# Topic: Chapter 4: Combinatorics and Mathematical Induction (Test 1)

Topic: Chapter 4: Combinatorics and Mathematical Induction
Q.1
The sum of the digits at the 10th place of all numbers formed with the help of 2, 4, 5, 7 taken all at a time is
A. 432
B. 108
C. 36
D. 18
Answer : Option B
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Q.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
A. 125
B. 124
C. 64
D. 63
Answer : Option B
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Q.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
A. 304 x 292
B. 303 x 293
C. 302 x 294
D. 30 x 295
Answer : Option A
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Q.4
The number of 5 digit numbers all digits of which are odd is
A. 25
B. 55
C. 56
D. 625
Answer : Option B
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Q.5
In 3 fingers, the number of ways four rings can be worn is ………..ways.
A. 43 - 1
B. 34
C. 68
D. 64
Answer : Option D
Explaination / Solution:

4 rings can be worn in 3 fingers in 3ways
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Q.6
If (n+5)P(n+1) = ( 11(n-1) /2 )(n+3)Pn, then the value of n are
A. 7 and 11
B. 6 and 7
C. 2 and 11
D. 2 and 6
Answer : Option B
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Q.7
The product of r consecutive positive integers is divisible by
A.  r!
B. (r - 1)!
C. (r + 1)!
D. rr
Answer : Option A
Explaination / Solution:

Product of r consecutive positive integers is divisible by r! (theorem)
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Q.8
The number of five digit telephone numbers having at least one of their digits repeated is
A. 90000
B. 10000
C. 30240
D. 69760
Answer : Option D
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Q.9
If a2-aC2 = a2-a C4 then the value of ’a’ is
A. 2
B. 3
C. 4
D. 5
Answer : Option B
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Q.10
There are 10 points in a plane and 4 of them are collinear. The number of straight lines joining any two points is
A. 45
B. 40
C. 39
D. 38
Answer : Option B
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