Straight Lines ...

In a test there were n questions. In the test $$\displaystyle 2^{n-i}$$ students gave wrong answers to i questions where $$\displaystyle i=1,2,3...,n$$. If the total number of wrong answers given is 2047 then n is

If $$^nC_3=^nC_{13}$$, then $$^{20}C_n$$ is.

The sides of a quadrilateral are all positive integers and three of them are $$5, 10, 20.$$ How many possible value are there for the fourth side?

Determine the area of the triangle whose vertices are $$\displaystyle \left( \frac { 1 }{ 2 } ,\frac { -1 }{ 2 }  \right) ,\left( 2,\frac { -1 }{ 2 }  \right) $$ and $$\displaystyle \left( 2,\frac { \sqrt { 3 } -1 }{ 2 }  \right) $$.

A college offers $$7$$ courses in the morning and $$5$$ courses in the evening. Find the number of ways a student can select exactly one course either in the morning or in the evening.

If $$m$$ denotes the number of $$5$$ digit numbers if each successive digits are in their descending order of magnitude and $$n$$ is the corresponding figure. When the digits and in their ascending order of magnitude then $$(m-n)$$ has the value

If $$ { _{  }^{ n }{ C } }_{ 4 },{ _{  }^{ n }{ C } }_{ 5 }$$ and $$ { _{  }^{ n }{ C } }_{ 6 }$$ are in AP, then $$n$$ is

Two classrooms A and B having capacity of $$25$$ and $$(n-25)$$ seats respectively. $$A_n$$ denotes the number of possible seating arrangements of room $$'A'$$, when 'n' students are to be seated in these rooms, starting from room $$'A'$$ which is to be filled up to its capacity. If $$A_n-A_{n-1}=25!(^{49}C_{25})$$ then 'n' equals:

The line $$\displaystyle 3x+2y=24$$ meets x-axis at A and y-axis at B. The perpendicular bisector of $$\displaystyle \overline { AB } $$ meets the line through (0, -1) and parallel to x-axis at C. Find the area of $$\displaystyle \Delta ABC$$.