Mathematics Test 123

Result

Mathematics Test 123

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Weekly Quiz Competition

Question 1
4 / -1

Equation of the circle passing through origin and having its centre in I quadrant and having intercepts of length 4 and 6 units on the x and y axis respectively :-

A
x² + y² – 4x – 6y = 0

B
x² + y² – 6x – 4y = 0

C
x² + y² – 3x – 2y = 0

D
x² + y² + 3x + 2y = 0

Solution
Question 2
4 / -1

Triangle formed by A(0,1,2), B(1,2,3) & C(2,3,3) is -

A
right angled

B
acute angled

C
obtuse angled

D
isosceles

Solution
Question 3
4 / -1

Which of the following line may be the tangent of circle x² + y² – 6x – 4y + 4 = 0 and passing through (6,8)-

A
3x – 4y = 14

B
3x + 4y = 50

C
y = 8

D
x = 6

Solution
Question 4
4 / -1

A
16

B
4

C
8

D
32

Solution
Question 5
4 / -1

A

B

C

D

Solution
Question 6
4 / -1

A

B

C

D
option 2 and option 3 are correct

Solution
Question 7
4 / -1

Let , and , then correct option/s is/are -

A
I₁ + I₂ = I₃

B
I₂ – I₃ = I₁

C
I₂ – I₃ = 0

D
All are correct

Solution
Question 8
4 / -1

A
0

B
1

C
2

D
option 1 and option 2 are correct

Solution
Question 9
4 / -1

If the circle x² + y²+ 2gy + 2ƒy = 0 bisects the circumference of the circles

x² + y²– 6x – 8y + 14 = 0 and x² + y²+ 2x – 4y + 2 = 0 then which of the following is/are true-

A
|ƒ| + |g| = 5

B
ƒ² + g²= 13

C
|ƒg| = 6

D
All are correct

Solution

Let S₁= x² + y²+ 2gy + 2ƒy = 0
S₂= x² + y² + 2x – 4y + 2 = 0
S₃= x²+ y²– 6x – 8y + 14 = 0
Radical axis of S₁ and S₂passes through centre of S₂ i.e. (–1, 2).
(2g – 2)x + (2ƒ + 4)y – 2 = 0
(2g – 2)(–1) + (2ƒ + 4)(2) – 2 = 0
–2g + 2 + 4ƒ + 8 – 2 = 0
–2g + 4ƒ + 8 = 0 ......(1)
Similarly S₁ and S₃
(2g + 6)x + (2ƒ + 8)y – 14 = 0
(2g + 6)3 + (2ƒ + 8)4 – 14 = 0
6g + 8ƒ + 36 = 0
3g + 4ƒ + 18 = 0 .......(2)

g = –2, ƒ = –3
Question 10
4 / -1

S ≡ x² + y² – 2x – 4y + 1 = 0 and S' ≡ x² + y² – 4x – 2y + 1 = 0 are the equations of two circles.

The equation of circle through intersection of S and S' and having its centre on the line 2x + y – 6 = 0 is

A
x² + y² + 6x + 3y + 1 = 0

B
x² + y² – 6x + 1 = 0

C
x² + y² + 6y + 1 = 0

D
x² + y² – 6x + 6y + 1 = 0

Solution