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This mock test of NDA I - Mathematics Question Paper 2013 for Defence helps you for every Defence entrance exam.
This contains 120 Multiple Choice Questions for Defence NDA I - Mathematics Question Paper 2013 (mcq) to study with solutions a complete question bank.
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QUESTION: 1

What is the positive square root of 7 + 4√3 ?

Solution:

QUESTION: 2

If A = {1,2},B = {2, 3} and C= { 3,4}, then what is the cardinality of (AxB)∩(AxC) ?

Solution:

QUESTION: 3

If α, β are the roots of the equation x^{2} +x+ 2 = 0, then what is equal to?

Solution:

QUESTION: 4

If *a* and *b *are rational and b is not perfect square, then the quadratic equation with rational coefficients whose one root is is

Solution:

QUESTION: 5

If A is a finite set having n elements, then the number of relations which can be defined in A is

Solution:

QUESTION: 6

If the positive integers a, b, c, d are in AP, then the numbers abc, abd, acd, bcd are in

Solution:

QUESTION: 7

Which one of the following is an example of non-empty set ?

Solution:

QUESTION: 8

What is one of the square roots of 3 + 4*i*, where i = √-1 ?

Solution:

QUESTION: 9

The number 83 is written in the binary system as

Solution:

QUESTION: 10

The relation R in the set Z of integers given by R = {(a, b): a-b is divisible by 5} is

Solution:

QUESTION: 11

what is equal to ?

Solution:

QUESTION: 12

What is 0.9 + 0.09 + 0.009 +.... equal to ?

Solution:

QUESTION: 13

How many real roots does the quadratic equationf(x) = x^{2 }+ 3|x| + 2 = 0 have ?

Solution:

QUESTION: 14

In a group of 50 people, two tests were conducted, one for diabetes and one for blood pressure. 30 people were diagnosed with diabetes and 40 people were diagnosed with high blood pressure, what is the minimum number of people who were having diabetes and high blood pressure ?

Solution:

QUESTION: 15

Consider the following statements:

1. The product of two non-zero matrices can never be identity matrix.

2. The product of two non-zero matrices can never be zero matrix.

Q. Which of the above statements is/are correct ?

Solution:

QUESTION: 16

Consider the following statements:

Q. Which of the above statements is/are correct ?

Solution:

QUESTION: 17

The cofactor of the element 4 in the determinant

Solution:

QUESTION: 18

If A is a square matrix of order 3 with |A| , then which one of the following is correct ?

Solution:

QUESTION: 19

Let A = {a, b,c, d) and B = {x, y, z }. W hat is the num ber o f elements in A * B ?

Solution:

QUESTION: 20

If C (28 ,2r) = C (28 , 2r - 4), then w hat is r equal to ?

Solution:

QUESTION: 21

If A is a subset of B, then which one of the following is correct ?

Solution:

QUESTION: 22

Solution:

QUESTION: 23

Let *f* be a function from the set of natural numbers to the set o f even natural num bers given by *f*(x) = 2x. Then *f* is

Solution:

QUESTION: 24

Solution:

QUESTION: 25

,then what is λ equal to ?

Solution:

QUESTION: 26

What is the angle (in circular measure) between the hour hand and the minute hand of a clock when the time is half past 4 ?

Solution:

QUESTION: 27

The angle of elevation of the top of a tower from two places situated at distances 21m. and x m. from the base of the tower are 45° and 60° respectively. What is the value of 7x ?

Solution:

QUESTION: 28

What is equal to ?

Solution:

QUESTION: 29

A person standing on the bank of a river observes that the angle subtended by a tree on the opposite of bank is 60°. When he retires 40 m. from the bank, he finds the angle to be 30°. What is the breadth of the river ?

Solution:

QUESTION: 30

If the angles of a triangle are 30° and 45° and the included side is (√3 +1), then what is the area of the tringle ?

Solution:

QUESTION: 31

What is sin^{2} 20° + sin^{2} 70° equal to ?

