Match the following lists:

Answer

`a to q, r, s ; bto r ; c to p , q ; d to p , q, r, s `

Explanation

`atoq,r, s, b tor,c to p, q, d to p,q,r,s.`
a. Suppose the coin is tossed n times. The probability of getting head or tail is `1//2.` The probability of not getting any head in n tosses in `(1//2)^(n).` The probability of getting at least one head is `1-(1//2)^(n)ge0.8`
`or ((1)/(2))^(n)le0.2 or 2^(n)ge5`
Therefore, the least value of n is 3.
b. The total number of mappings is `n^(n).` The number of one-one mappings in `n!` Hence the probability is
`(n!)/(n^(n))=3/32=6/64=(3!)/(4^(3))=(4!)/(4^(4))`
Comparing, we get `n=4`
c. Given equation is
`2x^(2)+2mx+m+1=0`
`D=4m^(2)-8(m+1)ge0`
`m^(2)-2m-2ge0`
`(m-1)^(2)-3ge0`
` impliesm=3,4,5,6,7,8,9,10`
Also, the number of ways of ways of choosing m is 10. Therefore, the required probability is 4/5.
`therefore5k=4`
d. `20p^(2)-13p+2le0`
`implies(4P-1)(5P-2)le0`
`implies1/4lePle2/5`
`implies1/4le1/5+1/5((4)/(5))+1/5((4)/(5))^(2)+...+1/5((4)/(5))^(n-1)le2/5`
`impliesn=2`
Hence, maximum as well as minimum valie of n is 2.