Elementary Properties of nPr and nCr
« First Topic in Next Topic: Permutation as an Arrangement »
Permutation and Combination

118911 If \(a, b, c\) are three natural numbers in \(A P\) and \(\mathbf{a}+\mathbf{b}+\mathbf{c}=21\) then the possible number of values of the ordered triplet \((a, b, c)\) is

1 15
2 14
3 13
4 None of these
BITSAT-2020
Permutation and Combination

118912 Find the value of
\({ }^1 P_1+2 .{ }^2 P_2+3 .{ }^3 P_3+4 .{ }^4 P_4+\ldots+n .{ }^n P_n\)

1 \({ }^{n+1} P_{n+1}\)
2 \({ }^{n+1} P_{n+1}-1\)
3 \({ }^{n+1} P_{n+1}-2\)
4 \({ }^{n+1} P_{n+1}+1\)
JCECE-2012
Permutation and Combination

118913 The value of \(2,6,10 \ldots(4 n-6)(4 n-2)\) is equal to

1 \(\mathrm{C}(2 \mathrm{n}, \mathrm{n})\)
2 \((\mathrm{n}+1)(\mathrm{n}+2)(\mathrm{n}+3) \ldots(2 \mathrm{n})\)
3 \(n ! P(2 n, n)\)
4 None of the above
CG PET- 2012
Permutation and Combination

118926 If \({ }^{\mathrm{n}} \mathrm{C}_4,{ }^{\mathrm{n}} \mathrm{C}_5\) and \({ }^{\mathrm{n}} \mathrm{C}_6\) are in A.P., then \(\mathrm{n}\) is

1 7 or 14
2 7
3 14
4 14 or 21
WB JEE-2011
NEET DIGITAL LIBRARY
Permutation and Combination

118911 If \(a, b, c\) are three natural numbers in \(A P\) and \(\mathbf{a}+\mathbf{b}+\mathbf{c}=21\) then the possible number of values of the ordered triplet \((a, b, c)\) is

1 15
2 14
3 13
4 None of these
BITSAT-2020
Permutation and Combination

118912 Find the value of
\({ }^1 P_1+2 .{ }^2 P_2+3 .{ }^3 P_3+4 .{ }^4 P_4+\ldots+n .{ }^n P_n\)

1 \({ }^{n+1} P_{n+1}\)
2 \({ }^{n+1} P_{n+1}-1\)
3 \({ }^{n+1} P_{n+1}-2\)
4 \({ }^{n+1} P_{n+1}+1\)
JCECE-2012
Permutation and Combination

118913 The value of \(2,6,10 \ldots(4 n-6)(4 n-2)\) is equal to

1 \(\mathrm{C}(2 \mathrm{n}, \mathrm{n})\)
2 \((\mathrm{n}+1)(\mathrm{n}+2)(\mathrm{n}+3) \ldots(2 \mathrm{n})\)
3 \(n ! P(2 n, n)\)
4 None of the above
CG PET- 2012
Permutation and Combination

118926 If \({ }^{\mathrm{n}} \mathrm{C}_4,{ }^{\mathrm{n}} \mathrm{C}_5\) and \({ }^{\mathrm{n}} \mathrm{C}_6\) are in A.P., then \(\mathrm{n}\) is

1 7 or 14
2 7
3 14
4 14 or 21
WB JEE-2011
Join With Us for More Updates
Permutation and Combination

118911 If \(a, b, c\) are three natural numbers in \(A P\) and \(\mathbf{a}+\mathbf{b}+\mathbf{c}=21\) then the possible number of values of the ordered triplet \((a, b, c)\) is

1 15
2 14
3 13
4 None of these
BITSAT-2020
Permutation and Combination

118912 Find the value of
\({ }^1 P_1+2 .{ }^2 P_2+3 .{ }^3 P_3+4 .{ }^4 P_4+\ldots+n .{ }^n P_n\)

1 \({ }^{n+1} P_{n+1}\)
2 \({ }^{n+1} P_{n+1}-1\)
3 \({ }^{n+1} P_{n+1}-2\)
4 \({ }^{n+1} P_{n+1}+1\)
JCECE-2012
Permutation and Combination

118913 The value of \(2,6,10 \ldots(4 n-6)(4 n-2)\) is equal to

1 \(\mathrm{C}(2 \mathrm{n}, \mathrm{n})\)
2 \((\mathrm{n}+1)(\mathrm{n}+2)(\mathrm{n}+3) \ldots(2 \mathrm{n})\)
3 \(n ! P(2 n, n)\)
4 None of the above
CG PET- 2012
Permutation and Combination

118926 If \({ }^{\mathrm{n}} \mathrm{C}_4,{ }^{\mathrm{n}} \mathrm{C}_5\) and \({ }^{\mathrm{n}} \mathrm{C}_6\) are in A.P., then \(\mathrm{n}\) is

1 7 or 14
2 7
3 14
4 14 or 21
WB JEE-2011
For More Updates join with Us
NEET Test Series from KOTA - 10 Papers In MS WORD WhatsApp Here
Permutation and Combination

118911 If \(a, b, c\) are three natural numbers in \(A P\) and \(\mathbf{a}+\mathbf{b}+\mathbf{c}=21\) then the possible number of values of the ordered triplet \((a, b, c)\) is

1 15
2 14
3 13
4 None of these
BITSAT-2020
Permutation and Combination

118912 Find the value of
\({ }^1 P_1+2 .{ }^2 P_2+3 .{ }^3 P_3+4 .{ }^4 P_4+\ldots+n .{ }^n P_n\)

1 \({ }^{n+1} P_{n+1}\)
2 \({ }^{n+1} P_{n+1}-1\)
3 \({ }^{n+1} P_{n+1}-2\)
4 \({ }^{n+1} P_{n+1}+1\)
JCECE-2012
Permutation and Combination

118913 The value of \(2,6,10 \ldots(4 n-6)(4 n-2)\) is equal to

1 \(\mathrm{C}(2 \mathrm{n}, \mathrm{n})\)
2 \((\mathrm{n}+1)(\mathrm{n}+2)(\mathrm{n}+3) \ldots(2 \mathrm{n})\)
3 \(n ! P(2 n, n)\)
4 None of the above
CG PET- 2012
Permutation and Combination

118926 If \({ }^{\mathrm{n}} \mathrm{C}_4,{ }^{\mathrm{n}} \mathrm{C}_5\) and \({ }^{\mathrm{n}} \mathrm{C}_6\) are in A.P., then \(\mathrm{n}\) is

1 7 or 14
2 7
3 14
4 14 or 21
WB JEE-2011
NEET DIGITAL LIBRARY