Solution:

QUESTION: 32

What is the value of the determinant

Solution:

QUESTION: 33

Consider the following:

Q. Which of the above is/are correct ?

Solution:

According to 'Distribution laW in set theorry the given both statements are wrong.

Statement 1 - Distribution law

Statement 2 - Distribution law

QUESTION: 34

Solution:

QUESTION: 35

If α, β are the roots of the equation ax^{2} + bx + b = 0, then what is the value of

Solution:

QUESTION: 36

A number in binary system is 110001. It is equal to which one of the following numbers in decimal system ?

Solution:

QUESTION: 37

The roots of the equation x^{2}—8x+ 16 = 0

Solution:

QUESTION: 38

What is equal to ?

Solution:

QUESTION: 39

What is (l - sin^{2}θ)(1 + tan^{2}θ) equal to ?

Solution:

QUESTION: 40

How many terms are there in the expansion of (1 +2x+x^{2})^{10}?

Solution:

QUESTION: 41

The sum of the first five terms and the sum of the first ten terms of an AP are same. Which one of the following is the correct statement?

Solution:

QUESTION: 42

lfA = {l,3,5,7},then what is the cardinality of the power set P(A)?

Solution:

Number of element in set A is 4.

Cardinality of the power set P(A) = 2^{4} = 16

QUESTION: 43

What is the difference in the roots of the equation x^{2 }- 10x + 9 = 0?

Solution:

QUESTION: 44

If 8x - 9y = 20 and 7x - 1Oy = 9, then what is 2x - y equal to?

Solution:

8x - 9y = 20 or 80x - 90y = 200 ...(1)

7x -10y = 9 or 63x - 90y = 81 ...(2)

Subtracting (2) from (1), we get

17x = 119

x = 7

8 x 7 - 9y = 20

9y = 36

y = 4

2x - y = 2 x 7 - 4 = 10

QUESTION: 45

The quadratic equation x2 + bx+4 = 0 will have real roots if

Solution:

If root are real

b^{2}- 4 x 4≥ 0

b^{2} ≥ 16

b ≤ - 4, b ≥ 4

QUESTION: 46

What is the seventh term of the sequence 0,3,8,15,24,.... ?

Solution:

0 + 3 = 3 ,3 + 5 = 8 ,8 + 7 = 15 ,15 + 9 = 24 ,2 4 + 11 = 3 5,

35+13=48

Sequence is 0,3,8,15,24,35,48

QUESTION: 47

What is tan 15° equal to?

Solution:

QUESTION: 48

Consider the following:

What is the correct order?

Solution:

QUESTION: 49

If cosx = 1/3, then what is sin x. cot x . cosec x. tan x equal to?

Solution:

sin x. cot x. cosec x. tan x

= (sin x. cosec x). (cot x. tan x)

= l x l = l

QUESTION: 50

What is log_{81}243 equal to?

Solution:

QUESTION: 51

If the three vertices of the parallelogram ABCD are .A(1, a), B(3, a), C(2, b), then D is equal to

Solution:

QUESTION: 52

The value of k for which the lines 2x + 3y + a = 0 and 5x + ky + a = 0 represent family of parallel lines is

Solution:

QUESTION: 53

What is the equation of the line which passes through (4, -5) and is perpendicular to 3x + 4y + 5 = 0?

Solution:

QUESTION: 54

The foci of the hyperbola

4x^{2} - 9y^{2 }- 1 = 0 are

Solution:

QUESTION: 55

For what value of k are the two straight lines 3x + 4y = 1 and 4x + 3y + 2k = 0 equidistant from the point (1,1)?

Solution:

QUESTION: 56

A point P moves such that its distances from (1,2) and (-2,3) are equal. Then the locus of P is

Solution:

QUESTION: 57

The equation of the locus of a point which is equidistant from the axes is

Solution:

QUESTION: 58

What angle does the line segment joining (5, 2) and (6,-15) subtend at (0,0)?

