NDA I - Mathematics Question Paper 2017 - Defence MCQ

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

The fifth term of an AP of n terms, whose sum is n² + n, is

The sum of all the two-digit odd numbers is

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

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?

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?

If S = {x: x² + 1 = 0, x is real}, then S is

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

If A =   and det(A³ ) = 125, then α is equal to

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

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

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

What is the value of tan 18°?

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?

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

Consider the following for triangle ABC:

Q. Which of the above are correct?

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

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

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

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?

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?

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?

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)?

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

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

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

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