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If N 1c3 N 1c4 Nc3 Then N Is Just Greater Than

1) 5 2) 6 3) 4 4) 7 Answer: (4) 7 Solution: n –1C3 + n –1C4 > nC3 nC4 > nC3 n!/[4!(n-4)!] > n!/[3!(n-3)!] ¼ > 1/n-3... View Article

From 12 Books The Difference Between Number Of Ways A Selection Of 5 Books

1) 64 2) 118 3) 132 4) 330 5) 462 Answer: (3) 132 Solution: When one specified book is always included, then 4 out of 11 will be chosen =... View Article

There Are Two Urns Urn A Has 3 Distinct Red Balls And Urn B Has 9 Distinct Blue Balls

1) 3 2) 36 3) 66 4) 108 Answer: (4) 108 Solution: Number of balls in URN A = 3 Number of balls in URN B = 9 Selection of two balls from... View Article

A Student Is Allowed To Select At Most N Books From A Collection Of 2 N 1books

1) 6 2) 5 3) 4 4) 3 Answer: (4) 3 Solution: Given, a student is allowed to select at most n books from 2n+1 books 2n+1C1 + 2n+1C2 +... View Article

A Teacher Takes 3 Children From Her Class To The Zoo At A Time As Often As She Can

1) 12 2) 10 3) 60 4) None of these Answer: (2) 10 Solution: Number of ways group of 3 can be divided from n number of students is equal to... View Article

Statement I The Number Of Ways Distributing 10 Identical Balls In 4 Distinct Boxes

1) Statement I is correct, Statement II is correct; Statement II is not a correct explanation for Statement I 2) Statement I is correct,... View Article

If X 11 2 3 4 5 Then The Number Of Different Ordered Pairs Y Z That Can Formed

1) 52 2) 35 3) 25 4) 53 Answer: (2) 35 Solution: We have, X = {11,2,3,4,5} There are total five elements Y⊆X,Z⊆X Let p∈X, then... View Article

Let An Denote The Number Of All Ndigit Positive Integers Formed By The Digits 0 1

1) 7 2) 8 3) 9 4) 11 Answer: (2) 8 Solution: As per the given condition, the possible number of ways to write is: For a1 = 1 For a2 = 10,... View Article

Let An Denote The Number Of All N Digit Positive Integers Formed

1) a17 = a16 + a15 2) c17 ≠ c16 + c15 3) b17 ≠ b16 + c16 4) a17 = c17 + b16 Answer: (1) a17 = a16 + a15 Solution: As per the given... View Article

Total Number Of Ways In Which 5 Balls Of Different Colors Can Be Distributed Among 3 Persons

1) 75 2) 150 3) 210 4) 243 Answer: (2) 150 Solution: Total number of distribution = 35 Number of possibility when a person does not get... View Article

A box contains 2 white balls, 3 black balls and 4 red balls. In how many ways can 3 balls be drawn from the box, if atleast one black ball is to be included in the draw? (1) 64 (2) 24 (3) 3 (4) 12

Answer: (1) 64 Given White balls = 2 Black balls = 3 Red balls = 4 Solution: Selection of 3 balls out of 9 = 9C3 . . 9C3 = 84... View Article

A Student Is To Answer 10 Out Of 13 Questions In An Examination He Must Choose At Least 4 From First Five Questions

1) 140 2) 196 3) 280 4) 346 Answer: (2) 196 Solution: Given, a student is to answer 10 out of 13 questions in an examination Student has to... View Article

Let A And B Be Two Sets Containing 2 Elements And 4 Elements The Number Of Subsets

1) 256 2) 220 3) 219 4) 211 Answer: (3) 219 Solution: Total number of elements = 2 x 4 = 8 Total subsets = 28 Subsets with zero elements... View Article

Determine N If 2nc2 Nc2 9 2

1) 5 2) 4 3) 3 4) 2 Answer: (1) 5 Solution: Given, 20C2:nC2=9:2 4(2n−1)=9(n−1) n−4=9n−9 9n−8n=−4+9 n=5... View Article

Find Nc21 If Nc10 Nc11

1) 1 2) 0 3) 11 4) 10 Answer: (1) 1 Solution: Given, nC10 = nC11 n!/10!(n-10)! = n!/11!(n-11)! 11×10!(n−11)!=0!(n−10)(n−11)! 11 =... View Article

If N Is An Integer With 0 Less Than Or Equal N Less Than Or Equal 11 Then Minimum Value Of N 11 N Is Attained When A Value Of N

1) 11 2) 5 3) 7 4) 9 Answer: (2) 5 Solution: We can write, 11Cn = 11!/n!(11-n)! Now as we know, to get the maximum value of 11Cn the value... View Article