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NDA I - Mathematics Question Paper 2017 - Question 1

The sum of the roots of the equation x^{2} + bx + c = 0 (where b and c are non-zero) is equal to the sum of the recipients of their squares. Then, are in

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NDA I - Mathematics Question Paper 2017 - Question 2

The sum of the roots of the equation ax^{2} + x + c = 0 (where a and c are non-zero) is equal to the sum of the reciprocals of their squares. Then a, ca^{2} , c^{2} are in

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NDA I - Mathematics Question Paper 2017 - Question 3

The value of [C (7, 0) + C (7, 1)] + [C (7, 1) + C (7, 2)] +⋯ + [C (7, 6) + C (7, 7)] is

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NDA I - Mathematics Question Paper 2017 - Question 4

The number of different words (eight-letter words) ending and beginning with a consonant which can be made out of the letters of the word ‘EQUATION’ is

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NDA I - Mathematics Question Paper 2017 - Question 5

The fifth term of an AP of n terms, whose sum is n^{2} + n, is

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NDA I - Mathematics Question Paper 2017 - Question 6

The sum of all the two-digit odd numbers is

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NDA I - Mathematics Question Paper 2017 - Question 7

The sum of the first n terms of the series is equal to

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NDA I - Mathematics Question Paper 2017 - Question 8

Consider the following in respect of sets A and B:

1. (A − B) ∪ B = A

2. (A − B) ∪ A = A

3. (A − B) ∩ B = ∅

4. A ⊆ B ⇒ A ∪ B = B

Which of the above are correct?

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NDA I - Mathematics Question Paper 2017 - Question 9

In the binary equation (1p101)_{2} + (10q1)_{2} = (100r00)_{2}

Where p, q and r are binary digits, what are the possible values of p, q and r respectively?

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NDA I - Mathematics Question Paper 2017 - Question 10

If S = {x: x^{2} + 1 = 0, x is real}, then S is

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NDA I - Mathematics Question Paper 2017 - Question 11

The expansion (x − y)^{2}, n ≥ 5 is done in the descending powers of x. If the sum of the fifth and sixth terms is zero, then x/y is equal to

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NDA I - Mathematics Question Paper 2017 - Question 12

If A = and det(A^{3} ) = 125, then α is equal to

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NDA I - Mathematics Question Paper 2017 - Question 13

If B is a non-singular matrix and A is a square matrix, then the value of det(B^{−1}AB) is equal to

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NDA I - Mathematics Question Paper 2017 - Question 14

If a ≠ b ≠ c , then one value of x which satisfies the equation is given by

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NDA I - Mathematics Question Paper 2017 - Question 15

If A = then what is AA^{T} equal to (where A^{T} is the transpose of A)?

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NDA I - Mathematics Question Paper 2017 - Question 17

Let x, y, z be positive real numbers such that x, y, z are in GP and tan−1 , tan−1 and tan−1 are in AP. Then which one of the following is correct?

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NDA I - Mathematics Question Paper 2017 - Question 18

If tan(α + β) = 2 and tan(α − β) = 1, then tan(2α ) is equal to

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NDA I - Mathematics Question Paper 2017 - Question 19

Consider the following for triangle ABC:

Q. Which of the above are correct?

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NDA I - Mathematics Question Paper 2017 - Question 20

If sec θ − cosec θ = 4/3, then what is (sin θ − cos θ) equal to?

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NDA I - Mathematics Question Paper 2017 - Question 21

If a vertex of a triangle is (1, 1) and the midpoints of two sides of the triangle through this vertex are (-1, 2) and (3, 2), then the centroid of the triangle is

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NDA I - Mathematics Question Paper 2017 - Question 22

The incentre of the triangle with vertices A(1, √3), B(0, 0) and C(2, 0) is

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NDA I - Mathematics Question Paper 2017 - Question 23

If the three consecutive vertices of a parallelogram are (-2, -1), (1,0) and (4, 3), then what are the coordinates of the fourth vertex?

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NDA I - Mathematics Question Paper 2017 - Question 24

The two circles x^{2} + y^{2} = r^{2} and x^{2} + y^{2} − 10x + 16 = 0 intersect at two distinct points. Then which one of the following is correct?

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NDA I - Mathematics Question Paper 2017 - Question 25

What is the equation of the circle which passes through the points (3, -2) and (-2, 0) and having its centre on the line 2x − y − 3 = 0?

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NDA I - Mathematics Question Paper 2017 - Question 26

What is the ratio in which the point C = (− 2/7, − 20/7) divides the line joining the points A (−2, −2) and B (2, −4)?

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NDA I - Mathematics Question Paper 2017 - Question 27

What is the equation of the ellipse having foci (±2, 0) and the eccentricity 1/4?

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NDA I - Mathematics Question Paper 2017 - Question 28

What is the equation of the straight line parallel to 2x + 3y + 1 = 0 and passes through the point (-1, 2)?

