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question_answer1)
In which of the following situations, does the list of numbers involved does not make an arithmetic progression?
(i) The taxi fare after each km when the fare is Rs. 20 for the first km and Rs. 11 for each additional km. |
(ii) The amount of air present in a cylinder when a vacuum pump removes \[\frac{1}{4}\]of the air remaining in the cylinder at a time. |
(iii) The cost of digging a well after every metre of digging, when it cost Rs. 250 for the metre and rises by Rs. 40 for each subsequent metre. |
(iv) The amount of money in the account every year, when Rs. 8000 is deposited at compound interest at 10% per annum. |
A)
(i) & (ii) done
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B)
(ii) & (iv) done
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C)
(iii) & (i) done
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D)
(i) & (iv) done
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question_answer2)
Which of the following are APs?
(i) \[\sqrt{2},\sqrt{8},\sqrt{18},\sqrt{32},....\] |
(ii) \[\sqrt{3},\sqrt{6},\sqrt{9},\sqrt{12},....\] |
(iii) \[{{1}^{2}},{{3}^{2}},{{5}^{2}},{{7}^{2}},.....\] |
(iv) \[{{1}^{2}},{{5}^{2}},{{7}^{2}},73,.....\] |
A)
(i) & (ii) done
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B)
(i) & (iii) done
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C)
(i) & (iv) done
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D)
(ii) & (iv) done
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question_answer3)
Choose the correct choice in the following 11th term of the\[AP-3,-\frac{1}{2},2,\]....... is
A)
28 done
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B)
22 done
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C)
- 38 done
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D)
\[-48\frac{1}{2}\] done
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question_answer4)
Which term of the AP 3, 8, 13, 18,..........is 78?
A)
10th done
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B)
12th done
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C)
14th done
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D)
16th done
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question_answer5)
Find the number of terms in the following AP: \[18,15\frac{1}{2},13,......-47\]
A)
21 done
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B)
25 done
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C)
31 done
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D)
27 done
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question_answer6)
150 is a term of the AP 11, 8, 5, 2,.........
A)
yes done
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B)
no done
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C)
- 148 is not a term of this A.P. done
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D)
- 149 is a term of this AP. done
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question_answer7)
If the 3rd and 9th terms of an AP are 4 and - 8 respectively, which term of this AP is zero?
A)
4th done
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B)
5th done
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C)
6th done
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D)
7th done
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question_answer8)
Which term of the AP 3, 15, 27, 39,......will be 132 more than its 54th term?
A)
55th done
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B)
60th done
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C)
65th done
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D)
70th done
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question_answer9)
Two APs have the same common difference. The difference between their 100th terms is 100, what is the difference between their 1000th terms?
A)
100 done
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B)
1000 done
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C)
1200 done
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D)
10000 done
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question_answer10)
How many three digit numbers are divisible by 7?
A)
102 done
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B)
114 done
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C)
126 done
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D)
128 done
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question_answer11)
For what value of n, are the nth terms of the APs 63, 65, 67,... and 3, 10, 17 equal?
A)
n = 6 done
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B)
n = 12 done
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C)
n = 13 done
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D)
n = 16 done
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question_answer12)
Find the 20th term from the last term of the AP 3, 8, 13,.?. 253.
A)
196 done
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B)
158 done
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C)
148 done
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D)
138 done
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question_answer13)
The sum of the 4th and 8th terms of an AP is 24 and the sum of the 6th and 10th terms is 44. Find the first three terms of the AP.
A)
- 13, - 8, - 3 done
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B)
- 24, - 18, -12 done
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C)
6, 12, 18 done
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D)
0, 2, 4 done
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question_answer14)
Given \[a=3,d=10,{{S}_{n}}=168\] find n and \[{{a}_{6}}\].
A)
6, 53 done
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B)
7, 54 done
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C)
8, 86 done
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D)
9, 90 done
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question_answer15)
In the series, \[{{T}_{n}}=2n+5\], find \[{{S}_{4}}\].
A)
20 done
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B)
40 done
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C)
60 done
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D)
80 done
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question_answer16)
Find the 21st term of an AP whose first term is 4 and the common difference is 3.
