The probabilities that a student passes in Mathematics,Physics and Chemistry are m, p and c, respectively. Of these subjects, the student has a 75% chance of passing in at least one, a 50% chance of passing in at least two and a 40% chance of passing in exactly two. Which of the following relations are true? (a) `p+m+c=19/20` (b) ` p+m+c=27/20` (c) `p m c=1/10` (d) `p m c=1/4`

If m_(p) is the mass of proton. m_(n) that of a neutron, M_(1) that of _(10)Ne^(20) nucleus and M_(2) that of _(20)Ca^(40) nucleus, then which of the following relations is//are not true?

A student takes examination in four subjects A, B, C, D. His chances of passing in A are 4/5 , in B are 3/4 , in C are 5/6 and in D are 2/3 . To qualify he must pass in A and atleast in two other subjects. What is the probability that he qualifies ?

A student appears for tests I, II and III. The student is considered successful if he passes in tests I, II or III or all the three. The probabilities of the Student passing in tests I,II and III are m, n and 1/2 respectively. If the probability of the student to be successful is 1/2 , then which one of the following is correct? (a) m (1+n)=1 (B) n (1+m) =1 (C) m=1 (D) mn=1

A Physical quantity P is given by P= (A^2sqrtB)/C , and the percentage errors in the measurements of A, B and C are 1% , 2 % and 4% respectively. Find the percentage error in P.

If A, B, and C are independent events such that P(A)=P(B)=P(C)=p , then find the probability of occurrence of at least two of A, B, and C.

In a college 30% students fail in Physics, 25% fail in Mathematics and 10% fail in both. One student is chosen at random. The probability that she fails in Physics if she has failed in Mathematics is a. 1//10 b. 1/3 c. 2/5 d. 9/(20)

For a student to qualify, he must pass at least two out of three exams. The probability that he will pass the 1st exam is p. If he fails in one of the exams, then the probability of his passing in the next exam, is p/2 otherwise it remains the same.Find the probability that he will qualify.

In A B C , points P and Q are on C A and C B , respectively such that C A=16 c m , C P=10 c m , C B=30 c m and C Q=25 c m . Is P Q ||A B ?

In an automobile factory, certain parts are to be fixed into the chassis in a section before it moves into another section. On a given day, one of the three persons A, B and C carries out this task. A has 45% chance, B has 35% chance and C has 20% chance of doing the task. The probability that A, B and C will take more than the allotted time is (1)/(6), (1)/(10) and (1)/(20) respectively. If it is found that the time taken is more than the allotted time, what is the probability that A has done the task ?

In Figure, M ,N and P are the mid-points of A B ,A C and B C respectively. If M N=3c m ,N P=3. 5c m and M P=2. 5c m , calculate B C ,A B and A Cdot