Elementary Properties of nPr and nCr
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Permutation and Combination

118920 If \({ }^{n-1} C_r=\left(k^2-3\right)\left({ }^n C_{r+1}\right)\), then \(k\) belongs to

1 \((\sqrt{3}, 2)\)
2 \((-\infty,-2)\)
3 \([-\sqrt{3}, \sqrt{3}]\)
4 \((2, \infty)\)
AMU-2011
Permutation and Combination

118921 For \(2 \leq r \leq n,{ }^n C_r+2 .{ }^n C_{r-1}+{ }^n C_{r-2}=\)

1 \({ }^{\mathrm{n}+1} \mathrm{C}_{\mathrm{r}-1}\)
2 \(2 \cdot{ }^{\mathrm{n}+1} \mathrm{C}_{\mathrm{r}+1}\)
3 \(2 \cdot{ }^{\mathrm{n}+2} \mathrm{C}_{\mathrm{r}}\)
4 \({ }^{\mathrm{n}+2} \mathrm{C}_{\mathrm{r}}\)
AMU-2010
Permutation and Combination

118922 The value of \({ }^0 \mathrm{P}_4+4^0 \mathrm{P}_3\) is

1 5040
2 2520
3 840
4 720
AP EAPCET-25.08.2021
Permutation and Combination

118927 If \((2 \leq r \leq n)\), then \({ }^n C_r+2 \cdot{ }^n C_{r+1}+{ }^n C_{r+2}\) is equal to

1 \(2^{\mathrm{n}} \mathrm{C}_{\mathrm{r}+2}\)
2 \({ }^{\mathrm{n}+1} \mathrm{C}_{\mathrm{r}+1}\)
3 \({ }^{\mathrm{n}+2} \mathrm{C}_{\mathrm{r}+2}\)
4 \({ }^{n+1} C_r\)
WB JEE-2018
NEET DIGITAL LIBRARY
Permutation and Combination

118920 If \({ }^{n-1} C_r=\left(k^2-3\right)\left({ }^n C_{r+1}\right)\), then \(k\) belongs to

1 \((\sqrt{3}, 2)\)
2 \((-\infty,-2)\)
3 \([-\sqrt{3}, \sqrt{3}]\)
4 \((2, \infty)\)
AMU-2011
Permutation and Combination

118921 For \(2 \leq r \leq n,{ }^n C_r+2 .{ }^n C_{r-1}+{ }^n C_{r-2}=\)

1 \({ }^{\mathrm{n}+1} \mathrm{C}_{\mathrm{r}-1}\)
2 \(2 \cdot{ }^{\mathrm{n}+1} \mathrm{C}_{\mathrm{r}+1}\)
3 \(2 \cdot{ }^{\mathrm{n}+2} \mathrm{C}_{\mathrm{r}}\)
4 \({ }^{\mathrm{n}+2} \mathrm{C}_{\mathrm{r}}\)
AMU-2010
Permutation and Combination

118922 The value of \({ }^0 \mathrm{P}_4+4^0 \mathrm{P}_3\) is

1 5040
2 2520
3 840
4 720
AP EAPCET-25.08.2021
Permutation and Combination

118927 If \((2 \leq r \leq n)\), then \({ }^n C_r+2 \cdot{ }^n C_{r+1}+{ }^n C_{r+2}\) is equal to

1 \(2^{\mathrm{n}} \mathrm{C}_{\mathrm{r}+2}\)
2 \({ }^{\mathrm{n}+1} \mathrm{C}_{\mathrm{r}+1}\)
3 \({ }^{\mathrm{n}+2} \mathrm{C}_{\mathrm{r}+2}\)
4 \({ }^{n+1} C_r\)
WB JEE-2018
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Permutation and Combination

118920 If \({ }^{n-1} C_r=\left(k^2-3\right)\left({ }^n C_{r+1}\right)\), then \(k\) belongs to

1 \((\sqrt{3}, 2)\)
2 \((-\infty,-2)\)
3 \([-\sqrt{3}, \sqrt{3}]\)
4 \((2, \infty)\)
AMU-2011
Permutation and Combination

118921 For \(2 \leq r \leq n,{ }^n C_r+2 .{ }^n C_{r-1}+{ }^n C_{r-2}=\)

1 \({ }^{\mathrm{n}+1} \mathrm{C}_{\mathrm{r}-1}\)
2 \(2 \cdot{ }^{\mathrm{n}+1} \mathrm{C}_{\mathrm{r}+1}\)
3 \(2 \cdot{ }^{\mathrm{n}+2} \mathrm{C}_{\mathrm{r}}\)
4 \({ }^{\mathrm{n}+2} \mathrm{C}_{\mathrm{r}}\)
AMU-2010
Permutation and Combination

118922 The value of \({ }^0 \mathrm{P}_4+4^0 \mathrm{P}_3\) is

1 5040
2 2520
3 840
4 720
AP EAPCET-25.08.2021
Permutation and Combination

118927 If \((2 \leq r \leq n)\), then \({ }^n C_r+2 \cdot{ }^n C_{r+1}+{ }^n C_{r+2}\) is equal to

1 \(2^{\mathrm{n}} \mathrm{C}_{\mathrm{r}+2}\)
2 \({ }^{\mathrm{n}+1} \mathrm{C}_{\mathrm{r}+1}\)
3 \({ }^{\mathrm{n}+2} \mathrm{C}_{\mathrm{r}+2}\)
4 \({ }^{n+1} C_r\)
WB JEE-2018
For More Updates join with Us
NEET Test Series from KOTA - 10 Papers In MS WORD WhatsApp Here
Permutation and Combination

118920 If \({ }^{n-1} C_r=\left(k^2-3\right)\left({ }^n C_{r+1}\right)\), then \(k\) belongs to

1 \((\sqrt{3}, 2)\)
2 \((-\infty,-2)\)
3 \([-\sqrt{3}, \sqrt{3}]\)
4 \((2, \infty)\)
AMU-2011
Permutation and Combination

118921 For \(2 \leq r \leq n,{ }^n C_r+2 .{ }^n C_{r-1}+{ }^n C_{r-2}=\)

1 \({ }^{\mathrm{n}+1} \mathrm{C}_{\mathrm{r}-1}\)
2 \(2 \cdot{ }^{\mathrm{n}+1} \mathrm{C}_{\mathrm{r}+1}\)
3 \(2 \cdot{ }^{\mathrm{n}+2} \mathrm{C}_{\mathrm{r}}\)
4 \({ }^{\mathrm{n}+2} \mathrm{C}_{\mathrm{r}}\)
AMU-2010
Permutation and Combination

118922 The value of \({ }^0 \mathrm{P}_4+4^0 \mathrm{P}_3\) is

1 5040
2 2520
3 840
4 720
AP EAPCET-25.08.2021
Permutation and Combination

118927 If \((2 \leq r \leq n)\), then \({ }^n C_r+2 \cdot{ }^n C_{r+1}+{ }^n C_{r+2}\) is equal to

1 \(2^{\mathrm{n}} \mathrm{C}_{\mathrm{r}+2}\)
2 \({ }^{\mathrm{n}+1} \mathrm{C}_{\mathrm{r}+1}\)
3 \({ }^{\mathrm{n}+2} \mathrm{C}_{\mathrm{r}+2}\)
4 \({ }^{n+1} C_r\)
WB JEE-2018