Multiple choice questions with answers / choose the correct answer with answers - Maths Book back 1 mark questions and answers with solution for Exercise Problems - Mathematics : Combinatorics and Mathematical Induction

**CHAPTER
: Combinatorics and Mathematical Induction**

**Choose
the correct or the most suitable answer**

1. The sum of the digits at the 10^{th}
place of all numbers formed with the help of 2, 4, 5, 7 taken all at a time is

(1) 432

**(2)
108 **

(3) 36

(4) 18

*Solution*

2. In an examination there are three
multiple choice questions and each question has 5 choices .

Number of ways in which a student can
fail to get all answer correct is

(1) 125

**(2)
124 **

(3) 64

(4) 63

*Solution*

3. The number of ways in which the
following prize be given to a class of 30 boys first and second in mathematics,
first and second in physics, first in chemistry and first in English is

**(1)
30 ^{4} x 29^{2} **

(2) 30^{3} x 29^{3}

(3) 30^{2} x 29^{4}

(4) 30 x 29^{5}.

*Solution*

4. The number of 5 digit numbers all
digits of which are odd is

(1) 25

**(2)
5 ^{5} **

(3) 5^{6}

(4) 625.

*Solution*

5. In 3 fingers, the number of ways four
rings can be worn is ………..ways.

(1) 4^{3} - 1

(2) 3^{4}

(3) 68

**(4)
64**

*Solution*

4 rings can be worn in 3 fingers in 34 ways

6. If ^{(n+5)}P_{(n+1)}
= ( 11(n-1) /2 )^{(n+3)}P_{n},
then the value of n are

(1) 7 and 11

**(2)
6 and 7 **

(3) 2 and 11

(4) 2 and 6.

*Solution*

7. The product of r consecutive positive
integers is divisible by

**(1)
r! **

(2) (r - 1)!

(3) (r + 1)!

(4) r^{r}.

*Solution*

Product of *r* consecutive positive integers is divisible by r! (theorem)

8. The number of five digit telephone
numbers having at least one of their digits repeated is

(1) 90000

(2) 10000

(3) 30240

**(4)
69760.**

*Solution*

9. If a^{2}-^{a}C_{2} = ^{a2}-^{a} C_{4}
then the value of ’a’ is

(1) 2

**(2)
3 **

(3) 4

(4) 5

*Solution*

10. There are 10 points in a plane and 4
of them are collinear. The number of straight lines joining any two points is

(1) 45

**(2)
40 **

(3) 39

(4) 38.

*Solution*

11. The number of ways in which a host
lady invite 8 people for a party of 8 out of 12 people of whom two do not want
to attend the party together is

(1) 2 x^{11}C_{7} +^{10}C_{8}

(2) ^{11}C_{7} +^{10}C_{8}

**(3)
^{12}C_{8} **

(4) ^{10}C_{6} + 2!.

*Solution*

12. The number of parallelograms that
can be formed from a set of four parallel lines intersecting another set of
three parallel lines.

(1) 6

(2) 9

(3) 12

**(4)
18**

*Solution*

13. Everybody in a room shakes hands
with everybody else. The total number of shake hands is 66. The number of
persons in the room is

(1) 11

**(2)
12 **

(3) 10

(4) 6

*Solution*

14. Number of sides of a polygon having
44 diagonals is

(1) 4

(2) 4!

**(3)
11 **

(4) 22

*Solution*

15. If 10 lines are drawn in a plane
such that no two of them are parallel and no three are concurrent, then the
total number of points of intersection are

**(1)
45 **

(2) 40

(3)10!

(4) 2^{10}

*Solution*^{}

16. In a plane there are 10 points are
there out of which 4 points are collinear, then the number of triangles formed
is

(1) 110

(2) ^{10}C_{3}

(3) 120

**(4)
116**

*Solution*

17. In ^{2n}C_{3} :^{n}
C_{3} = 11 : 1 then n is

(1) 5

**(2)
6 **

(3)11

(4)7

*Solution*

18. ^{(n}^{-}^{1)}C_{r} +^{(n}^{-}^{1)} C_{(r}_{-}_{1)} is

(1) ^{(n+1)}C_{r}

(2) ^{(n}^{-}^{1)}C_{r}

**(3)
^{n}C_{r} **

(4)^{n}C_{r}_{-}_{1}.

*Solution*

19. The number of ways of choosing 5
cards out of a deck of 52 cards which include at least one king is

(1) ^{52}C_{5}

(2) ^{48}C_{5}

(3)^{52}C_{5} +^{48}
C_{5}

**(4) ^{52}C_{5}
**

*Solution*

20. The number of rectangles that a
chessboard has………..

(1) 81

(2) 9^{9}

**(3)1296
**

(4) 6561

*Solution*

21. The number of 10 digit number that
can be written by using the digits 2 and 3 is

(1) ^{10}C_{2} + ^{9}C_{2}

**(2)
2 ^{10} **

(3)2^{10} - 2

(4) 10!

*Solution*

22. If P_{r} stands for ^{r}P_{r}
then the sum of the series 1 + P_{1} + 2P_{2} + 3P_{3}
+……….+ nP_{n} is

(1) P_{n+1}

**(2)
P _{n+1} **

(3) P_{n}_{-}_{1} + 1

(4)^{(n+1)}P_{(n}_{-}_{1)}

_{}

*Solution*_{}

23. The product of first n odd natural
numbers equals

(1) ^{2n}C_{n} x ^{n}P_{n}

**(2)
(1/2 ) ^{n} x^{2n}C_{n} xn P_{n} **

(3) (1/4 )^{n }x ^{2n}C_{n
}x ^{2n} P_{n}

(4)^{n}C_{n} x ^{n}P_{n}

_{}

*Solution*_{}

24. If ^{n}C_{4}, ^{n}C_{5},
^{n}C_{6} are in AP the value of n can be

**(1)
14 **

(2) 11

(3)9

(4)5

*Solution*

25. 1 + 3 + 5 + 7 +……….+ 17 is equal to

(1) 101

**(2)
81 **

(3) 71

(4) 61

*Solution*

Tags : Combinatorics and Mathematical Induction | Mathematics , 11th Mathematics : UNIT 4 : Combinatorics and Mathematical Induction

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11th Mathematics : UNIT 4 : Combinatorics and Mathematical Induction : Exercise 4.5: Choose the correct or the most suitable answer | Combinatorics and Mathematical Induction | Mathematics

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