Mg. A- R.1
2) A tea party is arranged for 16 persons along two sides of a long table with 8 chairs on each side. 4 persons wish to sit on one particular side and two on the other side. In how many ways can they be seated ?
3) A business man hosts a dinner to 21 guests. He is having 2 round tables which can accommodate 15 and 6 persons each. In how many ways can he arrange the guests ?
4) Find the number of a combinations and permutations of 4 letters taken from the word EXAMINATION.
5) Find the number of ways in which:
A) a selection
B) an arrangement of,
4 letters can be made from the letters of the word PROPORTION.
6) How many words can be formed by taking 4 letters at the time from the letters of the word MORADABAD ?
7) How many words each of 3 vowels and 2 consonants can be formed from the letters of the word INVOLUTE.
8) Find the number of permutations of n different things taken r at a time such that two specified things occur together?
9) ²⁰Cᵣ = ²⁰Cᵣ₋₁₀, then ¹⁸Cᵣ is equal to
A) 4896 B) 816 C) 1632 D) none
10) ²⁰Cᵣ= ²⁰Cᵣ₊₄ , then ʳC₃ is equal to
A) 54 B) 56 C) 58 D) none
11) ¹⁵C₃ᵣ = ¹⁵Cᵣ₊₃ , then r is equal to
A) 5 B) 4 C) 3 D) 2
12) ²⁰Cᵣ₊₁ = ²⁰Cᵣ₋₁ , then r is equal to
A) 10 B) 11 C) 19 D) 12
13) If C(n, 12)= C(n, 8), then C(22, n) is equal to
A) 231 B) 210 C) 252 D) 303
14) If ᵐC₁ = ⁿC₂ , then
A) 2m=n B) 2m=n(n+1) C) 2m=n(n -1) D) 2n =m(m -1)
15) ⁿC₁₂ = ⁿC₈ , then n=
A) 20 B) 12 C) 6 D) 30
16) ⁿCᵣ + ⁿCᵣ₊₁ =ⁿ⁺¹Cₓ , then x is
A) r B) r-1 C) n D) r+1
17) If (a²- a) C 2 = (a² - a) C 4, then a is
A) 2 B) 3 C) 4 D) none
18) ⁵C₁ + ⁵C₂ + ⁵C₃ + ⁵C₄ + ⁵C₅ is equal
A) 30 B) 31 C) 32 D) 33
19) Total number of words found by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants is equals to
A) 60 B) 120 C) 7200 D) none
20) There are 12 points in a plane. The number of the straight lines joining any two of them when 3 of them are collinear, is
A) 62 B) 63 C) 64 D) 65
Mg. A- R.2
1) 3 person entre Railway compartment. If there are 5 seats vacant, in how many ways can they take these seats?
A) 60 B) 20 C) 15 D) 125
2) In how many ways can a committee of 5 be made out of 6 men and 4 Women containing at least one woman ?
A) 246 B) 222 C) 186 D) none of these
3) There are 10 points in a plane and 4 of them are collinear. The number of straight line joining any two of them is.
A) 45 B) 40 C) 39 D) 38
4) There are 13 players of cricket, out of which 4 are bowlers. In how many ways a team of 11 be selected from them so as to included least two bowlers?
A) 72 B) 78 C) 42 D) none of these
5) If C₀ + C₁ + C₂ +....+ Cₙ = 256, then ²ⁿC₂ is
A) 56 B)120 C) 28 D) 91
6) The number of ways in which a host lady can invite for a party of 8 out of 12 people of whom two do not want to attend the party together is
A) 2. ¹¹C₇ + ¹⁰C₈ B) ¹⁰C₈ + ¹¹C₇ C) ¹²C₈ - ¹⁰C₆ D) none
7) Given 11 points, of which 5 lie on one circle, other than these 5, no 4 lie on one circle. Then the number of circles that can be drawn so that each contains at least 3 of the given points is
A) 216 B)156 C) 172 D) none of these
8) How many different committee of 5 can be formed from 6 men and 4 women on which exact 3 men and 2 women serve?
A) 6 B) 20 C) 60 D) 120
9) If ⁴³Cᵣ₋₆ = ⁴³C₃ᵣ₊₁ , then the value of r is
A) 12 B) 8 C) 6 D) 10 E) 14
10) The number of diagonals that can be drawn by joining the vertices of an octogon is
A) 20 B) 28 C) 8 D) 16
11) The value of (⁷C₀ + ⁷C₁)+(⁷C₁+ ⁷C₂) + ......+ (⁷C₆ + ⁷C₇) is
A) 2⁷- 1 B) 2⁸-2 C) 2⁸ -1 D) 2⁸
12) Among 14 players, 5 are bowlers, In how many ways a team of 11 may be formed with at least four bowlers ?
A) 265 B) 263 C) 264 D) 275
13) A lady gives a dinner party for 6 guests, The number of ways in which they may be selected from among 10 friends if two of the friends will not attend the party together is
A) 112 B) 140 C) 164 D) none
14) If ⁿ⁺¹C₃ = 2.ⁿC₂ , then n=
A) 3 B) 4 C) 5 D) 6
15) The number of parallelogram that can be formed from a set of four Parallel Lines intersecting another set of 3 Parallel Lines is
A) 6 B) 9 C) 12 D) 18
16) How many four letter words can be formed using the letters of the word ROAMING
a) 420 b) 210 c) 840 d) 480 e) 620
17) How many three letter words can be formed using the letters of the word PRACTICES?
a) 157 b) 257 c) 357 d) 457 e) 557
18) In a party, each person shook hands with
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