A)
57 done
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B)
60 done
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C)
66 done
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D)
64 done
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question_answer17)
Find the sum of 100 terms of the series \[1\left( 3 \right)+3\left( 5 \right)+5\left( 7 \right)+.....\]
A)
1353300 done
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B)
1253300 done
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C)
1453300 done
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D)
1753300 done
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question_answer18)
Divide 124 into four parts in such way that they are in AP and the product of the first and the 4th part is 128 less than the product of the 2nd and the 3rd parts, the parts are:
A)
27, 35, 45, 17 done
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B)
19, 27, 35, 43 done
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C)
21, 29, 33, 41 done
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D)
13, 33, 37, 41 done
clear
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question_answer19)
If \[\left| x \right|<1\], then find the sum of the series \[1+2x+3{{x}^{2}}+4{{x}^{3}}+\] ....... up to \[\infty \]
A)
\[\frac{2}{1-{{x}^{2}}}\] done
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B)
\[\frac{3}{{{(1-x)}^{2}}}\] done
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C)
\[\frac{x}{1-{{x}^{2}}}\] done
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D)
\[\frac{x}{{{(1-x)}^{2}}}\] done
clear
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question_answer20)
If \[\frac{5+9+13+....to\,\,n\,\,terms}{7+9+11+.....to\,\,(n+1)terms}=\frac{17}{16}\] then n =
A)
7 done
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B)
9 done
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C)
11 done
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D)
13 done
clear
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question_answer21)
Find the 20th term of the HP \[-2,6,\frac{6}{5},\frac{2}{3},.....\]
A)
\[\frac{3}{13}\] done
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B)
\[\frac{6}{73}\] done
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C)
\[\frac{3}{87}\] done
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D)
\[\frac{6}{97}\] done
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question_answer22)
For a sequence in AP, the sum of n terms of the sequence is \[3n-{{n}^{2}}\], then find the 101st term of the sequence,
A)
201 done
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B)
- 201 done
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C)
- 198 done
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D)
+ 198 done
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question_answer23)
Find the three numbers which are in GP such that their is 31 and their product is 125. The three numbers are:
A)
(1, 5, 25) done
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B)
(6, 32, 128) done
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C)
(4, 10, 17) done
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D)
(2, 8, 21) done
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question_answer24)
There is a sequence of slumbers such that they are m GP and sum to infinite of the numbers of terms of the sequence is 6 and the sum of their squares up to infinite terms is 18. The first term of the sequence is given by:
A)
16 done
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B)
4 done
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C)
6 done
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D)
1/3 done
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question_answer25)
If the three terms p, q, t are the\[{{\text{m}}^{\text{th}}}\],\[{{\text{n}}^{\text{th}}}\] and \[~{{\text{s}}^{\text{th}}}\]terms of GP. Then, the value of \[{{p}^{n-s}}.{{q}^{s-m}}.{{r}^{m-n}}\]
A)
1 done
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B)
2 done
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C)
4 done
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D)
0 done
clear
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question_answer26)
The harmonic mean between two numbers is \[9\frac{8}{13}\] and geometric mean is 25. The two numbers are:
A)
(6 and 16) done
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B)
(6 and 60) done
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C)
(5 and 125) done
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D)
(8 and 216) done
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question_answer27)
If\[{{\text{p}}^{\text{th}}}\] term of HP is equal to q and the \[{{\text{q}}^{\text{th}}}\]term of HP is equal to p, then \[{{\left( p+q \right)}^{th}}\] term of the series is
A)
\[\frac{pq}{p+q}\] done
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B)
\[\frac{{{p}^{2}}-{{q}^{2}}}{p+q}\] done
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C)
\[\frac{{{p}^{2}}-{{q}^{2}}}{p-q}\] done
clear
D)
\[\frac{{{p}^{2}}-{{q}^{2}}}{{{p}^{3}}-{{q}^{3}}}\] done
clear
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question_answer28)
If in an A.P., \[{{S}_{n}}={{n}^{2}}p\] and \[{{S}_{m}}={{m}^{2}}p\], where \[{{S}_{r}}\] denotes the sum of r terms of the A.P., then \[{{S}_{p}}\] is equal to
A)
\[(m-n){{p}^{2}}\] done
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B)
\[{{p}^{3}}\] done
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C)
\[{{p}^{2}}m\] done
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D)
\[\frac{1}{8}{{p}^{3}}\] done
clear
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question_answer29)
A number of bricks are arranged in a compete pyramid on a square base of side 13 cm. when each brick is a cube of 1 cm, then total number of bricks used, is given by
A)
1027 done
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B)
819 done
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C)
313 done
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D)
727 done
clear
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question_answer30)
Insert two harmonic means between \[\frac{1}{20}\] and \[\frac{1}{32}\]
A)
\[\frac{1}{24},\frac{1}{26}\] done
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B)
\[\frac{1}{24},\frac{1}{28}\] done
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C)
\[\frac{1}{26},\frac{1}{30}\] done
clear
D)
\[\frac{1}{30},\frac{1}{31}\] done
clear
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