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NDA I - Mathematics Question Paper 2017 - NDA MCQ


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30 Questions MCQ Test NDA (National Defence Academy) Past Year Papers - NDA I - Mathematics Question Paper 2017

NDA I - Mathematics Question Paper 2017 for NDA 2024 is part of NDA (National Defence Academy) Past Year Papers preparation. The NDA I - Mathematics Question Paper 2017 questions and answers have been prepared according to the NDA exam syllabus.The NDA I - Mathematics Question Paper 2017 MCQs are made for NDA 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for NDA I - Mathematics Question Paper 2017 below.
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NDA I - Mathematics Question Paper 2017 - Question 1

The sum of the roots of the equation x2 + 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 ax2 + x + c = 0 (where a and c are non-zero) is equal to the sum of the reciprocals of their squares. Then a, ca2 , c2 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 n2 + 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?

Detailed Solution for NDA I - Mathematics Question Paper 2017 - Question 8

By property, 

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: x2 + 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(A3 ) = 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−1AB) 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 AAT equal to (where AT is the transpose of A)?

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NDA I - Mathematics Question Paper 2017 - Question 16

What is the value of tan 18°?

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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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△ ABC is equilateral

⇒ Incentre = Centroid = (1, 1/√3)

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?

Detailed Solution for NDA I - Mathematics Question Paper 2017 - Question 23

4th vertex = (4 − 2 − 1, 3 − 1 − 0) = (1,2)

NDA I - Mathematics Question Paper 2017 - Question 24

The two circles x2 + y2 = r2 and x2 + y2 − 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?

Detailed Solution for NDA I - Mathematics Question Paper 2017 - Question 25

(ℎ − 3)2 + (2ℎ − 1)2 = (ℎ + 2)2 + (2ℎ − 3)2

⟹ ℎ = − 3/2
⟹ 2ℎ − 3 = −6
∴ r 2 = 1/4 + 36
Equation of circle is 
(x + 3/2)+ (y + 6)2 = 1/4+ 36
⟹ x2 + y2 + 3x + 12y + 2 = 0

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)?

Detailed Solution for NDA I - Mathematics Question Paper 2017 - Question 26

2k − 2/k + 1 = − 2/7

⟹ 8k = 6 ⟹ k = 3/4
ratio = 3: 4

NDA I - Mathematics Question Paper 2017 - Question 27

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

Detailed Solution for NDA I - Mathematics Question Paper 2017 - Question 27

2 = a/4 ⟹ a = 8

b2 = 64 − 4 = 60
Equation of ellipse is
x2/64 + y2/60 = 1

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)?

Detailed Solution for NDA I - Mathematics Question Paper 2017 - Question 28

Let equation of line is 2x + 3y + λ = 0 putting (−1, 2), we get λ = −4
⟹ equation of line is 2x + 3y − 4 = 0

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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