MCQ (Single Correct Answer)

1
A straight line x = y + 2 touches the circle 4(x2 + y2) = r2. The value of r is
NDA 2015 Paper 2
2
If the centre of the circle passing through the origin is (3, 4), then the intercepts cut-off by the circle on X-axis and Y-axis respectively, are
NDA 2015 Paper 2
3
What is the radius of the circle passing through the point (2, 4) and having centre at the intersection of the lines x $$-$$ y = 4 and 2x + 3y + 7 = 0 ?
NDA 2016 Paper 2
4
What is the distance between the centres of the two circles?
NDA 2016 Paper 1
5
If the circles intersect at two distinct points, then which one of the following is correct?
NDA 2016 Paper 1
6
On which line does the centre of the circle lie?
NDA 2016 Paper 1
7
What is the sum of the squares of the intercepts cut-off by the circle on the axes?
NDA 2016 Paper 1
8
The equation of the circle which passes through the points (1, 0), (0, $$-$$6) and (3, 4) is
NDA 2017 Paper 2
9
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?
NDA 2017 Paper 1
10
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 ?
NDA 2017 Paper 1
11
The equation of a circle whose end points of a diameter are (x1, y1) and (x2, y2) is
NDA 2018 Paper 2
12
If Y-axis touches the circle $${x^2} + {y^2} + gx + fy + {c \over 4} = 0$$, then the normal at this point intersects the circle at the point.
NDA 2018 Paper 2
13
A circle is drawn on the chord of a circle x2 + y2 = a2 as diameter. The chord lies on the line x + y = a. What is the equation of the circle?
NDA 2019 Paper 1
14
The circle x2 + y2 + 4x $$-$$ 7y + 12 = 0, cuts an intercept on Y-axis equal to
NDA 2019 Paper 1
15
In a circle of diameter 44 cm, the length of a chord is 22 cm. What is the length of minor arc of the chord?
NDA 2019 Paper 1
16

If (a, b) is the centre and c is the radius of the circle $x^2 + y^2 + 2x + 6y + 1 = 0$, then what is the value of $a^2 + b^2 + c^2$?

NDA Mathematics 21 April 2024
17

What is the value of $A_1$?

NDA Mathematics 21 April 2024
18

What is the value of $\frac{2(A_1 + A_2)}{ A_1 - 3A_2}$?

NDA Mathematics 21 April 2024
19
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 ?
NDA Mathematics 3 September 2023
20

Consider the following in respect of the circle 4x+ 4y- 4ax - 4ay + a2 = 0:

1. The circle touches both the axes. 

2. The diameter of the circle is 2a.

3. The centre of the circle lies on the line x + y = a.

How many of the statements given above are correct?

NDA Mathematics 3 September 2023
21
What is the area of minor segment ?
NDA Mathematics 16 April 2023
22
What is the area of major segment ?
NDA Mathematics 16 April 2023
23
What is the diameter of a circle inscribed in a regular polygon of 12 sides, each of length 1 cm ?
NDA Mathematics 4 September 2022
24
The centre of the circle passing through the origin and making positive intercepts 4 and 6 on the coordinate axes, lies on the line
NDA Mathematics 4 September 2022
25
What is the equation of the circle which touches both the axes in the first quadrant and the line y - 2 = 0?
NDA Mathematics 10 April 2022
26
What is the radius of the circle 4x2 + 4y2 - 20x + 12y - 15 = 0?
NDA Mathematics 18 April 2021
27
A chord subtends an angle 120° at the centre of a unit circle. What is the length of the chord?
NDA Mathematics 18 April 2021
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