 18 and 20. What is the mean if the incorrect observations are omitted?

Question 16

Geometrically

where

and Re is the real part, represents

Question 17

A cylindrical jar without a lid has to be constructed using a given surface area of a metal sheet. If the capacity of the jar is to be maximum, then the diameter of the jar must be k times the height of the jar .The value of k is

Question 18

The variance of 20 observations is 5. If each observation is multiplied by 3, then what is the new variance of the resulting observations?

Question 19

What is the domain of the function

?

Question 20

What are the degree and order respectively of the differential equation satisfying

(where

)?

Question 21

Consider the following statements :

1) at a point on the curve given slope of the tangent at that point.

2) If denotes acceleration of a particle, then gives velocity of the particle.

3) If gives displacement of a particle at time then gives its acceleration at that instant.

Which of the above statements is/are correct?

Question 22

If

is the universal set and

B then the set

is same as the set

Question 23

If

and

then what is

equal to?

Question 24

Consider the following in respect of the function

1) does not exist.

2) f(x) is differentiable at x = 0.

3) f(x) is continuous at x = 0.

Which of the above statements is/are correct?

Question 25

is equal to

Question 26

Consider the following statements :

1) Derivative of may not exist at some point.

2) Derivative of may exist finitely at some point.

3) Derivative of may be infinite (geometrically) at some point.

Which of the above statements are correct?

Question 27

What is

equal to?

Question 28

For the next four (04) items that follow :

such that and

What is the angle between and

Question 29

A variable plane passes through a fixed point

and cuts the axes in

and

respectively. The locus of the centre of the sphere

being the origin, is

Question 30

The equation

is satisfied by

Question 31

Let

.

Consider the following:

1)

2)

Which of the above is/are correct?

Question 32

what should be the value of λ such that the function defined below is continuous at x = π/2

Question 33

The smallest positive integer

for which

is

Question 34

If A = {x : x is a multiple of 2}, B = {x : x is a multiple of 5} and C= {x : x is a multiple of 10}, then

AO (BOC) is equal to

Question 35

The angle of elevation of a stationary cloud from a point 25 m above a lake is 15^o and the angle of depression of its image in the lake is 45^o. The height of the cloud above the lake level is