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Practice QuestionsMCQ (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
The equation of a circle is
(x2 - 4x + 3) + (y2 - 6y + 8) = 0
Which of the following statements are correct?
I. The end points of a diameter of the circle are at (1, 2) and (3, 4).
II. The end points of a diameter of the circle are at (1, 4) and (3, 2).
III. The end points of a diameter of the circle are at (2, 4) and (4, 2).
Select the answer using the code given below.
NDA Mathematics 1st September 2024
17
What is BAC equal to?
NDA Mathematics 1st September 2024
18
What are the coordinates of A?
NDA Mathematics 1st September 2024
19
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
20
What is the value of $A_1$?
NDA Mathematics 21 April 2024
21
What is the value of $\frac{2(A_1 + A_2)}{ A_1 - 3A_2}$?
NDA Mathematics 21 April 2024
22
If 3x + y - 5 = 0 is the equation of a chord of the circle x2 + y2 - 25 = 0, then what are the coordinates of the mid-point of the chord ?
NDA Mathematics 3 September 2023
23
Consider the following in respect of the circle 4x2 + 4y2 - 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
24
What is the area of minor segment ?
NDA Mathematics 16 April 2023
25
What is the area of major segment ?
NDA Mathematics 16 April 2023
26
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
27
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
28
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
29
What are the coordinates of the center of the circle?
NDA Mathematics 14 November 2021
30
If r is the radius of the circle, then which one of the following is correct?
NDA Mathematics 14 November 2021
31
What is the radius of the circle 4x2 + 4y2 - 20x + 12y - 15 = 0?
NDA Mathematics 18 April 2021
32
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