BITSAT SERIES Mathematics
Permutations And Combinations
38 previous year questions.
Volume: 38 Ques
Yield: High
High-Yield Trend
1
2026 1
2025 1
2023 3
2021 5
2020 2
2019 1
2018 3
2017 5
2016 2
2015 4
2014 3
2013 2
2012 2
2011 2
2010 Chapter Questions 38 MCQs
01
PYQ 2009
medium
mathematics ID: bitsat-2
If A=1,2,3,4,5 then the number of proper subsets of A is:
1
31
2
38
3
48
4
54
02
PYQ 2010
medium
mathematics ID: bitsat-2
In a polygon no three diagonals are concurrent. If the total number of points of intersection of diagonals interior to the polygon be 70, then the number of diagonals of the polygon is
1
20
2
28
3
8
4
None of these
03
PYQ 2010
medium
mathematics ID: bitsat-2
With 17 consonants and 5 vowels, the number of words of four letters that can be formed having two different vowels in the middle and one consonant, repeated or different at each end is
1
5780
2
2890
3
5440
4
2720
04
PYQ 2011
medium
mathematics ID: bitsat-2
If ²⁰Cᵣ = ²⁰Cᵣ-₁₀, then ¹⁵Cᵣ is equal to:
1
4896
2
816
3
1632
4
None of these
05
PYQ 2011
medium
mathematics ID: bitsat-2
The term independent of x in the expansion of (9x - 13√(x))¹8, x>0, is a times the corresponding binomial coefficient. Then a is:
1
3
2
(1)/(3)
3
−(1)/(3)
4
None of these
06
PYQ 2012
medium
mathematics ID: bitsat-2
In how many ways can 5 prizes be distributed among 4 boys when every boy can take one or more prizes?
1
1024
2
625
3
120
4
600
07
PYQ 2012
medium
mathematics ID: bitsat-2
The coefficient of in the expansion of is:
1
2
3
1
4
None of these
08
PYQ 2013
medium
mathematics ID: bitsat-2
In how many ways can 5 boys and 5 girls be seated at a round table so that no two girls may be together?
1
2
3
4
09
PYQ 2013
medium
mathematics ID: bitsat-2
A box contains two white balls, three black balls and four red balls. In how many ways can three balls be drawn from the box if at least one black ball is to be included in the draw?
1
84
2
60
3
129
4
114
10
PYQ 2013
medium
mathematics ID: bitsat-2
If denote the binomial coefficients in the expansion of , then the value of is
1
2
3
4
11
PYQ 2014
medium
mathematics ID: bitsat-2
The coefficient of in the expansion of is:
1
440
2
770
3
990
4
1001
12
PYQ 2014
medium
mathematics ID: bitsat-2
The number of all three element subsets of the set which contain is:
1
2
3
4
None of these
13
PYQ 2014
medium
mathematics ID: bitsat-2
In how many ways can a committee of 5 be formed out of 6 men and 4 women containing at least one woman?
1
246
2
222
3
186
4
None of these
14
PYQ 2014
medium
mathematics ID: bitsat-2
If represent the terms in the expansion of
, then
1
2
3
4
15
PYQ 2015
medium
mathematics ID: bitsat-2
If binomial coefficients of three consecutive terms of are in H.P., then the maximum value of is
1
2
3
4
None of these
16
PYQ 2015
medium
mathematics ID: bitsat-2
The total number of 4-digit numbers in which the digits are in descending order is
1
2
3
4
None of these
17
PYQ 2016
medium
mathematics ID: bitsat-2
If the sum of odd numbered terms and even numbered terms in the expansion of (x+a)ⁿ are A and B respectively, then the value of (x²-a²)ⁿ is
1
2
3
4
None
18
PYQ 2016
medium
mathematics ID: bitsat-2
All the words that can be formed using alphabets A, H, L, U and R are written in a dictionary (no alphabet is repeated). Rank of the word RAHUL is
1
71
2
72
3
73
4
74
19
PYQ 2016
medium
mathematics ID: bitsat-2
The number of values of r satisfying
³9C₃r-1=³9Cᵣ²-1=³9C₃r is
1
1
2
2
3
3
4
4
20
PYQ 2016
medium
mathematics ID: bitsat-2
If
sumᵣ=0ⁿ+2ⁿCᵣ=2⁸-1,
then n=
1
8
2
4
3
6
4
5
21
PYQ 2016
medium
mathematics ID: bitsat-2
If the third term in the expansion of
is , then may be
is , then may be
1
1
2
3
10
4
10⁻2/5
22
PYQ 2017
medium
mathematics ID: bitsat-2
If , then is equal to
1
0
2
1
3
2
4
None of these
23
PYQ 2017
medium
mathematics ID: bitsat-2
How many different nine digit numbers can be formed from the number 223355888 by rearranging its digits so that odd digits occupy even positions?
