Question 1 :
If the sum of $n$ terms of an AP is $\displaystyle { 3n }^{ 2 }-n$ and its common difference is $6$, then its first term is 
Question 2 :
Find the sum of the first $15$ terms of the following sequence having $n$th term as<br>${ y }_{ n }=9-5n\quad $
Question 4 :
If $a, b, c$ are in A.P. $b - a, c - b$ and $a$ in G.P., then $a:b:c$ is
Question 5 :
If the first 10 alphabet are removed and attached at the end of the alphabet series the fifth letter from the begining is -
Question 6 :
If the sum of 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 7 :
If a, b, c and d are in harmonic progression, then $\displaystyle\frac{1}{a}$,$\displaystyle\frac{1}{b}$,$\displaystyle\frac{1}{c}$ and$\displaystyle\frac{1}{d}$, are in ______ progression.
Question 8 :
The first, second and middle terms of an A.P. are a, b, c, respectively. Their sum is?
Question 9 :
Constant is subtracted from each term of an A.P. the resulting sequence is also an ______
Question 10 :
What does the series $ 1 + 3^{\tfrac{-1}{2}} + 3 + { \dfrac {1} {3 \sqrt {3} }} + .... $  represent?
Question 12 :
Given$f(x) = \left[ {\frac{1}{3} + \frac{x}{{66}}} \right]$ then$\sum\limits_{x = 1}^{66} {f(x)} $ is
Question 13 :
If the roots of the equation $\left( b-c \right) x^{ 2 }+\left( c-a \right) x+\left( a-b \right) =0$ are equal, then a,b,c will be in-
Question 14 :
The sum of the remaining terms in the group after $2000^{th}$ term in which $2000^{th}$ term lies is
Question 16 :
Given $\displaystyle \sum_{n=1}^{\infty}\frac{1}{n^{2}}=\frac{\pi ^{2}}{6}$ : the value of $\displaystyle \sum_{n=1}^{\infty}\frac{1+3+5+......+(2n-1)}{1^{3}+2^{3}+3^{3}+........n^{3}} $ is:<br/>
Question 17 :
The fourth term of an A.P. is $11$ and the eighth term exceeds twice the fourth term by $5$. Find the A.P. and the sum of first $50$ terms.
Question 19 :
Assertion: $\displaystyle a_{1}, \: a_{2}, \: a_{3}, \: ....., \: a_{n}$ are in AP<br><br>STATEMENT-1:- $\displaystyle \frac{1}{a_{1}a_{n}} + \frac{1}{a_{2}a_{n-1}} + \frac{1}{a_{3}a_{n-2}}+ .....+\frac{1}{a_{n}a_{1}} = \frac{2}{a_{1} + a_{n}}\left ( \frac{1}{a_{1}} + \frac{1}{a_{2}} + \frac{1}{a_{3}} + ... + \frac{1}{a_{n}} \right )$
Reason: STATEMENT-2 : - $\displaystyle a_{1} + a_{n} = a_{r} + a_{n - r}$ for $\displaystyle 1\leq r\leq n$
Question 20 :
If $9k -6,\ 5 k - 4\ , 6k - 17\ $ are in AP then the value of k is