Name ................................................
ONLINE JEE ADVANCED UNIT EXAM
Batch.................... Roll No. ...............
27-12- 2021 Batch: LT 23 All Hybrid
23Z/TP/C MATHEMATICS - Circle
Mark : 80 Time : 1 Hr
Section 1 - Single correct answer (9 Questions)
Each question has 4 options, Only one of these four options is the correct answer
Each correct answer will be awarded four mark. One mark will be deducted for each incorrect
answer.
1. The equation of the smallest circle passing through the intersection of the line x + y = 1 and the circle
x2 + y2 = 9 is
A) x2 + y2 + x + y – 8 = 0 B) x2 + y2 – x – y – 8 = 0
C) x2 + y2 – x + y – 8 = 0 D) x2 + y2 + 6x - 3y + 8 = 0
2. The equation of a circle which touches the y-axis and has its centre at (1,2) is
A) x 2 y 2 2x 4y 4 0 B) x 2 y 2 2x 4y 1 0
C) x 2 y 2 2x 4y 4 0 D) x 2 y 2 3x 4y 6 0
3. If the circle x 2 y 2 6x 8y 25 a 2 0 touches the axis of y, then ‘a’ equals
A) 0 B) 4 C) 2 D) 3
4. Find the equation of a circle passing through (1, 1), (2, –1) and (3, 2)
A) x2 + y2 + 7x – 8y + 4 = 0 B) x2 + y2 +– 5x – y + 4 = 0
C) x2 + y2 – 5x + 7y + 4 = 0 D) x2 + y2 + 8x – 7y + 9 = 0
5. If one end of a diameter of the circle x 2 + y2 - 10x - 14 y - 15 1 = 0 is (3,4) then find the coordinates of
the other end of the diameter
A) (2,1) B) (1,2) C) (1,1) D) (1,3)
6. Two circles x 2 y 2 2x 3 0 and x 2 y 2 4x 6y 8 0 are such that
A) they touch each other B) they intersect
C) one lies inside the other D) each lies outside the other
7. The equation of the circle which passes through the origin and cuts off intercepts 3 and 4 from the positive
parts of the axes respectively
2 2 2 2
3 2 5 3 2 5
A) x y 2 B) x y 2
2 2 2 2
2 2 2 2
2 2 5 2 2 5
C) x y 2 D) x y 2
3 4 3 3
8. The value of k for which the circles x2 + y2 - 3x + ky - 5 = 0 and 4x2 + 4y2 - 12x - y - 9 = 0 become
concentric is
A) 1/8 B) -1/8 C) 1/4 D) -1/4
9. The area of the portion of the circle x2 + y2 – 4y = 0 lying below the x – axis is
A) 0 B) 48 C) 12 D) 16
ONLINE JEE ADVANCED UNIT EXAM
Batch.................... Roll No. ...............
27-12- 2021 Batch: LT 23 All Hybrid
23Z/TP/C MATHEMATICS - Circle
Mark : 80 Time : 1 Hr
Section 1 - Single correct answer (9 Questions)
Each question has 4 options, Only one of these four options is the correct answer
Each correct answer will be awarded four mark. One mark will be deducted for each incorrect
answer.
1. The equation of the smallest circle passing through the intersection of the line x + y = 1 and the circle
x2 + y2 = 9 is
A) x2 + y2 + x + y – 8 = 0 B) x2 + y2 – x – y – 8 = 0
C) x2 + y2 – x + y – 8 = 0 D) x2 + y2 + 6x - 3y + 8 = 0
2. The equation of a circle which touches the y-axis and has its centre at (1,2) is
A) x 2 y 2 2x 4y 4 0 B) x 2 y 2 2x 4y 1 0
C) x 2 y 2 2x 4y 4 0 D) x 2 y 2 3x 4y 6 0
3. If the circle x 2 y 2 6x 8y 25 a 2 0 touches the axis of y, then ‘a’ equals
A) 0 B) 4 C) 2 D) 3
4. Find the equation of a circle passing through (1, 1), (2, –1) and (3, 2)
A) x2 + y2 + 7x – 8y + 4 = 0 B) x2 + y2 +– 5x – y + 4 = 0
C) x2 + y2 – 5x + 7y + 4 = 0 D) x2 + y2 + 8x – 7y + 9 = 0
5. If one end of a diameter of the circle x 2 + y2 - 10x - 14 y - 15 1 = 0 is (3,4) then find the coordinates of
the other end of the diameter
A) (2,1) B) (1,2) C) (1,1) D) (1,3)
6. Two circles x 2 y 2 2x 3 0 and x 2 y 2 4x 6y 8 0 are such that
A) they touch each other B) they intersect
C) one lies inside the other D) each lies outside the other
7. The equation of the circle which passes through the origin and cuts off intercepts 3 and 4 from the positive
parts of the axes respectively
2 2 2 2
3 2 5 3 2 5
A) x y 2 B) x y 2
2 2 2 2
2 2 2 2
2 2 5 2 2 5
C) x y 2 D) x y 2
3 4 3 3
8. The value of k for which the circles x2 + y2 - 3x + ky - 5 = 0 and 4x2 + 4y2 - 12x - y - 9 = 0 become
concentric is
A) 1/8 B) -1/8 C) 1/4 D) -1/4
9. The area of the portion of the circle x2 + y2 – 4y = 0 lying below the x – axis is
A) 0 B) 48 C) 12 D) 16
