The numbers `(a ,b ,c)` are selected by throwing a dice thrice, then the probability that `(a ,b ,c)` are in A.P. is a.`1//12` b. `1//6` c. `1//4` d. none of these

A four figure number is formed of the figures 1, 2, 3, 5 with no repetitions. The probability that the number is divisible by 5 is a. 3//4 b. 1//4 c. 1//8 d. none of these

A man alternately tosses a coin and throws a die beginning with the coin. The probability that he gets a head in the coin before he gets a 5 or 6 in the dice is a. 3//4 b. 1//2 c. 1//3 d. none of these

Let A ,B ,C ,D be independent events such that P(A)=1//2,P(B)=1//3, P(C)=1//5, a n dP(D)=1//6. Then theprobability that none of A ,B ,C ,a n dD occurs a. 1//180 b. 1//45 c. 1//18 d. none of these

If a , b ,a n dc are in G.P., then a+b ,2b ,a n db+c are in a. A.P b. G.P. c. H.P. d. none of these

If the angles A,B,C of a triangle are in A.P. and sides a,b,c, are in G.P., then prove that a^2, b^2,c^2 are in A.P.

Consider f(x) =x^3+ax^2+bx+c Parameters a, b, c are chosen as the face value of a fair dice by throwing it three times Then the probability that f(x) is an invertible function is (A) 5/36 (B) 8/36 (C) 4/9 (D) 1/3

Consider f(x) =x^3+ax^2+bx+c Parameters a, b, c are chosen as the face value of a fair dice by throwing it three times Then the probability that f(x) is an invertible function is (A) 5/36 (B) 8/36 (C) 4/9 (D) 1/3

The number of possible outcomes in a throw of n ordinary dice in which at least one of the die shows and odd number is a. 6^n-1 b. 3^n-1 c. 6^n-3^n d. none of these

If a^2+b^2,a b+b c ,a n db^2+c^2 are in G.P., then a ,b ,c are in a. A.P. b. G.P. c. H.P. d. none of these

If a ,b ,c are in A.P., the a/(b c),1/c ,1/b will be in a. A.P b. G.P. c. H.P. d. none of these