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Topic Question Set

Q 41 :

The number of ways, in which 16 oranges can be distributed to four children such that each child gets at least one orange, is  [2026]

  • 403

     

  • 429

     

  • 455

     

  • 384

     

(3)

Let oranges be identical, then

x1+x2+x3+x4=16,  and x1,x2,x3,x4≥1

or x1'+x2'+x3'+x4'=12

so total number of solutions are

=C312+3=C315=455

Q 42 :

Let S denote the set of 4-digit numbers abcd such that a>b>c>d and P denote the set of 5-digit numbers having product of its digits equal to 20. Then n(S)+n(P) is equal to ______  [2026]



(260)

For n(s)=C410=210

(5,4,1,1,1),  (5,2,2,1,1)

For n(p)=5!3!+5!2!2!=50

n(s)+n(p)=210+50=260

Q 43 :

Let S={x3+ax2+bx+c: a,b,c∈ℕ and a,b,c≤20} be a set of polynomials. Then the number of polynomials in S, which are divisible by x2+2, is    [2026]

  • 10

     

  • 20

     

  • 120

     

  • 6

     

(1)