The differential equation of the curve for which the initial ordinate of any tangent is equal to the corresponding subnormal
is linear
is homogeneous of second degree
has separable variables
is of second order
The differential equation of all parabolas each of which has a latusrectum 4a and whose axes are parallel to the Y-axis is
of order 1 and degree 2
of order 2 and degree 3
of order 2 and degree 1
of order 2 and degree 2
The value of the parameter a such that the area bounded by y = a2x2 + ax + 1, coordinate axes and the line x = 1 attains its least value is equal to
- 1
If n integers taken at random are multiplied together, then the probability that the last digit of the product is 1, 3, 7 or 9 is
4 -
None
B.
In any number, the last digits can be 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. Therefore, the last digit of each number can be chosen in 10 ways. Thus, the exhaustive number of ways in 10°. If the last digit be 1, 3, 7 or 9, then none of the numbers can be even or end in 0 or 5.
Thus, we have a choice of 4 digits viz. 1, 3, 7 or 9 with which each of n numbers should end. So, favourable number of ways is 4n.
Hence, required probability =
A bag contains (n + 1) coins. It is known that one of these coins shows heads on both sides, whereas the other coins are fair. One coin is selected at random and tossed. If the probability that toss results in heads is , then the value of n is
5
4
3
None of these
If A and B are two given events, then P(A ∩ B) is
equal to P(A) + P(B)
equal to P(A) + P(B) + P(A B)
not less than P(A) + P(B) - 1
not greater than P(A) + P(B) - P(A B)