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NDA I - Mathematics Question Paper 2013 - Question 1

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

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NDA I - Mathematics Question Paper 2013 - Question 2

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

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NDA I - Mathematics Question Paper 2013 - Question 3

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

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NDA I - Mathematics Question Paper 2013 - 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

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NDA I - Mathematics Question Paper 2013 - Question 5

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

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NDA I - Mathematics Question Paper 2013 - Question 6

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

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NDA I - Mathematics Question Paper 2013 - Question 7

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

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NDA I - Mathematics Question Paper 2013 - Question 8

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

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NDA I - Mathematics Question Paper 2013 - Question 9

The number 83 is written in the binary system as

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NDA I - Mathematics Question Paper 2013 - Question 10

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

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NDA I - Mathematics Question Paper 2013 - Question 12

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

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NDA I - Mathematics Question Paper 2013 - Question 13

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

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NDA I - Mathematics Question Paper 2013 - 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 ?

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NDA I - Mathematics Question Paper 2013 - 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 ?

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NDA I - Mathematics Question Paper 2013 - Question 16

Consider the following statements:

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

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NDA I - Mathematics Question Paper 2013 - Question 17

The cofactor of the element 4 in the determinant

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NDA I - Mathematics Question Paper 2013 - Question 18

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

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NDA I - Mathematics Question Paper 2013 - 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 ?

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NDA I - Mathematics Question Paper 2013 - Question 20

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

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NDA I - Mathematics Question Paper 2013 - Question 21

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

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NDA I - Mathematics Question Paper 2013 - 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

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NDA I - Mathematics Question Paper 2013 - 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 ?

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NDA I - Mathematics Question Paper 2013 - 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 ?

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NDA I - Mathematics Question Paper 2013 - 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 ?

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NDA I - Mathematics Question Paper 2013 - 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 ?

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NDA I - Mathematics Question Paper 2013 - Question 31

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

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NDA I - Mathematics Question Paper 2013 - Question 33

Consider the following:

Q. Which of the above is/are correct ?

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NDA I - Mathematics Question Paper 2013 - Question 35

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

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NDA I - Mathematics Question Paper 2013 - Question 36

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

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NDA I - Mathematics Question Paper 2013 - Question 37

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

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NDA I - Mathematics Question Paper 2013 - Question 39

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

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NDA I - Mathematics Question Paper 2013 - Question 40

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

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NDA I - Mathematics Question Paper 2013 - 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?

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NDA I - Mathematics Question Paper 2013 - Question 42

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

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NDA I - Mathematics Question Paper 2013 - Question 43

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

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NDA I - Mathematics Question Paper 2013 - Question 44

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

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NDA I - Mathematics Question Paper 2013 - Question 45

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

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NDA I - Mathematics Question Paper 2013 - Question 46

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

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NDA I - Mathematics Question Paper 2013 - Question 48

Consider the following:

What is the correct order?

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NDA I - Mathematics Question Paper 2013 - Question 49

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

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NDA I - Mathematics Question Paper 2013 - 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

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NDA I - Mathematics Question Paper 2013 - 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

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NDA I - Mathematics Question Paper 2013 - Question 53

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

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NDA I - Mathematics Question Paper 2013 - Question 54

The foci of the hyperbola

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

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NDA I - Mathematics Question Paper 2013 - 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)?

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NDA I - Mathematics Question Paper 2013 - Question 56

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

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NDA I - Mathematics Question Paper 2013 - Question 57

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

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NDA I - Mathematics Question Paper 2013 - Question 58

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

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NDA I - Mathematics Question Paper 2013 - Question 59

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

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NDA I - Mathematics Question Paper 2013 - Question 60

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

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NDA I - Mathematics Question Paper 2013 - Question 61

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

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NDA I - Mathematics Question Paper 2013 - Question 62

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

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NDA I - Mathematics Question Paper 2013 - Question 63

The radius of the circle

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

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NDA I - Mathematics Question Paper 2013 - Question 64

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

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NDA I - Mathematics Question Paper 2013 - Question 65

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

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NDA I - Mathematics Question Paper 2013 - Question 66

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

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NDA I - Mathematics Question Paper 2013 - Question 67

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

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NDA I - Mathematics Question Paper 2013 - Question 68

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

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NDA I - Mathematics Question Paper 2013 - Question 69

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

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NDA I - Mathematics Question Paper 2013 - 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

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NDA I - Mathematics Question Paper 2013 - Question 71

Consider the following functions:

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

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NDA I - Mathematics Question Paper 2013 - Question 72

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

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NDA I - Mathematics Question Paper 2013 - 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 ?

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NDA I - Mathematics Question Paper 2013 - Question 75

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

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NDA I - Mathematics Question Paper 2013 - Question 79

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

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NDA I - Mathematics Question Paper 2013 - Question 80

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

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NDA I - Mathematics Question Paper 2013 - Question 83

What is the order of the differential equation

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NDA I - Mathematics Question Paper 2013 - Question 84

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

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

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NDA I - Mathematics Question Paper 2013 - Question 85

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

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NDA I - Mathematics Question Paper 2013 - Question 88

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

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NDA I - Mathematics Question Paper 2013 - Question 90

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

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NDA I - Mathematics Question Paper 2013 - Question 91

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

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NDA I - Mathematics Question Paper 2013 - Question 92

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

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NDA I - Mathematics Question Paper 2013 - Question 95

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