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NDA I - Mathematics Question Paper 2017 - Question 29

What is the acute angle between the pair of straight lines √2x + √3y = 1 and √3x + 2y = 2?

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NDA I - Mathematics Question Paper 2017 - Question 30

If the centroid of a triangle formed by (7, x), (y, −6) and (9, 10) is (6, 3) , then the values of x and y are respectively

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NDA I - Mathematics Question Paper 2017 - Question 31

Let S be the set of all persons living in Delhi. We say that x, y in S are related if they were born in Delhi on the same day. Which one of the following is correct?

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NDA I - Mathematics Question Paper 2017 - Question 32

Let A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Then the number of subsets of A containing two or three elements is

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NDA I - Mathematics Question Paper 2017 - Question 34

If the difference between the roots of the equation x2 + kx + 1 = 0 is strictly less than √5, where |k| ≥ 2, then k can be any element of the interval

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NDA I - Mathematics Question Paper 2017 - Question 35

If the roots of the equation x2 + px + q = 0 are in the same ratio as those of the equation x2 + lx + m = 0, then which one of the following is correct?

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NDA I - Mathematics Question Paper 2017 - Question 36

The value of

Where n is not a multiple of 3 and , is

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NDA I - Mathematics Question Paper 2017 - Question 37

Three-digit numbers are formed from the digits 1, 2, and 3 in such a way that the digits are not repeated. What is the sum of such three-digit numbers?

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NDA I - Mathematics Question Paper 2017 - Question 38

What is the sum of the series 0.3 + 0.33 + 0.333 + ⋯ n terms?

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NDA I - Mathematics Question Paper 2017 - Question 39

If ω, ω^{2} are the cube roots of unity, then (1 + ω)(1 + ω^{2} )(1 + ω^{3})(1 + ω + ω^{2} ) is equal to

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NDA I - Mathematics Question Paper 2017 - Question 40

If the sum of m terms of an AP is n and the sum of n terms is m, then the sum of (m + n) terms is

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NDA I - Mathematics Question Paper 2017 - Question 41

The modulus and principal argument of the complex number are respectively

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NDA I - Mathematics Question Paper 2017 - Question 42

If the graph of a quadratic polynomial lies entirely above the x-axis, then which one of the following is correct?

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NDA I - Mathematics Question Paper 2017 - Question 43

If |z + 4| ≤ 3, then the maximum value of |z + 1| is

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NDA I - Mathematics Question Paper 2017 - Question 44

The number of roots of the equation z^{2} = 2z̅ is

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NDA I - Mathematics Question Paper 2017 - Question 45

If cot α and cot β are the roots of the equation x^{2} + bx + c = 0 with b ≠ 0, then the value of cot(α + β) is

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NDA I - Mathematics Question Paper 2017 - Question 46

The equations x + 2y + 3z = 12x + y + 3z = 25x + 5y + 9z = 4

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NDA I - Mathematics Question Paper 2017 - Question 49

If then which one of the following is correct?

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NDA I - Mathematics Question Paper 2017 - Question 50

Consider the set A of all matrices of order 3 × 3 with entries 0 or 1 only. Let B be the subset of A consisting of all matrices whose determinant is 1. Let C be the subset of A consisting of all matrices whose determinant is -1. Then which one of the following is correct?

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NDA I - Mathematics Question Paper 2017 - Question 54

If A = 3/5 where 450° < 540°, then cos ��/2 is equal to

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NDA I - Mathematics Question Paper 2017 - Question 56

From the top of a lighthouse, 100 m high, the angle of depression of a boat is tan−1 ( 5/12). What is the distance between the boat and the lighthouse?

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NDA I - Mathematics Question Paper 2017 - Question 57

The maximum value of sin (x + π/6) + cos (x + π/6) in the interval (0, π/2) is attained at

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NDA I - Mathematics Question Paper 2017 - Question 58

If K = sin ( π/18) sin (5π/18) sin (7π/18), then what is the value of K?

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NDA I - Mathematics Question Paper 2017 - Question 60

If sin θ = 3 sin(θ + 2α), then the value of tan(θ+ α) + 2 tan α is equal to

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NDA I - Mathematics Question Paper 2017 - Question 62

Let f: [−6, 6] → R be defined by f(x) = x^{2} − 3. Consider the following:

Which of the above is/are correct?

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NDA I - Mathematics Question Paper 2017 - Question 67

What is the length of the longest interval in which the function is increasing?

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NDA I - Mathematics Question Paper 2017 - Question 69

What is the maximum value of the function

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NDA I - Mathematics Question Paper 2017 - Question 70

Let f(x) be an indefinite integral of sin^{2} x.

Consider the following statements:

Statement 1: The function f(x) satisfies f(x + π) = f (x) for all real x.

Statement 2: sin2(x + π) = sin^{2} x for all real x.

