MCQ 11 Mark
$11^{th}$ term of an AP: $– 3,$ $-\frac{1}{2}$ $, 2, . . .$ is $...........$
- A
$28$
- ✓
$22$
- C
$-38$
- D
$-48\frac{1}{2}$
AnswerWe have given the AP: $– 3,$ $-\frac{1}{2}$, $2, . . .$
Here, $a = - 3,$ $d = a_2-a_1$ d = $\frac{-1}{2}-(-3)=\frac{-1}{2}+3=\frac{-1+6}{2}=\frac{5}{2}$ and $n = 11$
We know that, $a_n$ = a + (n – 1)d
Or, $a_{11}$ = - 3 + (11 – 1)$\times\frac{5}{2}$
$= - 3 + 10$$\times\frac{5}{2}$
$= -3 + 5$ $\times$ $5$
$= - 3 + 25$
$a_{11}$$= 22$
View full question & answer→MCQ 21 Mark
$30^{th}$ term of an AP: $10, 7, 4, ......$ is $..............$
AnswerWe have AP: $10, 7, 4,...$
Here, $a = 10, d = 7 - 10 = - 3$ and $n = 30$
We know:
$a_n$ $= a + (n - 1)d$
or, $a_{30}$ $= 10 + (30 - 1)(-3)$
$= 10 + 29(-3)$
$= 10 - 87$
$a_{30}$ $= -77$
View full question & answer→MCQ 31 Mark
Sum of first three terms of AP is $51$ and product of first and third term is $240$ . Then the common difference of the following is ................ AP.
View full question & answer→MCQ 41 Mark
If $n^{\text {th }}$ term of an AP is $3 n+1$ then its $30^{\text {th }}$ term is ............. .
View full question & answer→MCQ 51 Mark
If $n^{\text {th }}$ term of an $AP$ is $2 n+1$ then its sum of $n$ terms is ............. .
- A
$n(n-2)$
- ✓
$n(n+2)$
- C
$n(n+1)$
- D
$n(n-1)$
AnswerCorrect option: B. $n(n+2)$
$n(n+2)$
View full question & answer→MCQ 61 Mark
If $k+2,4 k-6,3 k-2$ are consecutive terms of AP then $k=\ldots \ldots . . . .$.
View full question & answer→MCQ 71 Mark
$10^{\text {th }}$ term of an AP $\sqrt{2}, \sqrt{8}, \sqrt{18}, \ldots$ is ........... .
- A
$\sqrt{162}$
- ✓
$\sqrt{200}$
- C
$\sqrt{242}$
- D
$\sqrt{288}$
AnswerCorrect option: B. $\sqrt{200}$
$\sqrt{200}$
View full question & answer→MCQ 81 Mark
Sum of first $n$ terms of AP are $a, 3 a, 5 a$, ...is .......... .
- A
$n a$
- B
$(2 n-1) a$
- ✓
$n^2 a$
- D
$n^2 a^2$
AnswerCorrect option: C. $n^2 a$
$n^2 a$
View full question & answer→MCQ 91 Mark
The common difference of two AP is same and difference of their ten lakhs term is $11222333$ . Then difference of their $100^{\text {th }}$ term is ............. .
- ✓
$11222333$
- B
$333222111$
- C
$222333111$
- D
$333111222$
AnswerCorrect option: A. $11222333$
$11222333$
View full question & answer→MCQ 101 Mark
The numbers $2,7$ and $k+4$ are in AP then $k=$ ........... .
View full question & answer→MCQ 111 Mark
The $n^{\text {th }}$ term of an AP $8,3,-2, \ldots$ is ........... .
- A
$-2+3 n$
- B
$5-13 n$
- ✓
$13-5 n$
- D
$8+3 n$
AnswerCorrect option: C. $13-5 n$
$13-5 n$
View full question & answer→MCQ 121 Mark
For an AP it $a=-7.2, d=3.6$ and $a_n=7.2$ then $n=\ldots \ldots . .$.
View full question & answer→MCQ 131 Mark
The sum of first $16$ terms of an AP $10,6,2, \ldots$ is .......... .
- ✓
$-320$
- B
$320$
- C
$-352$
- D
$-400$
AnswerCorrect option: A. $-320$
$-320$
View full question & answer→MCQ 141 Mark
The $10^{\text {th }}$ term of AP $5,8,11,14, \ldots$ is ............ .
View full question & answer→MCQ 151 Mark
The sum of first $10$ terms of AP $-5,-2,-1, \ldots$ is ......... .
