Sample QuestionsPermutations , combinations and binomial expansion questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
If $10x$ $n! = 240$ then find the value of $n$.
Answer: D.
View full solution →How many terms are there in the expansion of $(x+a)^{n-1}$ ?
Answer: A.
View full solution →If $(n+ 1)! = 120$ then find the value of $n$.
Answer: B.
View full solution →Find the value of ${ }^{ n } C _{ 0 }+{ }^n C _{ n }.....$
Answer: C.
View full solution →Which of the following is equivalent to ${ }^{ n } C _{ r } ?$
Answer: B.
View full solution →If $56 \times n !=8 !$ then find the value of $n$.
View full solution →If $n P _{ 3 }=210$, find the value of $n$.
View full solution →If ${ }^n C _{ 2 }=15$, then find the value of $n$.
View full solution →There are $5$ empty seats in the coach of a train. In how many ways will $3$ persons be seated ?
View full solution →Write the general term of the expansion $(x+a)^n$.
View full solution →In how many ways $3$ members of a family; husband, wife and a daughter can be arranged in a row for a group photograph ?
View full solution →If $^{(n+2)} P_{3}:^{(n+1)} P_{3}=10: 7$ then find $n$.
View full solution →If $\frac{n !}{2}=60$ then find value the of $n$.
View full solution →Expand $\left(x-\frac{2}{x}\right)^{5}$
View full solution →Expand $(2 x-a)^{5}$
View full solution →How many $5$ digit numbers can be formed using all the digits $2, 5, 0, 7$ and $9$ ?
View full solution →Expand $(1+x)^{6}$ and verify it by putting $x=1$ on both the sides.
View full solution →Expand $\left(\sqrt{a}+\frac{1}{\sqrt{a}}\right)^{4}$
View full solution →Expand $\left(\frac{a}{b}-\frac{b}{a}\right)^{4}$.
View full solution →$2$ cards are selected from a pack of $52$ cards. In how many ways, this selection can be done such that
$(1)$ One is a face card and the other is a number card ?
$(2)$ both are of different colours ?
$(3)$ both are of same suit ?
View full solution →Obtain the value of $(\sqrt{3}+\sqrt{2})^{4}+(\sqrt{3}-\sqrt{2})^{4}$ using binomial expansion method.
View full solution →Obtain the value of $(\sqrt{3}+2)^{5}-(\sqrt{3}-2)^{5}$ using binomial expansion method.
View full solution →Find the values of the following :
$(1)$ ${ }^{8} \mathrm{C}_{3}$
$(2)$ ${ }^{20} \mathrm{C}_{3}$
$(3)$ ${ }^{5} \mathrm{C}_{4}$
$(4)$ ${ }^{6} \mathrm{C}_{6}$
View full solution →In how many ways can $5$ boys and $2$ girls be arranged in a row such that,
$(1)$ both the girls are together ?
$(2)$ both the girls are not together ?
View full solution →Find the values of the following :
$(1)$ ${ }^{8} \mathbf{P}_{3}$
$(2)$ ${ }^{60} P_{2}$
$(3)$ ${ }^{7} \mathbf{P}_{6}$
$(4)$ ${ }^{5} \mathbf{P}_{5}$
View full solution →Using all the digits $2, 5, 7, 8$, four digit numbers are to be formed.
$(1)$ How many such numbers can be made ?
$(2)$ How many of them will be even numbers ?
$(3)$ How many of them will be divisible by $5 ?$
$(4)$ How many of them will be greater than $5000 ?$
View full solution →There are $6$ engineers and $4$ managers in a company. In how many ways can a committee of $5$ members be made such that
$(1)$ there are at least $2$ managers ?
$(2)$ there are at the most $2$ engineers ?
$(3)$ engineers are in majority ?
View full solution →Arrangements are made using all the letters of the word $\text{YOUNG}$. If all these arrangements are arranged in the order of dictionary, what will be the rank of the word $\text{YOUNG ?}$
View full solution →Putting $x=2$ in the expansion of $(1+x)^{4}$ verify both side.
View full solution →Find the Value of the following using binomial expansion: $(2+\sqrt{5})^{5}+(2-\sqrt{5})^{5}$
View full solution →