Solution:

QUESTION: 59

The length of latus rectum of the ellipse 4x^{2} + 9y^{2} = 36 is

Solution:

QUESTION: 60

What is the equation to the straight line passing through (5,-2) and (-4,7)?

Solution:

QUESTION: 61

What is the angle between the lines x + y = 1 and x - y = 1 ?

Solution:

QUESTION: 62

The axis of the parabola y^{2}+ 2x = 0 is

Solution:

y^{2} + 2x = 0 => y^{2} = -2x, which is in the form

y2 = -4ax. Therefore axis of parabola is x-axis.

QUESTION: 63

The radius of the circle

x^{2}+y^{2} + x + c = 0 passing through the origin is

Solution:

QUESTION: 64

The centroid o fth e triangle with vertices (2 ,3 ), (- 2 , - 5 ) and (3,5) is at

Solution:

QUESTION: 65

The equation of the line, the reciprocals of whose intercepts on the axes are m and n, is given by

Solution:

QUESTION: 66

If 0 is the acute angle between the diagonals of a cube, then which one of the following is correct ?

Solution:

QUESTION: 67

What is the equation of the sphere with unit radius having centre at the origin?

Solution:

QUESTION: 68

What is the sum of the squares of direction cosines of x-axis ?

Solution:

Sum of squares of direction cosines

= (1)^{2} + (0)^{2} + (0)^{2 = 1}

QUESTION: 69

What is the distance of the line 2x + y + 2y = 3 from the origin ?

Solution:

QUESTION: 70

If the projections of a straight line segment on the coordinate axes are 2 ,3 ,6 , th en the length o f the segment is

Solution:

QUESTION: 71

Consider the following functions:

Q. Which of the above functions is/are continuous ?

Solution:

QUESTION: 72

What is the derivative of x^{3} with respect to x^{2 }?

Solution:

QUESTION: 73

What is equal to?

Solution:

QUESTION: 74

A function *f* :R→ R is defined a s *f *(x) = x^{2} for x≥ 0 and *f *(x)= -x for x< 0.

Consider the following statements in respect of the above function:

1. The function is continuous at x = 0.

2. The function is differentiable at x = 0.

Q. Which of the above statements is/are correct ?

Solution:

QUESTION: 75

If f (x) = 2x^{2} +3x - 5 at x = -1, then what is *f* '(0) + 3 *f* "(-1) = 0 equal to?

Solution:

QUESTION: 76

What is equal to?

Solution:

QUESTION: 77

What is equal to?

Solution:

QUESTION: 78

What is equal to?

Solution:

QUESTION: 79

The maximum value of the functionf(x) = x^{3} + 2x^{2} - 4x + 6 exists at

Solution:

QUESTION: 80

The minimum value of the function *f*(x) = exists at

Solution:

At x = 4 , f( x ) = 0

QUESTION: 81

What is equal to?

Solution:

QUESTION: 82

what is equal to?

Solution:

QUESTION: 83

What is the order of the differential equation

Solution:

Highest order derivative, present in the differential equations is , therefore its order is one.

QUESTION: 84

v = 2cosx + 3sinx satisfies which ofthe following differential equations?

Q. Select the correct answer using the code given below.

Solution:

y = 2cosx + 3sinx

QUESTION: 85

The differential equation of all circles whose centres are at the origin is

Solution:

QUESTION: 86

what is equal to?

Solution:

QUESTION: 87

what is equal to?

Solution:

QUESTION: 88

What is the area bounded by the lines x = 0, y = 0 and x + y + 2 = 0?

Solution:

QUESTION: 89

What is the derivative of sin (sin x) ?

Solution:

QUESTION: 90

What is the derivative of | x - l | at x = 2 ?

Solution:

QUESTION: 91

What is the area of the parabola x^{2} = y bounded by the line y = l ?

Solution:

QUESTION: 92

What is the area bounded by y = tanx, y = 0 and x = π/4?

Solution:

QUESTION: 93

What is equal to?

Solution:

QUESTION: 94

what is equal to?

Solution:

QUESTION: 95

If the angle between the vectors , then what is the value of m?