View full question & answer→MCQ 161 Mark
If $n^{\text {th }}$ term of AP is $6 n-4$ then common difference is ............ .
View full question & answer→MCQ 171 Mark
For an arithmetic progression if $a_{18}-a_{14}=32$ then $d=\ldots \ldots . . .$.
View full question & answer→MCQ 181 Mark
For an AP if $a_1=1, a_n=20$ and $S _n=399$ then $n=\ldots \ldots \ldots$.
View full question & answer→MCQ 191 Mark
For an AP $21, 42, 63, 84, ..., ..........$ term is $210$ .
- A
$9^{\text {th }}$ term
- ✓
$10^{\text {th }}$ term
- C
$11^{\text {th }}$ term
- D
$8^{\text {th }}$ term
AnswerCorrect option: B. $10^{\text {th }}$ term
$10^{\text {th }}$ term
View full question & answer→MCQ 201 Mark
If $\frac{6}{5}, a$, and 4 are in AP then $a=$ ............
- A
$1$
- B
$13$
- ✓
$\frac{13}{5}$
- D
$\frac{25}{6}$
AnswerCorrect option: C. $\frac{13}{5}$
$\frac{13}{5}$
View full question & answer→MCQ 211 Mark
For an $AP -5, \frac{-5}{2}, 0, \frac{5}{2}, \ldots 11^{\text {th }}$ term is ............ .
View full question & answer→MCQ 221 Mark
If common difference of AP is 5 then $a_{18}-a_{13}=\ldots .$.
View full question & answer→MCQ 231 Mark
The sum of three consecutive terms of AP is $48$ . The product of first and last term is $252$ . Find the common difference $d$.
View full question & answer→MCQ 241 Mark
If $S _1=2+4+\ldots+2 n$ and $S _2=1+3+5 \ldots+(2 n-1)$ then $S _1: S _2=\ldots \ldots \ldots$.
- ✓
$\frac{(n+1)}{n}$
- B
$\frac{n}{(n+1)}$
- C
$n^2$
- D
$n+1$
AnswerCorrect option: A. $\frac{(n+1)}{n}$
$\frac{(n+1)}{n}$
View full question & answer→MCQ 251 Mark
For an AP the possible value of $S _n-2 S _{n-1}+ S _{n-2}$ is .............
View full question & answer→MCQ 261 Mark
If $a_4=7, a_7=4$ then $a_{10}=$ ............. .
View full question & answer→MCQ 271 Mark
$2 k+1,13,5 k-3$ are consecutive terms of an AP then find $k$.
View full question & answer→MCQ 281 Mark
For an AP $5, 7, 9, 11, 13, 15,$ sixth prime number is ...........
View full question & answer→MCQ 291 Mark
For an AP if $a_{25}-a_{20}=15$ then $d=$ .............
View full question & answer→MCQ 301 Mark
For an AP value of $a_{18}-a_8$ is ............. .
AnswerCorrect option: B. $10 d$
$10 d$
View full question & answer→MCQ 311 Mark
Find the four numbers in AP whose sum is $72$ and in which the greatest number is twice the least.
- A
$4,8,12,16$
- ✓
$12,16,20,24$
- C
$10,12,14,16$
- D
$2, 4, 6, 8$
AnswerCorrect option: B. $12,16,20,24$
$12,16,20,24$
View full question & answer→MCQ 321 Mark
If $a =2$ and $d =4$ then find $S _{20}=$ ?
View full question & answer→MCQ 331 Mark
If $S _n=2 n^2+3 n$ then find $d$.
View full question & answer→MCQ 341 Mark
If $a_3=8$ and $a_7=24$ then find $a_{10}$.
View full question & answer→MCQ 351 Mark
Which of the following is not an AP ?
- A
$1,2,3,4, \ldots$
- B
$2,5,8,11, \ldots$
- ✓
$1, \frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \ldots$
- D
$1, \frac{1}{2}, 0,-\frac{1}{2}, \ldots$
AnswerCorrect option: C. $1, \frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \ldots$
$1, \frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \ldots$
View full question & answer→MCQ 361 Mark
Which of the following list is an $AP$ ?
