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Online Practice: Meaning of P(n,r) and C(n,r) for JEE

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Part of Permutations and Combinations in JEE Main Mathematics.

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Q1MathsUnit 4: Permutations and Combinations
Arrange the following values of nn in ascending order. A:nP5=nP6⇒n=\boldsymbol{A}:^{n} \boldsymbol{P}_{5}=^{n} \boldsymbol{P}_{6} \Rightarrow \boldsymbol{n}= B:nP12=nP8⇒n=\boldsymbol{B}:^{\boldsymbol{n}} \boldsymbol{P}_{12}=^{\boldsymbol{n}} \boldsymbol{P}_{\boldsymbol{8}} \Rightarrow \boldsymbol{n}= C:nC(n−3)=10⇒n=\boldsymbol{C}:^{n} \boldsymbol{C}_{(\boldsymbol{n}-\mathbf{3})}=\mathbf{1 0} \Rightarrow \boldsymbol{n}= D:(n+1)P5:nP6=1:2⇒n=\boldsymbol{D}:^{(\boldsymbol{n}+1)} \boldsymbol{P}_{5}:^{\boldsymbol{n}} \boldsymbol{P}_{6}=\mathbf{1}: \boldsymbol{2} \Rightarrow \boldsymbol{n}=
Q2MathsUnit 4: Permutations and Combinations
If r>1,r>1, then nPrnCr\frac{n P_{r}}{n C_{r}} is This question has multiple correct options
Q3MathsUnit 4: Permutations and Combinations
If nPr=30240^{n} \boldsymbol{P}_{r}=\mathbf{3 0 2 4 0} and nCr=252,^{n} \boldsymbol{C}_{r}=\mathbf{2 5 2}, then the ordered pair (n,r)(n, r) is equal to:
Q4MathsUnit 4: Permutations and Combinations
If nC3=nC9,^{n} C_{3}=^{n} C_{9}, then nC2=^{n} C_{2}=

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