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if the pair of lines ax2 + 2hxy + by2 + 2gx + 2fy + c = 0
The circle x2 + y2 - 8x + 4y + 4 = 0 touches
The foci of the ellipse 25(x+1)2 + 9(y+2)2 = 225 are
The differential equation of the family of lines passing through the origin is
The area bounded by the curve y = x2 - 4x, x-axis and line x = 2 is
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
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
If two dice are thrown, find the probability of getting an odd number of on one and multiple of 3 on the other is
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
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
The orthocentre of a triangle whose vertices are [(2),((√3-1)/2)], ((1/2),-(1/2)) and (2,-(1/2)) is
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