Question 1 :
The distance between the points $(3,5)$ and $(x,8)$ is $5$ units. Then the value of $x$ 
Question 2 :
A line is of length $10$ m and one end is $(2,-3)$, the $x$ - co-ordinate of the other is $8$, then its $y$- coordinate is:
Question 3 :
If a point $C$ be the mid-point of a line segment $AB$, then $AC = BC = (...) AB$.
Question 4 :
Harmonic conjugate of the point $C(5, 1)$ with respect to the point $A(2, 10)$ and $B(6, -2)$ is?
Question 6 :
In what ratio, does $P(4, 6)$ divide the join of $A(-2, 3)$ and $B(6, 7)$
Question 7 :
The centroid of the triangle with vertices (2,6), (-5,6) and (9,3) is
Question 8 :
If $A$ and $B$ are the points $(-3,4)$ and $(2,1)$, then the co-ordinates of the point $C$ on $AB$ produced such that $AC=2BC$ are 
Question 9 :
The ratio, in which the line segment joining (3, -4) and (-5, 6) is divided by the x-axis is
Question 10 :
The coordinates of $A$ and $B$ are $(1, 2) $ and $(2, 3)$. Find the coordinates of $R $, so that $A-R-B$  and   $\displaystyle \frac{AR}{RB} = \frac{4}{3}$.<br/>
Question 11 :
Distance between A(x, y) and B(-4, 7) is $\sqrt{41}.$ Find x and y, if A's ordinate is thrice of its abscissa.
Question 12 :
Select the correct option.<br>The value of $p$, for which the points $A(3,1) , B (5, p)$ and $C (7, -5)$ are collinear, is
Question 13 :
The coordinates of a point at a distance $\sqrt{5}$ from the point $(3, 4)$ and having the same abcissa and ordinate are<br>
Question 14 :
Find the perimeter of the triangle formed by the points $(3, 5), (4, 8)$ and $(5, 6)$.
Question 15 :
The point $A(-5,\,8)$  ______ on circle of radius $6$ and centre $(8,\,9)$.
Question 16 :
If the co-ordinates of two points A and B are (3, 4) and (5, -2) respectively then the co-ordinates of any point P if PA = PB and area of$\displaystyle \Delta PAB=10$ is
Question 17 :
Which of the following is true for the points $X$ and $Y$ if the co-ordinates of the mid-points $P$ of $\overline {XY}$ are $(-2, 3)$?
Question 18 :
The curve $y=ax^3+bx^2+cx+5$ touches the x-axis at $P(-2,0)$ and cuts the y-axis at a point $Q$ where its gradient is $3$. Then the value of ${a,b,c} $ is 
Question 19 :
If $( x , y )$ is equidistant from $P (-3 , 2 )$ and $Q (2, -3)$, then
Question 20 :
Find a point on the y-axis which is equidistant from the points $(-3,4)$ and $(2,3)$.<br/>
Question 21 :
If $P\left( x,y,z \right) $ is a point on the line segment joining $Q\left( 2,2,4 \right) $ and $R\left( 3,5,6 \right) $ such that the projections of $OP$ on the axis are $\cfrac { 13 }{ 5 } ,\cfrac { 19 }{ 5 } ,\cfrac { 26 }{ 5 } $ respectively, then $P$ divides $QR$ in the ratio
Question 22 :
If $(-6, -4), (3, 5), (-2, 1)$ are the vertices of a parallelogram, then remaining vertex can be
Question 23 :
If two vertices of a parellelogram are $(3,2)$ and $(-1,0)$ and the diagonals intersect at $(2, -5)$, then the other two vertices are:
Question 24 :
Consider the points $A(0,\ 1)$ and $B(2,\ 0)$, and $P$ be a point on the line $4x+3y+9=0$. The coordinates of $P$ such that $|PA-PB|$ is maximum are
Question 25 :
$ABC$ is an equilateral triangle. If the coordinates of two of its vertices are ($1, 3)$ and $(-2, 7)$ the coordinates of the third vertex can be<br>
Question 26 :
3, 7, 11, 15, 19, ...... are in AP. find 25th term.
