JEE Questions for Maths Permutations And Combinations Quiz 2 - MCQExams.com

The value of 50C4 +
Maths-Permutations and Combinations-43484.png
  • 56C4
  • 56C3
  • 55C3
  • 55C4
A father with 8 children takes 3 at a time to the zoological garden, as often as he can without taking the same 3 children together more than once. The number of times he will go to the garden, is
  • 112
  • 56
  • 336
  • None of these
Number of divisors of the form (4n + 2), n ≥ 0 of the integer 240 is
  • 4
  • 8
  • 10
  • 3
There are 5 wads leading to a town from a village. the number of different ways in which a villager can go to the town and return back, is
  • 20
  • 25
  • 5
  • 10
The number of ways in which one can select three distinct integers between 1 and 30, both inclusive, whose sum is even, is
  • 455
  • 1575
  • 1120
  • 2030
  • 1930
If P(n ,r)=1680 and C(n , r) = 70 , then 69n + r! is equal to
  • 128
  • 576
  • 256
  • 625
  • 1152
In a club election, the number of contestants is one more than the number of maximum candidates for which a voter can vote. If the total number of ways in which a voter can vote is 126, then the number of contestants is
  • 4
  • 5
  • 6
  • 7
A three-digit number n is such that the last two digits of it are equal and differ from the first. The number of such n's is
  • 64
  • 72
  • 81
  • 900
In how many ways, can 21 English and 19 Hindi books be placed in a row so that no two Hindi books are together?
  • 1540
  • 1450
  • 1504
  • 1405
Out of thirty points in a plane, eight of them are col linear. The number of straight lines that can be formed by joining these points, is
  • 296
  • 540
  • 408
  • 348
There are 10 points in a plane, out of these 6 are collinear. If N is the number of triangles formed by joining these points, then
  • N >190
  • N ≤ 100
  • 100 < N ≤ 140
  • 140 ≤ N ≤ 190
Three straight lines L1, L2 and 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 L2. The maximum number of triangles formed with vertices at these points are
  • m+n+kC3
  • m+n+kC3 - mC3 - nC3
  • m+n+kC3 + mC3 + nC3
  • None of the above
Out of 8 given points, 3 are collinear. How many different straight lines can be drawn by joining any two points from those 8 points?
  • 26
  • 28
  • 27
  • 25
The number of diagonals in a octagon will be
  • 28
  • 20
  • 10
  • 16
There is a set of in parallel lines intersecting a set of another n parallel lines in a plane. The number of parallelograms formed, is
  • m-1C2 . n-1C2
  • mC2 . nC2
  • m-1C2. nC2
  • mC2 .n-1C2
If a polygon of n sides has 275 diagonals, then n is equal to
  • 25
  • 35
  • 20
  • 15
The number of triangles which can be formed by using the vertices of a regular polygon of (n +sides is 220. Then, n is equal to
  • 8
  • 9
  • 10
  • 11
  • 12
Let Tn denote the number of triangles which can be formed using the vertices of a regular polygon of n sides. If Tn+1 - Tn = 21, then n equals
  • 5
  • 7
  • 6
  • 4

