Simple Applications
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Permutation and Combination

119311 If \(5^{97}\) is divided by 52 , the remainder obtained is

1 3
2 5
3 4
4 0
5 1
Kerala CEE-2018
Permutation and Combination

119312 The number of diagonals in a hexagon is

1 8
2 9
3 10
4 11
5 12
Kerala CEE-2017
Permutation and Combination

119313 The sum
\(S=1 / 9 !+1 / 3 ! 7 !+1 / 5 ! 5 !+1 / 7 ! 3 !+1 / 9\) ! is equal to

1 \(2^{10} / 8\) !
2 \(2^9 / 10\) !
3 \(2^7 / 10\) !
4 \(2^6 / 10\) !
5 \(2^5 / 8\) !
Kerala CEE-2017
Permutation and Combination

119316 The value of \(\frac{1}{2 !}+\frac{2}{3 !}+\ldots+\frac{999}{1000 !}\) is equal to

1 \(\frac{1000 !-1}{1000 !}\)
2 \(\frac{1000 !+1}{1000 !}\)
3 \(\frac{999 !-1}{999 !}\)
4 \(\frac{999 !+1}{999 !}\)
5 \(\frac{1000 !-999 !}{1000 !}\)
Kerala CEE-2009
Permutation and Combination

119314 If \(n\) is any positive integer, the \(\frac{1}{2^n}\left({ }^{2 n} P_n\right)\) is equal to

1 \(2 \cdot 4 \cdot 6 \dot \quad (2n)\)
2 \(1 \cdot 2 \cdot 3 \dot\qquad\) n
3 \(1 \cdot 3 \cdot 5 \dot \qquad(2 \mathrm{n}-1)\)
4 \(1 \cdot 2 \cdot 3 \dot \qquad(3n)\)
5 \(2 \cdot 4 \cdot 6\dot \qquad (2 n+2)\)
Kerala CEE-2012
NEET DIGITAL LIBRARY
Permutation and Combination

119311 If \(5^{97}\) is divided by 52 , the remainder obtained is

1 3
2 5
3 4
4 0
5 1
Kerala CEE-2018
Permutation and Combination

119312 The number of diagonals in a hexagon is

1 8
2 9
3 10
4 11
5 12
Kerala CEE-2017
Permutation and Combination

119313 The sum
\(S=1 / 9 !+1 / 3 ! 7 !+1 / 5 ! 5 !+1 / 7 ! 3 !+1 / 9\) ! is equal to

1 \(2^{10} / 8\) !
2 \(2^9 / 10\) !
3 \(2^7 / 10\) !
4 \(2^6 / 10\) !
5 \(2^5 / 8\) !
Kerala CEE-2017
Permutation and Combination

119316 The value of \(\frac{1}{2 !}+\frac{2}{3 !}+\ldots+\frac{999}{1000 !}\) is equal to

1 \(\frac{1000 !-1}{1000 !}\)
2 \(\frac{1000 !+1}{1000 !}\)
3 \(\frac{999 !-1}{999 !}\)
4 \(\frac{999 !+1}{999 !}\)
5 \(\frac{1000 !-999 !}{1000 !}\)
Kerala CEE-2009
Permutation and Combination

119314 If \(n\) is any positive integer, the \(\frac{1}{2^n}\left({ }^{2 n} P_n\right)\) is equal to

1 \(2 \cdot 4 \cdot 6 \dot \quad (2n)\)
2 \(1 \cdot 2 \cdot 3 \dot\qquad\) n
3 \(1 \cdot 3 \cdot 5 \dot \qquad(2 \mathrm{n}-1)\)
4 \(1 \cdot 2 \cdot 3 \dot \qquad(3n)\)
5 \(2 \cdot 4 \cdot 6\dot \qquad (2 n+2)\)
Kerala CEE-2012
Join With Us for More Updates
Permutation and Combination

119311 If \(5^{97}\) is divided by 52 , the remainder obtained is

1 3
2 5
3 4
4 0
5 1
Kerala CEE-2018
Permutation and Combination

119312 The number of diagonals in a hexagon is

1 8
2 9
3 10
4 11
5 12
Kerala CEE-2017
Permutation and Combination

119313 The sum
\(S=1 / 9 !+1 / 3 ! 7 !+1 / 5 ! 5 !+1 / 7 ! 3 !+1 / 9\) ! is equal to

1 \(2^{10} / 8\) !
2 \(2^9 / 10\) !
3 \(2^7 / 10\) !
4 \(2^6 / 10\) !
5 \(2^5 / 8\) !
Kerala CEE-2017
Permutation and Combination

