## Permutation and Combination Quiz-10

As per analysis for previous years, it has been observed that students preparing for JEE MAINS find Mathematics out of all the sections to be complex to handle and the majority of them are not able to comprehend the reason behind it. This problem arises especially because these aspirants appearing for the examination are more inclined to have a keen interest in Mathematics due to their ENGINEERING background.

Furthermore, sections such as Mathematics are dominantly based on theories, laws, numerical in comparison to a section of Engineering which is more of fact-based, Physics, and includes substantial explanations. By using the table given below, you easily and directly access to the topics and respective links of MCQs. Moreover, to make learning smooth and efficient, all the questions come with their supportive solutions to make utilization of time even more productive. Students will be covered for all their studies as the topics are available from basics to even the most advanced.

Q1.The number of numbers of 4 digits which are not divisible by 5, are
•  7200
•  3600
•  14400
•  1800
Solution

(a) Total number of four digit numbers =9×10×10×10 =9000
Total number of four digit numbers which divisible by 5 =9×10×10×2=1800
∴ Required number of ways =9000-1800=7200
Q2.The number of ways in which n ties can be selected from a rack displaying 3 n different ties is
•  (3n !)/(2n !)
•  3×n !
•  (3n) !
•  (3n !)/(n !2n !)
Solution
(d) Required number of ways = 3n Cn=(3n !)/(n ! 2n !)

Q3.  How many even numbers of 3 different digits can be formed from the digits 1, 2, 3, 4, 5, 6, 7, 8, 9
(repetition of digits is not allowed)?
•  224
•  280
•  324
•  None of these
Solution
(a) The number will be even if last digit is either 2, 4, 6 or 8 ie the last digit can be filled in 4 ways and remaining two digits can be filled in 8P2 ways.
Hence, required number of number of three different digits = 8P2×4=224
Q5.Three straight lines L1,L2,L3 are parallel and lie in the same plane. A total of m points are taken on
L1,n points on L2,k points on L3. The maximum number of triangles formed with vertices at these points are
•  m+n+kC3
•  m+n+kC3-mC3-nC3-kC3
•  m+n+kC3+mC3+nC3
•  None of these
Solution
(b) Total number of points on a three lines are m+n+k
∴ maximum number of triangles = m+n+kC3-mC3-nC3-kC3 (subtract those triangles in which point on the same line)

Q5.If r>p>q, the number of different selections of p+q thing taking r at a time, where p things are identical
and q other things are identical, is
•  p+q-r
•  p+q-r+1
•  r-p-q+1
•  None of these
Solution

Q6.Let 1, 2, 3, 4 are four numbers. How many numbers can be made using all four numbers?
•  1
•  3
• 2
•  64
Solution
(d) Given four numbers 1, 2, 3 and 4 Number of numbers of one digit=4P1=4
Number of numbers of three digit numbers=4P3=24
Number of numbers of three digit numbers=4P1=24
And four digit numbers=4P4=24
∴ Total number of numbers that can be formed =4+12+24+24=64

Q7.A polygon has 170 diagonals. How many sides will it have?
•  12
•  17
•  20
•  25
Solution
(c) 20

Q8.If (n-1) C6+ (n-1) C7> (n-1) C6, then
•  n>4
•  n>12
•  n≥13
•  n>13
Solution

Q9.The number of diagonals in a octagon will be
•  28
•  20
•  10
•  16
Solution
(b) In a octagon there are eight sides and eight points
∴ Required number of diagonals =8C2-8=28-8=20

Q10. If a,b,c,d,e are prime integers, then the number of divisors of ab2 c2 de excluding 1 as a factor is
•  94
•  72
•  36
• 71
Solution
(d) The number of divisors of ab2 c2 de =(1+1)(2+1)(2+1)(1+1)(1+1)-1 =2.3.3.2.2.-1=71

#### Written by: AUTHORNAME

AUTHORDESCRIPTION

## Want to know more

Please fill in the details below:

## Latest NEET Articles\$type=three\$c=3\$author=hide\$comment=hide\$rm=hide\$date=hide\$snippet=hide

Name

ltr
item
BEST NEET COACHING CENTER | BEST IIT JEE COACHING INSTITUTE | BEST NEET & IIT JEE COACHING: Permutation-and-combination-quiz-10
Permutation-and-combination-quiz-10