Maths-Permutations and Combinations-43505.png
  • 3
  • 2
  • 1
  • 0
  • 4
If 2n+1pn-1 : 2n-1pn = 3 : 5, then the value of n is
  • 4
  • 3
  • 2
  • 1
  • 5
Eight different letters of an alphabet are given. Words of four letters from these are formed. The number of such words with at least one letter repeated, is
  • (8/– 8P4
  • 8 4 + (8/4)
  • 8 4 – 8P4
  • 8 4 – (8/4)
A box contains 2 white balls, 3 black balls and 4 red balls. In how many ways can 3 balls be drawn from the box, if atleast one black ball is to be included in the draw?
  • 64
  • 24
  • 3
  • 12
Let an, denotes the number of all n-digit positive integers formed by the digits 0, 1 or both such that no consecutive digits in them are 0. Let bn = the number of such n-digit integers ending with digit 1 and cn = the number of such n-digit integers ending with digit 0.
Which of the following is correct?
  • a17 = a16 + a15
  • c17 ≠ c16 + c15
  • b17 ≠ b16 + c16
  • a17 = c17 + b16
Let an, denotes the number of all n-digit positive integers formed by the digits 0, 1 or both such that no consecutive digits in them are 0. Let bn = the number of such n-digit integers ending with digit 1 and cn = the number of such n-digit integers ending with digit 0.
The value of b6 is
  • 7
  • 8
  • 9
  • 11
There are two urns. Urn A has 3 distinct red balls and urn B has 9 distinct blue balls. From each urn two balls are taken out at random and then transferred to the other. The number of ways in which this can be done, is
  • 3
  • 36
  • 66
  • 108
From 12 books, the difference between number of ways a selection of 5 books when one specified book is always excluded and one specified book is always included, is
  • 64
  • 118
  • 132
  • 330
  • 462
If n –1C3 + n –1C4 > nC3 , then n is just greater than
  • 5
  • 6
  • 4
  • 7
In a cricket championship, there are 36 matches. The number of teams, if each plays 1 match with other are
  • 9
  • 10
  • 8
  • 12
If n+2C8 : n –2P4 = 57/16, then n is equal to
  • 19
  • 2
  • 20
  • 5
Four dice are rolled. The number of possible outcomes in which atleast one dice shows 2 is
  • 625
  • 671
  • 1023
  • 1296
7 relatives of a man comprises 4 ladies and 3 gentlemen.His wife has also 7 relatives, 3 of them are ladies and 4 gentlemen. In how many ways, can they invite a dinner party of 3 ladies and 3 gentlemen so that there are 3 of man's relative and 3 of the wife's relative?
  • 485
  • 500
  • 486
  • 102
How many different words can be formed by jumbling the letters in the word 'MISSISSIPPI' in which no two S are adjacent?
  • 7 . 6C4 . 8C4
  • 8. 6C4 . 7C4`
  • 6 .7 . 8C4
  • 6 .8. 7C4
All possible two factors products are formed from numbers 1, 2, 3, 4, ..., 200. The number of factors out of the total obtained which are multiples of 5, is
  • 5040
  • 7180
  • 8150
  • None of these
If 189C35 + 189Cχ = 190Cχ, then χ is equal to
  • 34
  • 35
  • 36
  • 37
The number of selecting atleast 4 candidates from 8 candidates is
  • 270
  • 70
  • 163
  • None of these
There arc 5 letters and 5 different envelopes. The number of ways in which all the letters can be put in wrong envelope, is
  • 119
  • 44
  • 59
  • 40
There are 10 lamps in a hall. Each one of them can be switched on independently. The number of ways in which the hall can be illuminated, is
  • 210
  • 10!
  • 1023
  • 102
At an election, a voter may vote for any number of candidates not greater than the number to be elected. 'fhere are 10 candidates and 4 are to he elected. If a voter votes for atleast one candidate, then the number of ways in which he can vote, is
  • 6210
  • 385
  • 1110
  • 5040
Consider the set of eight vectors
Maths-Permutations and Combinations-43526.png
  • 5
  • 4
  • 1
  • 3

Maths-Permutations and Combinations-43528.png
  • n/2
  • n/2 - 1
  • n - 1

  • Maths-Permutations and Combinations-43529.png
Let p be a prime number such that p ≥ 23. Let x = p! + 1. The number of primes in the list n +1, n + 2, n + 3,...., n + p – 1 is
  • p – 1
  • 2
  • 1
  • none of these
In a room there are 12 bulbs of the same wattage, each having a separate switch. The number of ways to light the room with different amount of illumination is
  • 122 – 1
  • 212
  • 212 – 1
  • none of these
The number of proper divisors of 2p.6q.15r is
  • (p + q +(q + r +(r + 1)
  • (p + q +(q + r +(r +– 2
  • (p + q) (q + r) r – 2
  • none of these
The number of even proper divisors of 1008 is
  • 23
  • 21
  • 20
  • none of these
If one test (on screening paper basis) was conducted on Batch A, maximum number of marks is (90 ×= 270. 4 students get the marks lower than 80. Coaching institute decided to inform their guardians, that is why their result card were sent to their home. The number of ways, in which all the letters were put in wrong envelopes, is
  • 8
  • 9
  • 10
  • none of these
The number of prime numbers among the numbers 105! + 2, 105! + 3, 105! + 4,...105! + 104 and 105! + 105 is
  • 31
  • 32
  • 33
  • none of these
If eleven members of a committee sit at a round table so that the President and Secretary always sit together, then the number of arrangement is
  • 10! × 2
  • 10!
  • 9! × 2
  • None of these
The number of ways in which 6 men and 5 women can dine at a round table if no two women are to sit together is given by
  • 6! × 5!
  • 30
  • 5! × 4!
  • 7! × 5!
The number of ways four boys can be seated around a round-table in four chairs of different colours is
  • 24
  • 12
  • 23
  • 64
The number of circular permutations of n different objects is
  • n!
  • n
  • (n – 2)!
  • (n – 1)!
0:0:1


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