119316 The value of \(\frac{1}{2 !}+\frac{2}{3 !}+\ldots+\frac{999}{1000 !}\) is equal to

1 \(\frac{1000 !-1}{1000 !}\)
2 \(\frac{1000 !+1}{1000 !}\)
3 \(\frac{999 !-1}{999 !}\)
4 \(\frac{999 !+1}{999 !}\)
5 \(\frac{1000 !-999 !}{1000 !}\)
Kerala CEE-2009
Permutation and Combination

119314 If \(n\) is any positive integer, the \(\frac{1}{2^n}\left({ }^{2 n} P_n\right)\) is equal to

1 \(2 \cdot 4 \cdot 6 \dot \quad (2n)\)
2 \(1 \cdot 2 \cdot 3 \dot\qquad\) n
3 \(1 \cdot 3 \cdot 5 \dot \qquad(2 \mathrm{n}-1)\)
4 \(1 \cdot 2 \cdot 3 \dot \qquad(3n)\)
5 \(2 \cdot 4 \cdot 6\dot \qquad (2 n+2)\)
Kerala CEE-2012
For More Updates join with Us
Permutation and Combination

119311 If \(5^{97}\) is divided by 52 , the remainder obtained is

1 3
2 5
3 4
4 0
5 1
Kerala CEE-2018
Permutation and Combination

119312 The number of diagonals in a hexagon is

1 8
2 9
3 10
4 11
5 12
Kerala CEE-2017
Permutation and Combination

119313 The sum
\(S=1 / 9 !+1 / 3 ! 7 !+1 / 5 ! 5 !+1 / 7 ! 3 !+1 / 9\) ! is equal to

1 \(2^{10} / 8\) !
2 \(2^9 / 10\) !
3 \(2^7 / 10\) !
4 \(2^6 / 10\) !
5 \(2^5 / 8\) !
Kerala CEE-2017
Permutation and Combination

119316 The value of \(\frac{1}{2 !}+\frac{2}{3 !}+\ldots+\frac{999}{1000 !}\) is equal to

1 \(\frac{1000 !-1}{1000 !}\)
2 \(\frac{1000 !+1}{1000 !}\)
3 \(\frac{999 !-1}{999 !}\)
4 \(\frac{999 !+1}{999 !}\)
5 \(\frac{1000 !-999 !}{1000 !}\)
Kerala CEE-2009
Permutation and Combination

119314 If \(n\) is any positive integer, the \(\frac{1}{2^n}\left({ }^{2 n} P_n\right)\) is equal to

1 \(2 \cdot 4 \cdot 6 \dot \quad (2n)\)
2 \(1 \cdot 2 \cdot 3 \dot\qquad\) n
3 \(1 \cdot 3 \cdot 5 \dot \qquad(2 \mathrm{n}-1)\)
4 \(1 \cdot 2 \cdot 3 \dot \qquad(3n)\)
5 \(2 \cdot 4 \cdot 6\dot \qquad (2 n+2)\)
Kerala CEE-2012
NEET DIGITAL LIBRARY
Permutation and Combination

119311 If \(5^{97}\) is divided by 52 , the remainder obtained is

1 3
2 5
3 4
4 0
5 1
Kerala CEE-2018
Permutation and Combination

119312 The number of diagonals in a hexagon is

1 8
2 9
3 10
4 11
5 12
Kerala CEE-2017
Permutation and Combination

119313 The sum
\(S=1 / 9 !+1 / 3 ! 7 !+1 / 5 ! 5 !+1 / 7 ! 3 !+1 / 9\) ! is equal to

1 \(2^{10} / 8\) !
2 \(2^9 / 10\) !
3 \(2^7 / 10\) !
4 \(2^6 / 10\) !
5 \(2^5 / 8\) !
Kerala CEE-2017
Permutation and Combination

119316 The value of \(\frac{1}{2 !}+\frac{2}{3 !}+\ldots+\frac{999}{1000 !}\) is equal to

1 \(\frac{1000 !-1}{1000 !}\)
2 \(\frac{1000 !+1}{1000 !}\)
3 \(\frac{999 !-1}{999 !}\)
4 \(\frac{999 !+1}{999 !}\)
5 \(\frac{1000 !-999 !}{1000 !}\)
Kerala CEE-2009
Permutation and Combination

119314 If \(n\) is any positive integer, the \(\frac{1}{2^n}\left({ }^{2 n} P_n\right)\) is equal to

1 \(2 \cdot 4 \cdot 6 \dot \quad (2n)\)
2 \(1 \cdot 2 \cdot 3 \dot\qquad\) n
3 \(1 \cdot 3 \cdot 5 \dot \qquad(2 \mathrm{n}-1)\)
4 \(1 \cdot 2 \cdot 3 \dot \qquad(3n)\)
5 \(2 \cdot 4 \cdot 6\dot \qquad (2 n+2)\)
Kerala CEE-2012