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

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NDA I - Mathematics Question Paper 2017 - Question 71

What are the degree and order respectively of the differential equation

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NDA I - Mathematics Question Paper 2017 - Question 72

What is the differential equation corresponding to by eliminating a?

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NDA I - Mathematics Question Paper 2017 - Question 73

What is the general solution of the differential equation

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NDA I - Mathematics Question Paper 2017 - Question 74

Let . Then what is f′(5) equal to where f′(x) is the derivative of f(x)]?

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NDA I - Mathematics Question Paper 2017 - Question 75

If f (x) and g(x) are continuous functions satisfying f(x) = f(a − x) and g(x) + g(a − x) = 2, then what is equal to?

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NDA I - Mathematics Question Paper 2017 - Question 76

For two department events A and B, it is given that P (A) = 0 ∙ 2 and P(B) = 0 ∙ 5. If A ⊆ B , then the values of conditional probabilities P(A|B) and P(**B**|A) are respectively.

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NDA I - Mathematics Question Paper 2017 - Question 77

A point is chosen at random inside a circle. What is the probability that the point is closer to the centre of the circle than to its boundary?

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NDA I - Mathematics Question Paper 2017 - Question 78

If two regression lines between height (x) and weight (y) are 4y − 15x + 410 = 0 and 30x − 2y − 825 = 0, then what will be the correlation coefficient between height and weight?

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NDA I - Mathematics Question Paper 2017 - Question 79

In an examination, 40% of candidates got second class. When the data are represented by a pie chart, what is the angle corresponding to second class?

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NDA I - Mathematics Question Paper 2017 - Question 80

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.

Q. Which of the following is correct in respect of the above statements?

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NDA I - Mathematics Question Paper 2017 - Question 81

A card is drawn from a well-shuffled ordinary deck of 52 cards. What is the probability that it is an ace?

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NDA I - Mathematics Question Paper 2017 - Question 82

If the data are moderately non-symmetrical, then which one of the following empirical relationships is correct?

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NDA I - Mathematics Question Paper 2017 - Question 83

Data can be represented in which of the following forms?

1. Textual form 2. Tabular form 3. Graphical form Select the correct answer using the code given below:

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NDA I - Mathematics Question Paper 2017 - Question 84

For given statistical data, the graphs for less than ogive and more than ogive are drawn. If the point at which the two curves intersect is P, then abscissa of point P gives the value of which one of the following measures of central tendency?

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NDA I - Mathematics Question Paper 2017 - Question 85

Consider the following statements:

1. Two events are mutually exclusive if the occurrence of one event prevents the occurrence of the other.

2. The probability of the union of two mutually exclusive events is the sum of their individual probabilities.

Which of the above statements is/are correct?

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NDA I - Mathematics Question Paper 2017 - Question 86

If the regression coefficient of x and y and y on x are − 1/2and − 1/8respectively, then what is the correlation coefficient between x and y?

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NDA I - Mathematics Question Paper 2017 - Question 87

A sample of 5 observations has mean 32 and median 33. Later it is found that an observation was recorded incorrectly as 40 instead of 35. If we correct the data, then which one of the following is correct?

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NDA I - Mathematics Question Paper 2017 - Question 88

If two fair dice are thrown, then what is the probability that the sum is neither 8 nor 9?

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NDA I - Mathematics Question Paper 2017 - Question 89

Let A and B are two mutually exclusive events with P (A) = 1/3 and P(B) = 1/4. What is the value of P(A̅ ∩ B̅ )?

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NDA I - Mathematics Question Paper 2017 - Question 90

The mean and standard deviation of a binomial distribution are 12 and 2 respectively. What is the number of trials?

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NDA I - Mathematics Question Paper 2017 - Question 91

A straight line with direction cosines 〈0, 1, 0〉 is

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NDA I - Mathematics Question Paper 2017 - Question 92

(0, 0, 0), (a, 0, 0), (0, b, 0) and (0, 0, c) are four distinct points. What are the coordinates of the point which is equidistant from the four points?

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NDA I - Mathematics Question Paper 2017 - Question 93

The points P(3, 2, 4), Q(4, 5, 2), R(5, 8, 0) and S(2, −1, 6) are

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NDA I - Mathematics Question Paper 2017 - Question 94

The line passing through the points (1, 2, −1) and (3, −1, 2) meets the yz plane at which one of the following points?

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NDA I - Mathematics Question Paper 2017 - Question 95

Under which one of the following conditions are the lines and perpendicular?

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NDA I - Mathematics Question Paper 2017 - Question 96

and are three coplanar vectors and then which one of the following is correct?

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NDA I - Mathematics Question Paper 2017 - Question 97

Let ABCD be a parallelogram whose diagonals intersect at P and let O be the origin. What is ⃗ equal to?

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NDA I - Mathematics Question Paper 2017 - Question 98

ABCD is a quadrilateral whose diagonals are AC and BD. Which one of the following is correct?

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NDA I - Mathematics Question Paper 2017 - Question 99

If then which one of the following is correct?