Question 27 :
How many terms of the series $54+51+48+45+.......$ must be taken to make $513$?
Question 28 :
An A.P. has $23$ terms, sum of the middle three terms is $144$, the sum of last three terms is $264$. Find the $8^{th}$ term
Question 29 :
If the common difference of an A.P. is $3$, then $a_{20}-a_{15}$ is<br/>
Question 30 :
What is the first four terms of the A.P. whose first term is $-1$ and common difference is $0.5$?
Question 31 :
Is it an AP?<br/><br/>$1, 4, 7, 10, 13, 16, 19, 22, 25, ...$
Question 33 :
In the word 'Albuquerque' if we assign a number to the letters, equal to the number of times the letter is used in the word. The sum of the number would be -
Question 34 :
Find the $20th$ term from the last term of the AP $3,8, 13,....253.$
Question 35 :
Which term of the progression 5, 8, 11, 14, .....is 320?
Question 36 :
If $t_{5}, t_{10}$ and $t_{25}$ are $5^{th}, 10^{th}$ and $25^{th}$ terms of an AP respectively, then the value of $\begin{vmatrix}t_{5} & t_{10} & t_{25}\\ 5 & 10 & 25\\ 1 & 1 & 1\end{vmatrix}$ is<br/>
Question 37 :
The first term of an arithmetic sequence is equal to $6$ and the common difference is equal to $3$. Find a formula for the $n^{th}$ term and the value of the $50^{th}$ term.
Question 38 :
If two terms of an arithmetic progression are known, then the two terms can be represented using which of the formula below?
Question 39 :
From an $A.P.$first and last term is $13$and $216$respectively. Common difference is $7$. Find the sum of all terms.
Question 40 :
What is the sum of the first $n$ terms if the first term is $2$, the common difference is $5$ and the $n^{th}$ term is $122$ in an arithmetic series?<br/>
Question 41 :
In an A.P of which $a$ is the first term, if the sum of the first $p$ terms is zero, then the sum of the next $q$ term is:
Question 42 :
Calculate the sum of even numbers between $12$ and $90$ which are divisible by $8$.
Question 43 :
Assertion: Let the positive numbers $a, b, c $ be in A.P., then $\dfrac {1}{bc}, \dfrac {1}{ac}, \dfrac {1}{ab}$ are also in A.P.
Reason: If each term of an A.P. is divided by $abc$, then the resulting sequence is also in A.P.
Question 44 :
If the sum of the first $2n$ terms of the A.P $2,5,8,...$ is equal to the sum of the first $n$ terms of the A.P $57,59,61,...$ then $n$ equals
Question 45 :
Find the second term and $nth$ term of an AP whose $6th$ term is $12$ and $8th$ term is $22.$
Question 46 :
Assertion: There exists no A.P. whose three terms are $\sqrt 3, \sqrt 5$ and $\sqrt 7$.
Reason: If $t_p, t_q$ and $t_r$ are three distinct terms of an A.P., then $\frac {\displaystyle t_r-t_p}{\displaystyle t_q-t_p}$ is a rational number.
Question 47 :
The least value of $n$ such that $1+3+5+7....n$ terms $\ge 500$ is
Question 48 :
In an A.P. of $n$ terms, $a$ is the first term, $b$ is the second last term and $c$ is the last term, then the sum of all of its term equals
Question 49 :
The $8^{th}$ term of the sequence $1, 1, 2, 3, 5, 8, ....$ is
Question 50 :
A man saves Rs. 200 in each of the first threemonths of his service. In each of the subsequentmonths his saving increases by Rs. 40 morethan the saving of immediately previous month.His total saving from the start of service will beRs. 11040 after