- A
$2, 4, 5, 8$
- B
$3,5,7,11$
- ✓
$3.5,5,6.5,8, \ldots$
- D
$1,4,9,16, \ldots$
AnswerCorrect option: C. $3.5,5,6.5,8, \ldots$
$3.5,5,6.5,8, \ldots$
View full question & answer→MCQ 371 Mark
$11^{\text {th }}$ term of the $AP -3,-\frac{1}{2}, 2, \ldots$ is
- A
$28$
- ✓
$22$
- C
$-38$
- D
$-48 \frac{1}{2}$
View full question & answer→MCQ 381 Mark
$30^{\text {th }}$ term of the AP $10,7,4, \ldots$ is
View full question & answer→MCQ 391 Mark
Sum of first $n$ terms of A.P. $\sqrt{2}, \sqrt{8}, \sqrt{18}, \sqrt{32}$ is _______
AnswerCorrect option: C. $\frac{n(n+1)}{\sqrt{2}}$
$\frac{n(n+1)}{\sqrt{2}}$
View full question & answer→MCQ 401 Mark
$11^{\text {th }}$ teram is in $AP 2,7,12, \ldots$.
View full question & answer→MCQ 411 Mark
For A.P. $a=10$ and common difference $d=10$ then $a_{11}=$ _______
View full question & answer→MCQ 421 Mark
For any $AP a_{20}=$ _______
- A
$a+20 d$
- B
$a-20 d$
- ✓
$a+19 d$
- D
$a-19 d$
AnswerCorrect option: C. $a+19 d$
$a+19 d$
View full question & answer→MCQ 431 Mark
Common difference is of AP : $4,9,14, \ldots$.
View full question & answer→MCQ 441 Mark
For, AP $2,$ $\square, 26$ then what is the missing terms in the box.
View full question & answer→MCQ 451 Mark
For any AP,$a_{10}=$..........
View full question & answer→MCQ 461 Mark
The common difference of the A.P. $\frac{1}{3 q}, \frac{1-6 q}{3 q}, \frac{1-12 q}{3 q}, \ldots .$. is
Answer(c) : The common difference of the A.P.
$\frac{1}{3 q}, \frac{1-6 q}{3 q}, \frac{1-12 q}{3 q}, \ldots . .$. , is given by
$
\frac{1-6 q}{3 q}-\frac{1}{3 q}=\frac{1-6 q-1}{3 q}=\frac{-6 q}{3 q}=-2
$
View full question & answer→MCQ 471 Mark
If $k, 2 k-1$ and $2 k+1$ are three consecutive terms of an $A.P.,$ then the value of $k$ is
AnswerWe have, $k, 2 k-1$ and $2 k+1$ are three consecutive terms of an $A.P.$
$\therefore (2 k-1)-(k)=(2 k+1)-(2 k-1)$
$\Rightarrow k-1=2$
$\Rightarrow k=3$
View full question & answer→MCQ 481 Mark
The next term of the $A.P. \sqrt{18}, \sqrt{50}, \sqrt{95}, \ldots$ is
- A
$\sqrt{146}$
- B
$\sqrt{128}$
- ✓
$\sqrt{162}$
- D
$\sqrt{200}$
AnswerCorrect option: C. $\sqrt{162}$
Common difference $(d)$ of $A.P. \sqrt{18}, \sqrt{50}$, $\sqrt{95}, \ldots$, is given by
$\sqrt{50}-\sqrt{18}=\sqrt{2 \times 25}-\sqrt{2 \times 9}=5 \sqrt{2}-3 \sqrt{2}=2 \sqrt{2}$
$\therefore$ Fourth term$, a_4=a+3 d=\sqrt{18}+3 \times(2 \sqrt{2})$
$\quad=3 \sqrt{2}+6 \sqrt{2}=9 \sqrt{2}=\sqrt{2 \times 81}=\sqrt{162}$
View full question & answer→MCQ 491 Mark
The value of $a_{30}-a_{20}$ for the A.P. $2,7,12,17, \ldots$ is
Answer(c) : Given A.P. is $2,7,12,17, \ldots .$.
Here, $a=2, d=7-2=5$
Since $n^{\text {th }}$ term of an A.P. is $a_n=a+(n-1) d$
$
\therefore a_{30}=a+29 d=2+29(5)=147
$
and $a_{20}=a+19 d=2+19(5)=97$
Now, $a_{30}-a_{20}=147-97=50$
View full question & answer→MCQ 501 Mark
In an A.P., $a=-10, n=6$ and $a_n=10$, then the value of $d$ is
Riya and Diya said the following :
Riya : Common difference $=4$
Diya : Which of them is/are correct?
Answer(a) : Given, $a=-10, n=6, a_n=10$
Since, $a_n=a+(n-1) d$
$
\Rightarrow 10=-10+(6-1) d \Rightarrow 20=5 d \Rightarrow d=4
$
View full question & answer→