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MATHS M.C.Q (1 Marks)

PART - 1 CH - 6 Permutations and Combinations · Rajasthan Board (RBSE) STD 11 Science (Rajasthan - English Medium). 25 questions.

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M.C.Q (1 Marks)

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25 questions · timed · auto-graded

MCQ 11 Mark
If ${ }^n C _r$, represents the number of combinations of $n$ objects by taking $r$ objects together, then the expression ${ }^n C _{r+1}+{ }^n C _{r-1}+2 \times{ }^n C _r$ is equal to :
  • A
    ${ }^{n+2} C _r$
  • ✓
    ${ }^{n+2} C _{r+1}$
  • C
    ${ }^{n+1} C _r$
  • D
    ${ }^{n+1} C _{r+1}$
Answer
Correct option: B.
${ }^{n+2} C _{r+1}$
(B)
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MCQ 21 Mark
There are 4 points on the circumference of a circle, how many triangles can be formed by combining them :
  • ✓
    4
  • B
    6
  • C
    8
  • D
    12
Answer
Correct option: A.
4
(A)
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MCQ 31 Mark
${ }^n P _r \div{ }^n C _r$ is equal to :
  • A
    $n~!$
  • B
    $(n-r)$ !
  • C
    $\frac{1}{r!}$
  • ✓
    $r$ !
Answer
Correct option: D.
$r$ !
(D)
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MCQ 41 Mark
If ${ }^{n-1} C _3+{ }^{n-1} C _4>{ }^n C _3$ then the value of $x$ is:
  • A
    $7$
  • B
    $<7$
  • ✓
    $>7$
  • D
    None of these
Answer
Correct option: C.
$>7$
(C )
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MCQ 51 Mark
The number of ways in which 3 men and 2 men can sit on a bus, while the number of men and women sitting each side in 3 , will be :
  • A
    $5 !$
  • ✓
    ${ }^6 C _5 \times 5$ !
  • C
    $6!\times{ }^6 C _5$
  • D
    $5!+{ }^6 C _5$
Answer
Correct option: B.
${ }^6 C _5 \times 5$ !
(B)
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MCQ 71 Mark
If ${ }^{18} C _{ r }={ }^{18} C _{ r +2}$, then the value of ${ }^{ r } C _5$ is :
  • A
    66
  • ✓
    56
  • C
    46
  • D
    64
Answer
Correct option: B.
56
(B)
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MCQ 81 Mark
How many words will be formed from the letters of the word INDIA?
  • A
    50
  • ✓
    60
  • C
    40
  • D
    80
Answer
Correct option: B.
60
(B)
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MCQ 91 Mark
In how many ways can the letters of the word PENCIL be arranged, if N always comes after E?
  • A
    420
  • B
    720
  • ✓
    120
  • D
    520
Answer
Correct option: C.
120
(C )
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MCQ 101 Mark
In the word COMBINE, the number of permutations keeping the vowels at odd places and taking all the letters is :
  • A
    96
  • B
    144
  • C
    512
  • ✓
    576
Answer
Correct option: D.
576
(D)
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MCQ 131 Mark
The value of $n!$ is :
  • ✓
    $n \times n-1$ !
  • B
    $(n-1) \times n$ !
  • C
    $n(n-1)$ !
  • D
    None of these
Answer
Correct option: A.
$n \times n-1$ !
(A)
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MCQ 141 Mark
An organization requires one man and one woman. If 10 women and 15 men apply, then in how many ways be selection be made?
  • A
    125
  • ✓
    150
  • C
    145
  • D
    180
Answer
Correct option: B.
150
(B)
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MCQ 151 Mark
There are 16 vacant posts of clerks in an office. In how many ways can there be filled out of 20 applicants?
  • A
    13800
  • B
    969
  • C
    13876
  • ✓
    4845
Answer
Correct option: D.
4845
(D)
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MCQ 161 Mark
How many words can be made from the letter of EXAMINATION?
  • A
    $\frac{9!}{2!2!2!}$
  • ✓
    $\frac{11!}{2!2!2!}$
  • C
    $\frac{11!}{2!2!}$
  • D
    None of these
Answer
Correct option: B.
$\frac{11!}{2!2!2!}$
(B)
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MCQ 171 Mark
How many words can be made from the letters of the word GARDEN so that the vowels are in alphabetical order?
  • ✓
    360
  • B
    240
  • C
    120
  • D
    480
Answer
Correct option: A.
360
(A)
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MCQ 191 Mark
There are 6 points on the circumference of a circle, the number of straight lines joining them will be :
  • A
    30
  • ✓
    15
  • C
    12
  • D
    20
Answer
Correct option: B.
15
(B)
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MCQ 211 Mark
${ }^{61} C _{57}-{ }^{60} C _{56}$ is equal to :
  • A
    ${ }^{61} C _{58}$
  • ✓
    ${ }^{60} C _{57}$
  • C
    ${ }^{60} C _{58}$
  • D
    ${ }^{60} C _{56}$
Answer
Correct option: B.
${ }^{60} C _{57}$
(B)
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MCQ 221 Mark
${ }^{47} C _4+\sum_{r=1}^5{ }^{52-r} C _3$ is equal to :
  • A
    ${ }^{51} C _4$
  • ✓
    ${ }^{52} C _4$
  • C
    ${ }^{53} C _4$
  • D
    None of these
Answer
Correct option: B.
${ }^{52} C _4$
(B)
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MCQ 231 Mark
How many words can be made from the letters of BHILWARA?
  • ✓
    $\frac{8!}{2!}$
  • B
    $8$ !
  • C
    $7$ !
  • D
    $\frac{6!}{2!}$
Answer
Correct option: A.
$\frac{8!}{2!}$
(A)
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M.C.Q (1 Marks) - MATHS STD 11 Science Questions - Vidyadip