1
16
2
36
3
60
4
180
24
PYQ 2017
medium
mathematics ID: bitsat-2
Statement–1: A five digit number divisible by 3 is to be formed using the digits 0,1,2,3,4 and 5 with repetition. The total number formed are 216. Statement–2: If sum of digits of any number is divisible by 3 then the number must be divisible by 3.
1
Statement–1 is true, Statement–2 is true, and Statement–2 is a correct explanation for Statement–1
2
Statement–1 is true, Statement–2 is true, but Statement–2 is not a correct explanation
3
Statement–1 is true, Statement–2 is false
4
Statement–1 is false, Statement–2 is true
25
PYQ 2018
medium
mathematics ID: bitsat-2
In how many ways can 12 gentlemen sit around a round table so that three specified gentlemen are always together?
1
2
3
4
3!9!
26
PYQ 2019
medium
mathematics ID: bitsat-2
If binomial coefficients of three consecutive terms of (1+x)ⁿ are in H.P., then the maximum value of n is
1
2
3
4
None of these
27
PYQ 2019
medium
mathematics ID: bitsat-2
The total number of 4-digit numbers in which the digits are in descending order, is
1
2
3
4
None of these
28
PYQ 2020
medium
mathematics ID: bitsat-2
If the third term in the expansion of [x+x\log_¹⁰ˣ]⁵ is 10⁶, then x may be
1
1
2
3
10
4
10⁻2/5
29
PYQ 2020
medium
mathematics ID: bitsat-2
If
sumᵣ=0ⁿ(r+2)/(r+1)ⁿCᵣ=(2ⁿ-1)/(6),
then n=
1
8
2
4
3
6
4
5
30
PYQ 2020
medium
mathematics ID: bitsat-2
The number of real roots of the equation
3⁹C₃r-1-3⁹Cᵣ²=3⁹Cᵣ²-1-3⁹C₃r
is
1
1
2
2
3
3
4
4
31
PYQ 2020
easy
mathematics ID: bitsat-2
If the sum of odd-numbered terms and even-numbered terms in the expansion of (x+a)ⁿ are A and B respectively, then the value of (x²-a²)ⁿ is
32
PYQ 2020
medium
mathematics ID: bitsat-2
All the words that can be formed using alphabets A, H, L, U and R are written as in a dictionary (no alphabet is repeated). The rank of the word RAHUL is
1
71
2
72
3
73
4
74
33
PYQ 2021
medium
mathematics ID: bitsat-2
If sumᵣ=0ⁿ(-1)ʳfracⁿCᵣⁿ+3Cᵣ=(3)/(a+3), then a-n is equal to
1
0
2
1
3
2
4
None of these
34
PYQ 2021
medium
mathematics ID: bitsat-2
Statement–1: A five digit number divisible by 3 is to be formed using the digits 0, 1, 2, 3, 4 and 5 with repetition. The total number formed are 216. Statement–2: If sum of digits of any number is divisible by 3 then the number must be divisible by 3.
1
Statement–1 is true, Statement–2 is true, Statement–2 is a correct explanation for Statement–1
2
Statement–1 is true, Statement–2 is true; Statement–2 is NOT a correct explanation for Statement–1
3
Statement–1 is true, Statement–2 is false
4
Statement–1 is false, Statement–2 is true
35
PYQ 2021
medium
mathematics ID: bitsat-2
How many different eight digit numbers can be formed from the number 22335588 by rearranging its digits if odd digits occupy even positions?
1
16
2
36
3
60
4
180
36
PYQ 2023
medium
mathematics ID: bitsat-2
Number of words from the letters of the word BHARAT in which B and H will never come together is:
1
210
2
240
3
422
4
400
37
PYQ 2025
medium
mathematics ID: bitsat-2
How many different 4-letter words can be formed from the letters of the word "BINARY" without repetition?
1
360
2
720
3
840
4
1260
38
PYQ 2026
medium
mathematics ID: bitsat-2
A person travels from Hyderabad to Goa and returns, but does not use the same bus for both journeys. If there are 25 buses available for each direction, how many ways can the round trip be made?
1
600
2
625
3
650
4
700