R K Bansal Solutions for Exercise 1: MIXED PRACTICE

If $n^{th}$term of an $\mathrm{A}.\mathrm{P}.$ is $(2n-1).$ Find its $7^{th}$ term.

If the sum of first $n$ terms of an $\mathrm{A}.\mathrm{P}.$ is $3n^2+2n,$ find its $r^{th}$ term.
 

What point on $x-$axis is equidistant from the points $(6, 7)$ and $(4,-3)?$
 

Calculate the ratio in which the line segment $\mathrm{A}(6, 5)$ and $\mathrm{B}(4, -3)$ is divided by the line $y=2.$

The line $4x+5y+20=0$ meets $x-$axis at point $\mathrm{A}$ and $y-$axis at point $\mathrm{B}.$ Find the co-ordinates of point $\mathrm{P}$ in $\mathrm{AB}$ such that $\mathrm{AB} : \mathrm{BP} = 5 : 3.$
 

Show that $2x + 7$ is a factor of $2x^3 + 7x2 - 4x - 14.$ Hence , solove the equation :

$2x3 + 7x2 -4x - 14 = 0$.

What number should be subtracted from $2x^3-5x^2+5x+8$ so that the resulting polynominal has a factor $2x - 3 ?$

If the sum of first $20$ terms of an A.P. is same as the sum of its first $28$ terms. Find the sum of its $48$ terms.