Solution:

QUESTION: 96

What is the vector perpendicular to both the vectors ?

Solution:

QUESTION: 97

The position vectors of the points A and B are respectively What is the length of AB?

Solution:

QUESTION: 98

The vectors are orthogonal to each other. Then the locus of the point (x, y ) is

Solution:

QUESTION: 99

What is the value of P for which the vector is of 3 units length?

Solution:

QUESTION: 100

If are three vectors such that is perpendicular to then what is t equal to ?

Solution:

QUESTION: 101

The mean of 20 observations is 15. On checking, it was found that two observations were wrongly copied as 3 and 6. If wrong observations are replaced by correct values 8 and 4, then the correct mean is

Solution:

QUESTION: 102

The arithmetic mean of the squares of the first n natural numbers is

Solution:

QUESTION: 103

Consider the following statements :

1. Both the regression coefficients have same sign.

2. If one of the regression coefficients is greater than unity, the other must be less than unity.

Q. Which of the above statements is /are correct?

Solution:

QUESTION: 104

Which one of the following measures is determined only after the construction of cumulative frequency distribution ?

Solution:

After construction of cumulative frequency distribution, we can find out median easily

QUESTION: 105

Coefficient of correlation is the measure of

Solution:

QUESTION: 106

If three events A, B,C are mutually exclusive, then which one of the following is correct?

Solution:

A, B and C are mutually exclusive

QUESTION: 107

What is thevariance of the first 11 natural numbers ?

Solution:

Variance o f 11 natural numbers = =10

QUESTION: 108

If A and B are independent events such that equal to?

Solution:

QUESTION: 109

In a binomial distribution, the occurrence and the non occurrence of an event are equally likely and the mean is 6 . The number of trials required is

Solution:

QUESTION: 110

A die is tossed twice. What is the probability of getting a sum of 10?

Solution:

Number of possible outcomes = 36

When sum is 10, samples are (5,5), (4,6) and (6,4)

Required probability = 3/36 = 1/12

QUESTION: 111

Threed ice are thrown. What is the probability of getting a triplet?

Solution:

Number of possible outcomes = 216 triplets=(1,1,1), (2,2,2), (3,3,3), (4,4,4), (5,5,5), (6,6,6)

Required probability = 6/216 = 1/36

QUESTION: 112

Consider the following statements:

1. If A and B are exhaustive events, then their union is the sample space.

2. IfA and B are exhaustive events, then their intersection must be an empty event.

Q. Which of the above statements is/are correct?

Solution:

QUESTION: 113

Consider the following statements :

1. The algebraic sum of the deviations of a set of n values from its arithmetic mean is zero.

2. In the case of frequency distribution ,mode is the value of variable which corresponds to maximum frequency.

Q. Which of the statements above given is /are correct?

Solution:

QUESTION: 114

Which one of the following may be the parameter of a binomial distribution ?

Solution:

For binomial distribution

p < 1, q < 1 a n d p + q = 1

QUESTION: 115

What is the number of outcomes when a coin is tossed and then a die is rolled only in case a head is shown on the coin?

Solution:

Possible outcomes are (Head, 1), (Head, 2), (Head, 3), (Head, 4), (Head, 5), (Head, 6), Tail

QUESTION: 116

If then what is equal to?

Solution:

QUESTION: 117

What is the propability that there are 5 Mondays in the month of February 2016?

Solution:

February 2016 has exactly 5 Mondays.

QUESTION: 118

Consider the following statements:

1. Pie diagrams are suitable for categorical data.

2. The arc length of a sector of a pie diagram is proportional to the value of the component represented by the sector.

Q. Which of the statements given above is/are correct ?

Solution:

QUESTION: 119

In a relay race, there are six teamsA, B, C, D, E and E What is the probability that A, B, C finish first, second, third respectively ?

Solution:

QUESTION: 120

The variance of 20 observations is 5. If each observation is multiplied by 2, then what is the new variance of the resulting observations ?

Solution:

Detailed Method:

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