1
NDA Mathematics 3 September 2023
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language
Given that 16p2 + 49q2 - 4r2 - 56pq = 0. Which one of the following is a point on a pair of straight lines (px + qy + r) (px + qy - r) = 0?
A
$ \left(2, \frac{7}{2}\right) $
B
$ \left(2,-\frac{7}{2}\right)$
C
(4, -7)
D
(4, 7)
2
NDA Mathematics 3 September 2023
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language
If 3x + y - 5 = 0 is the equation of a chord of the circle x+ y2 - 25 = 0, then what are the coordinates of the mid-point of the chord ?
A
$ \left(\frac{3}{4}, \frac{1}{4}\right)$
B
$ \left(\frac{3}{2}, \frac{1}{2}\right) $
C
$ \left(\frac{3}{4},-\frac{1}{4}\right) $
D
$ \left(\frac{3}{2},-\frac{1}{2}\right)$
3
NDA Mathematics 3 September 2023
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language

Consider the following in respect of the equation $\frac{x^2}{24-k}+\frac{y^2}{k-16}=2$.

1. The equation represents an ellipse if k = 19.

2. The equation represents a hyperbola if k = 12.

3. The equation represents a circle if k = 20.

How many of the statements given above are correct?

A
Only one
B
Only two
C
All three
D
None
4
NDA Mathematics 3 September 2023
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language

Consider the following statements in respect of hyperbola $\frac{x^2}{\cos ^2 \theta}-\frac{y^2}{\sin ^2 \theta}=1$ :

1. The two foci are independent of θ.

2. The eccentricity is sec θ.

3. The distance between the two foci is 2 units.

How many of the statements given above are correct?

A
Only one
B
Only two
C
All three
D
None
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