Question 1 :
_____ is a list of numbers in which each term is obtained by adding a fixed number to the preceding term except the first term.

Question 2 :
The first and the last term of A.P. are $7$ and $630$ respectively. If the common difference is $7$, how many terms are there and what is their sum?

Question 3 :
Find the $\displaystyle 10^{th}$ term from end of the AP $4, 9, 14, ....., 254$.

Question 4 :
If $7th$ and $13th$ terms of an $A.P$. Be $34$ and $64$, respectively, then its $18th$ terms is:

Question 5 :
If $f(x)$is a differentiable function in the interval $(0,\infty)$such that $f(1)=1$ and $\lim _{ t\rightarrow x }{ \frac { { t }^{ 2 }f\left( x \right) -{ x }^{ 2 }f\left( t \right) }{ t-x } } =1$<br>

Question 6 :
The series of natural numbers is divided into groups $(1), (2,3,4), (3,4,5,6,7), (4,5,6,7,8,9,10), ...$ Find the sum of the numbers in nth group.

Question 7 :
If $log_5 \,2, log_5 (2^x - 3)$ and $log_5 \left(\dfrac{17}{2} + 2^{x-1}\right)$ are in AP, then the value of $x$ is

Question 8 :
IF $S_n = ^nC_0. ^nC_1 + ^nC_1. ^nC_2 + .... + ^nC_{n - 1}. ^nC_n \, and \, \dfrac{S_{n + 1}}{S_n} = \dfrac{15}{4}$, then n =

Question 9 :
The nature of the roots of a quadratic equation is determined by the:<br>

Question 10 :
A quadratic equation in $x$ is $ax^2 + bx + c = 0$, where $a, b, c$ are real numbers and the other condition is<br/>

Question 12 :
If $\alpha , \beta , \gamma $ are the real roots of the equation $x^{3}-3px^{2}+3qx-1=0$, then the centroid of&#160;the triangle with vertices $\displaystyle \left ( \alpha , \frac{1}{\alpha } \right )$, $\left ( \beta , \dfrac{1}{\beta } \right )$ and $\displaystyle \left ( \gamma , \frac{1}{\gamma } \right )$ is at the point

Question 13 :
Consider quadratic equation $ax^2+(2-a)x-2=0$, where $a \in R$.If exactly one root is negative, then the range of $a^2+2a+5$ is

Question 14 :
If k be the ratio of the roots of the equation$ \displaystyle x^{2}-px+q=0 $ , the value of$ \displaystyle \frac{k}{1+k^{2}} $ is

Question 15 :
If a,b,c &gt;0 and $a=2b+3c$, then the roots of the equation $ax^2+bx+c=0$ are real if