Series

Q.

What is the next term in the series $8,12,24,60...$?

Q. If the sum of first $11$ terms of an A.P., $a_1,a_2,a_3,.....$ is $0(a_1\ne 0)$ then the sum of the A.P., $a_1,a_3,a_5,....,a_{23}$ is $k{a}_1$, where $k$ is equal to:

1. $-\frac{121}{10}$
2. $-\frac{72}{5}$
3. $\frac{72}{5}$
4. $\frac{121}{10}$

Q.

If the sum of the first $2n$ terms of A.P $2,5,8,\dots$ is equal to the sum of the first $n$ terms of A.P $57,59,61,\dots .$, then $n$ is equal to:

1. $10$

2. $12$

3. $11$

4. $13$

Q. If $P=$ {$1,2$}, form the set $P\times P\times P$.

Q.

Find the missing number $3,3,6,18,72,360,?$.

Q. Find the sum of series to n terms:
$1\times 2+2\times 3+3\times 4+4\times 5+....$

Q. If $T_n=3n-1$ of an A.P., then

1. $a=2$
2. $d=3$
3. $T_5=15$
4. $S_3=15$

Q.

Let $x_1,x_2,\dots x_n$ be in an AP. $x_1+x_4+x_9+x_{11}+x_{20}+x_{22}+x_{27}+x_{30}=272$ then $x_1+x_3+\dots +x_{30}$ is equal to

1. $1020$

2. $1200$

3. $716$

4. $2720$

Q. Sum of the series $3,9,27,...$ upto $6$ terms

1. $512$
2. $1092$
3. $364$
4. $728$

Q. The value of expression
$3(1!)-4(2!)+5(3!)-6(4!)+.....-2008(2006!)+(2007!)$ is

1. $-2007$
2. $-1$
3. $2007$
4. $1$

Q.

Find the sum of the expressions

$2a^2+ab-b^2;-a^2+2ab+3b^2;3a^2-10ab+4b^2$

Q.

While catching fireflies, you and a friend decide to have a competition.

After $m$ minutes, you have $\left(3m+13\right)$ fireflies and your friend has $\left(4m+6\right)$ fireflies.

$a)$ How many fireflies are caught each minute during the competition?
$b)$ How many fireflies are caught before the competition starts?

Q. For all $n\ge 1$, prove that $1^2+2^2+3^2+4^2+\dots +n^2=\frac{n(n+1)(2n+1)}{6}$

Q. The A.M., G.M. and H.M. in any series are equal then

1. the distribution is symmetric
2. all the values are same
3. the distribution is unimodal
4. None of these

Q.

Solve: $\left(109\right)+(-75)$

Q. If the sum of $n$ terms of a series is given by $S_n=n^2-n,$ then its ${10}^{th}$ term is

Q. The sum of infinite terms of the following series $1+\frac{4}{5}+\frac{7}{5^2}+\frac{10}{5^3}+..$ will be

1. $\frac{3}{16}$
2. $\frac{25}{8}$
3. $\frac{35}{4}$
4. $\frac{35}{16}$

Q. If in a A.P. the third term is $3$, the sixth term is $5$ and $n^{th}$ term is $\frac{203}{3}$, then the value of $n$ is

Q. The sum of the series $\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{3.4}....$ upto $\infty$ is equal to

1. ${\log }_{e}2$
2. $2{\log }_{e}2$
3. ${\log }_e\left(\frac{4}{e}\right)$
4. ${\log }_{e}2-1$

Q. Fill in the blanks with the most appropriate word.
You're a brilliant cook! If I _____ cook as well as you, I _____ a restaurant.

1. Can / will open
2. Could / would open
3. Could / will open
4. Can / would open

Q. Find the sum of the series 3.6+4.7+5.8upto (n-2) terms.

Q.

The ${20}^{th}$ term of the series 2$\times$4+4$\times$6+6$\times$8+......... will be

1. 1600

2. 1680

3. 840

4. 420

Q. Find square of $31$

Q. Let $(1+x)(1+x+x^2)(1+x+x^2+x^3)......(1+x+x^2+....+x^{30})=a_0+a_{1}x+a_2{x}^2+........+a_{465}{x}^{465}$

then sum of $a_0+a_2+a_4+........+a_{464}$ is

1. $\left(31\right)!$
2. $\frac{\left(31\right)!}{2}$
3. $\left(30\right)!$
4. $\frac{\left(60\right)!}{2}$

Q. The sum of the series $1+\frac{1^2+2^2}{2!}+\frac{1^2+2^2+3^3}{3!}+\frac{1^2+2^2+3^2+4^2}{4!}+.....$ is

1. $\frac{17}{6}e$
2. 3e
3. $\frac{13}{6}e$
4. $\frac{19}{6}e$

Q. Give the answer in one word:
Write the formula of square root of a quantity $y$ by Newton-Raphson method.

Q. What is the least value of $n$ such that $(1+3+3^2+.....+3^n)$ exceeds $2000$?

1. $7$
2. $5$
3. $8$
4. $6$

Q. Solve: ${25}^{\frac{1}{2}},{100}^{\frac{1}{2}},{27}^{\frac{1}{3}}$

Q. The sum of the terms of two $A.P$ are in the ratio $(3n+8);(7n+15)$. Find the ratio of their $12th$ term.

Q.

In how many ways two students can exchange greeting cards to each other?

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