Find $n$ when ${^nC_{12}}={^nC_6}$ —* BISE Gujranwala(2015)*

Evaluate ${^{20}C_{17}}$ without calculator —* BISE Gujranwala(2015)*

How many $6-digit$ numbers can be formed from the digits $2,2,3,3,4,4$? How many of them with lie between $400,000$ and $430,000$? —* BISE Gujrawala(2015)*

How many words can be formed from the letter $``PLANE"$ using all letters (no letter is repeated) —* BISE Gujrawala(2017)*

Prove that $^nC_4=^nC_{n-r}$ —* BISE Gujrawala(2017)*

Find the numbers of diagonals of a $6-digits$ figures —* BISE Gujrawala(2017)*

A coin is tossed four times, find the probability that top shows all heads. —* BISE Gujranwala(2017)*

Show that $n^3-n$ is divisible by $6$ for $n=2,3$ —* BISE Gujrawala(2017)*

Find the value of $n$ when $^nP_2=30$ —* BISE Sargodha(2015)*

Find numbers of diagonals of $6-dided$ figure. —* BISE Sargodha(2015)*

Find the value of $n$. $^nC_{12}=^nC_6$ —* BISE Sargodha(2015)*

Determine the probability of getting two heads in two successive tosses of a coin? —* BISE Sargodha(2015)*

Prove that $^{n-1}C_r+^{n-1}C_{r-1}=^nC_r$ —* BISE Sargodha(2015)*

If $\frac{a_5}{a_3}=\frac{4}{9}$, $a_2=\frac{4}{9}$ in $G.P$. Find $a_n$ —* BISE Sargodha(2015)*

Find $n$, when $^{11}P_n=11.10.9$—* BISE Sargodha(2015), BISE Sargodha(2016) *

In how many way can a hockey team of $11$ be selected out of $15$ players. —* BISE Sargodha(2015)*

A die is thrown. Find the probability that the dots on the top are prime number or odd number. —* BISE Sargodha(2015)*

The sum of $9$ teams of an $A.P.$ is $171$ and its eighth team is $31$. Find the series. —* BISE Sargodha(2015)*

Prove that $^nC_r+^nC_{r-1}=^{n+1}C_r$ —* BISE Sargodha(2015)*

Find the sum of $\frac{9}{4}+\frac{3}{2}+1+\frac{2}{3}+\ldots\infty$ —* BISE Sargodha(2016)*

Evaluate $^{20}C_{17}$ —* BISE Sargodha(2016)*

Prove that $^{n-1}C_r+^{n-1}C_{r-1}=^n C_r$ —* BISE Sargodha(2016)*

Prove that $^nC_r=^nC_{n-r}$ —* BISE Sargodha(2017)*

In how many ways can $4$ keys be arranged on a circular key ring? —* BISE Sargodha(2017)*

How many words can be formed from the letters of the word $``objective"$ using all letters without repeating anyone? —* BISE Lahore(2017)*

Find the values of $n$ and $r$ when $^nC_r=35$ and $^nP_r=210$ —* FBISE(2016), BISE Lahore(2017)*

If $S=\{1,2,3,\ldots9\}$, Even $A=\{2,4,6,8\}$, $B=\{1,3,5\}$. Find $P(A \cup B)$ —* BISE Lahore(2017)*

A die is thrown. Find probability that the dots on the top are prime numbers or odd numbers. —* BISE Lahore(2017)*

Find the values of $n$ and $r$ when $^{n-1}C_{r-1}:^nC_r:^{n+1}C_{r+1}=3:6:10$ —* FBISE(2017)*

Show that sum of $n$ $AM's$ between $a$ and $b$ is equal to $n$ times their $AM's$ —* FBISE(2017)*