Mathematics Test 206

Result

Mathematics Test 206

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Weekly Quiz Competition

Question 1
4 / -1

if the pair of lines ax² + 2hxy + by² + 2gx + 2fy + c = 0

A
2f gh = bg² + ch²

B
bg² ≠ ch²

C
abc = 2fgh

D
none of these

Solution
Question 2
4 / -1

The circle x² + y² - 8x + 4y + 4 = 0 touches

A
x-axis

B
y-axis

C
both x and y-axis

D
does not touch the axis
Question 3
4 / -1

The foci of the ellipse 25(x+1)² + 9(y+2)² = 225 are

A
(-1,2),(6,1)

B
(-1,-2),(1,6)

C
(1-,2),(1,-6)

D
(-1,2),(-1,-6)

Solution
Question 4
4 / -1

The differential equation of the family of lines passing through the origin is

A
x dy/dx + y = 0

B
X+dy/dx = 0

C
dy/dx = y/x

D
dy/dx = x

Solution
Question 5
4 / -1

The area bounded by the curve y = x² - 4x, x-axis and line x = 2 is

A
(16/3) sq.unit

B
(-16/3) sq.unit

C
(4/7) sq.unit

D
cannot be calculated

Solution
Question 6
4 / -1

The probabilities of solving a problem by three student A,B,C are 1/2, 1/3, 1/4 respectively. The probability that problem will be solved is

A
1/4

B
1/2

C
3/4

D
1/3

Solution

We have, probability that A can solve the problem = P(A) = 1/2 ,

And in this way P(B) = 1/3 and P(C) = 1/4.

P(A cannot solve the problem) = 1 – P(A) = 1/2 ,

P(B cannot solve the problem) = 1 – P(B) = 1 – 1/3 = 2/3,

P(C cannot solve the problem) = 1 – P(C) = 1 – 1/4 = 3/4.

P(A, B, and C cannot solve the problem) = 1/2 x 2/3 x 3/4 = 1/4.

Therefore , P(Problem will be solve) = 1 – P(Problem is not solved by any of them)

= 1 – 1/4 = 3/4
Question 7
4 / -1

If two dice are thrown, find the probability of getting an odd number of on one and multiple of 3 on the other is

A
1/3

B
2/3

C
1/6

D
13/36

Solution

Odd no. on the first die

1, 3, 5

multiple of 3 on the other die

3, 6

now let's see the combination of these two events happening simultaneously

as the question says

(1,3) , (1,6) , (3,3) , (3,6) , (5,6) , (5,3)

total no of favourable events = 6

total no of events throwing two dice simultaneously = 6² = 36

so probability = 6/36 = 1/6
Question 8
4 / -1

If the roots of ax² + bx + c = 0 are α,β and roots of Ax² + Bx + C = 0 are α + K, β + K, then B² - 4AC/b² - 4ac is equal to

A
a/A

B
A/a

C
(a/A)²

D
(A/a)²
Question 9
4 / -1

The orthocentre of a triangle whose vertices are [(2),((√3-1)/2)], ((1/2),-(1/2)) and (2,-(1/2)) is

A
[(3/2),((√3-2)/2)]

B
[(2),(-1/2)]

C
[(5/4),((√3-2)/4)]

D
[(1/2),-(1/2)]
Question 10
4 / -1

A
0

B
-1

C
2

D
1

Solution