Series

Q.

If $n^{th}$ term of a series be $3+n\left(n-1\right)$, then the sum of $n$ terms of the series is:

1. $\frac{n^2+n}{3}$

2. $\frac{n^3+8n}{3}$

3. $\frac{n^2+8n}{5}$

4. $\frac{n^2-8n}{3}$

Q. Identify the missing term in the sequence:
7, 12, 19, , 39.

1. 24
2. 31
3. 28
4. 26

Q.

The interval (2, 4] written in set builder form is

1. {x : 2 < x < 4}

2. {x : 2 < x ≤ 4}

3. {x : 2 ≤ x < 4}

4. {x : 2 ≤ x ≤ 4}

Q.

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

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Q.

If $4+7+2=281435,7+3+9=212781,6+2+7=121456$ then $8+4+6=?$

Q.

Find the number of common terms to the sequences 2, 4, 6, ...... 100 and 3, 6, 9, ...... 99

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Q. Find the sum of the following series up to n terms: (i) 5 + 55 + 555 + … (ii) .6 +.66 +. 666 +…

Q.

How many terms of the A.P, -6, $\frac{-11}{2},-5$ ........... are needed to give the sum -25 ?

Q. Find the sum of n terms of the series 5+11+19+29+41

Q.

Select the option for "?" that continues the pattern in question $7$, $16$, $8$, $27$, $9$, ?

1. $27$

2. $10$

3. $40$

4. $37$

Q. The number of arrangements of the word "DELHI" in which E precedes I is
(a) 30
(b) 60
(c) 120
(d) 59

Q. The sum to 5 terms of the series $\frac{3}{1^2}+\frac{5}{1^2+2^2}+\frac{7}{1^2+2^2+3^2}+...$ is

1. $5$
2. $6$
3. $8$
4. $10$

Q. Find the 20 th term in the following sequence whose n th term is

Q. Find the 20 th term of the series 2 × 4 + 4 × 6 + 6 × 8 + … + n terms.

Q. 12.a, --1, an, n2

Q. Write the sum to n terms of the series $\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{n(n+1)}$.

Q. Last month a certain music club offered a discount to preferred customers. After the first compact disc purchased, preferred customers paid 3.99$foreachadditionalcompactdiscpurchased.Ifapreferredcustomerpurchasedatotalof$6$compactdiscsandpaid$\ $15.95$ for the first compact disc, then the dollar amount that the customer paid for the $6$ compact discs is equivalent to which of the following?

1. $5\left(4.00\right)+15.90$
2. $5\left(4.00\right)+15.95$
3. $5\left(4.00\right)+16.00$
4. $5(4.00-0.01)+15.90$
5. $5(4.00-0.05)+15.95$

Q. How many words, with or without meaning can be formed from the letters of the word 'MONDAY', assuming that no letter is repeated, if (i) 4 letters are used at a time (ii) all letters are used at a time (iii) all letters are used but first letter is a vowel?

Q.

In how many ways, can the letters of the word PENCIL be arranged so that

1) N is always next to E

2) N and E are always together.

Q.

1. $T_{12}=T_{13}$
2. $\frac{15}{11x^2}\cdot T_{11}=T_{12}$
3. $\frac{15}{23x^2}\cdot T_{12}=T_{13}$
4. $T_{12}+T_{13}=25$

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

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

Q. $\underset{x\to 1}{\lim }\frac{x^2-\sqrt{x}}{\sqrt{x}-1}$

Q.

$\frac{1}{1.2}$ + $\frac{1}{2.3}$ + $\frac{1}{3.4}$ +.......+ ......... $\frac{1}{n.(n+1)}$ equals

1. $\frac{1}{n(n+1)}$

2. $\frac{n}{n+1}$

3. $\frac{2n}{n+1}$

4. $\frac{2}{n(n+1)}$

Q. How many numbers greater than 50000 can be formed using 2, 5, 5, 6, 7??

Q. M=$\{1,2,3,4,5,6,7\}$
Each number in set $N$ is generated by dividing each number in set $M$ by $2$. Calculate the arithmetic mean of numbers in $N$.

1. $1$
2. $\frac{3}{2}$
3. $\frac{7}{4}$
4. $2$
5. $4$

Q. 19. If a, b and c are in geometric progression, then a-b/b-c is equal to,

Q. In how many ways can the letters of the word 'ARRANGE' be arranged so that the two R's are never together?

Q. In how many ways can the letters of the word 'ARRANGE' be arranged so that the two R's are never together?