Q1.

A boy has 3 library tickets and 8 books of his interest in the library of these 8, he does not want to borrow Mathematics part - II  unless  Mathematics part - II  is also borrowed ? In how many ways can be choose the three books to be borrowed ? 

  • 41

  • 51

  • 81

  • 71

Solution:

NA

Q2.

An examination paper consists of 12 questions divided into two parts A and B . Part A contains 7 questions and part B contains 5 questions . A condidates is required to attempt 8 questions selecting at least 3 from  each part. In how many maximum ways can the candidate select the questions ?   

  • 35

  • 175

  • 210

  • 420

Solution:

NA 

Q3.

Given : P (7, k) = 60 P(7, k - 3). Then : 

  • k = 9 

  • k = 8

  • k = 5

  • k = 0

Solution:

NA

Q4.

If nPr = nPr + 1 and nPr = nC r =  nC r - 1 = then find the value of 'n' .  

  • 2

  • 3

  • 4

  • 5

Solution:

NA

Q5.

How many six digit telephone numbers can be formed by using 10 distinct digits ?

  • 108

  • 610

  • 10C6

  • 10P6

Solution:

NA

Q6.

The number of ways of arranging 6 boys and 4 girls in a row so that all 4 girls are together is :

  • 6!. 4!

  • 2(7!. 4!)

  • 7!. 4!

  • 2(6!. 4!)

Solution:

NA

Q7.

How many numbers not exceeding 1000 can be made from the digits 1, 2, 3, 4, 5, 6, 7, 8, 9 if  repetition is not allowed . 

  • 364

  • 585

  • 728

  • 819

Solution:

NA

Q8.

The letter of the word "VIOLENT" are arranged so that the vowels occupy even place only. The number of permutations is ________ . 

  • 144

  • 120

  • 34

  • 75

Solution:

NA

Q9.

\(^{13}C_6 + 2 ^{13}C_5 + ^{13}C_4 = ^{15}C_x\) then, x = _____________ . 

  • 6

  • 7

  • 8

  • 9

Solution:

NA

Q10.

A polygon has 44 diagonals then the number of its sides are :

  • 8

  • 11

  • 10

  • 9

Solution:

NA

Q11.

If \(^{15}C_{3r} = ^{15}C_{r + 3}\) , then 'r' is equal is 

  • 2

  • 3

  • 4

  • 5

Solution:

NA

Q12.

In how many ways can a family consist of three children here different birthdays in a leap year . 

  • \(^{365}C_{3}\)

  • \(^{365}C_{3} - 3\)

  • 366 x 365 x 364

  • \(^{366}C_{3}\)

Solution:

NA

Q13.

If six times the number of permutations of 'n' items taken 3 at a time is equal to seven times the number of permutation of (n - 1) itens taken 3 at a time, then the value of 'n' will be : 

  • 7

  • 9

  • 13

  • 21

Solution:

NA

Q14.

An examination paper wih 10 questions consists of 6 questions in mathematics and 4 questions in statistics part. At least one question from each part is to be attempted in how many ways can this be done:

  • 1239

  • 450

  • 945

  • 86

Solution:

NA

Q15.

npr = 720,    ncr = 120, then find the value of r:

  • 1

  • 2

  • 3

  • 4

Solution:

NA

Q16.

There are 10 students in a class including 3 girls. the number of ways to arrange them in a row when any two girls out of three never comes together:

  • 8p3 . 7!

  • 10p3 . 10!

  • 324

  • 9!

Solution:

NA

Q17.

There are five flags of different colours. How many different signals can be generated by hoisting the flags on a vertical pole(one below the other), if each signal requires the use of two flags ?

  • 20

  • 10

  • 30

  • 4

Solution:

NA

Q18.

Find the total number of ways of answering 5 multiple choice questions, each question having four choices:

  • 64

  • 45

  • 216

  • 54

Solution:

NA

Q19.

How many different numbers of seven digits divisible by 10 can be formed by using the digits 1, 2, 0, 1, 2, 2, 5 ?

  • 65

  • 50

  • 70

  • 60

Solution:

NA

Q20.

How many different numbers each of six digits can be formed by using the digits 1, 2, 1, 2, 0, 2 ? 

  • 45

  • 50

  • 55

  • 70

Solution:

NA