Four persons independently solve a certain problem correctly with proabilities `1/2,3/4,1/4,1/8.` Then the probability that the problem is solved corr

Here `barp=0.3rArrp=0.7andq=0.3,n=5andr=4` `therefore` Required probability = `""^(5)C_(4)(0.7)^(4)(0.3)`

Correct Answer - 6 `T=2pisqrt((l)/(g)) implies (DeltaT)/(T) = (1)/(2) (Deltal)/(l) (1)/(2)(alphaDeltatheta) implies DeltaT = (T)/(2)(alphaDeltatheta)= ((10xx8.64 xx 10^(4))/(2)) (7xx10^(-7)) (20) = 6s`

Correct Answer - `(.^(7)P_(5))/(7^(5))` In an 8-floor house, there are 7 floors above the ground floor. Each person can leave the cabin at any of the seven floors, i.e., each person...

Correct Answer - C The probabilities of solving the question by these three students are `1//3,2//7and 3//8,` respectively. Therefore, `P(A)=(1)/(3),P(B)=2/7,P(C)=3/8` Then probability of question solved by only one student is `P((A...

Correct Answer - C Possiblities of getting 9 are `(5,4),(4,5),(6,43),(3,6).` `thereforep=(4)/(36)=1/9andq=1-1/9=8/9` Therefore, the required probability is `""^(3)C_(2)q^(1)p^(2)=(3)((8)/(9))((1)/(9))^(2)=(8)/(143)`

Correct Answer - B::D `P(X_(1))=1/2,P(X_(2))=1/4,P(X_(3))=1/4` `P(X)=P(X_(1)nnX_(2)nnX_(3))+P(X_(1)nnX_(2)^(C)nnX_(3))` `+P(X_(1)^(C)nnX_(2)nnX_(3))+P(X_(1)nnX_(2)nnX_(3)^(C))=1/4` (1) `P(X_(1)^(C)//X)=(P(XnnX_(1)^(C)))/(P(X))=(1//32)/(1//4)=1/8` (2) P [exactly two engines of the shp are functioning `|X]=(7//32)/(1//4)=7/8` (3) `P((X)/(X_(2)))=(P(XnnX_(2)))/(P(X_(2)))=(5//32)/(1//4)=5/8` (4) `P((X)/(X_(1)))=(P(XnnX_(1)))/(P(X_(1)))=(7//32)/(1//2)=7/16`

Domestic problem

Correct Answer - B `(b)` Total no of outcomes `=6^(6)` Number of ways of choosing `4` other different numbers is `"^(6)C_(2)` and choosing `2` out of remaining `4` can be lone...

Correct Answer - A `(a)` Let us first distribute `4` left gloves to four person in `4!` ways. If no one gets the corresponding right glove then no. of ways `=4!(1-(1)/(1!)+(1)/(2!)-(1)/(3!)+(1)/(4!))=9`...

Correct Answer - `(Y)/(3)`,3Y