(Mathematics-Part-2) NDA/NA Solved Paper 2017-I

Total Questions: 50

1. 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

Correct Answer: (d)
Solution:


2. The incentre ofthe trianglewith vertices A (1, √3), B (0, 0) and C (2, 0) is

Correct Answer: (d)
Solution:


3. 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?

Correct Answer: (a) (1,2)
Solution:


4. 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?

Correct Answer: (a) 2<r<8
Solution:

For the circle, x² +y² = r², centre (0, 0) radius =r
Ifthe circle x² + y² - 10x +16=0 is compared with
general form
x²+y²+2g+2fy+c=0, we get
2g=-10,2f=0, c=16
⇒ g=-5, f= 0
∴ centre (+5,0)

5. 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?

Correct Answer: (b) x² + y² + 3x + 12y + 2 = 0
Solution:


6. 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)?

Correct Answer: (b) 3:4
Solution:

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

Correct Answer: (a)
Solution:

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

Correct Answer: (a) 2x + 3y - 4 = 0
Solution:

The equation of line parallel to
2x+3y+1= 0 is 2x+3y+K=0
It is passing through point (-1, 2)
∴ 2+6+K=0⇒K=-4
⇒ 2(-1)+3 (2)+K=0
∴ Eqn. is 2x+3y-4=0

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

Correct Answer: (a)
Solution:

10. 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

Correct Answer: (a) 5,2
Solution: