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question_answer1)
Which among the following is an Arithmetic progression?
A)
\[\frac{1}{2},\frac{7}{10},\frac{9}{10},1,....\] done
clear
B)
\[\sqrt{3},\sqrt{27},\sqrt{75},\sqrt{147},...\] done
clear
C)
\[{{2}^{3}},{{2}^{6}},{{2}^{9}},{{2}^{12}},...\] done
clear
D)
\[-\,2,\text{ }0,\,-2,\text{ }0,\,-2,\] done
clear
E)
None of these done
clear
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question_answer2)
If \[\mathbf{1}{{\mathbf{8}}^{\mathbf{th}}}\mathbf{term}\text{ }\mathbf{of}\text{ }\mathbf{an}\text{ }\mathbf{A}.\mathbf{P}.\text{ }\mathbf{is}\text{ }\mathbf{26}\text{ }\mathbf{and}\text{ }\mathbf{3}{{\mathbf{2}}^{\mathbf{th}}}\]of an A.P. is - 16, of the A.P. is______
A)
\[-\]51 done
clear
B)
51 done
clear
C)
\[-\]27 done
clear
D)
77 done
clear
E)
None of these done
clear
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question_answer3)
Find the sum of n terms of the series whose \[{{n}^{th}}\] term is 3n - 2.
A)
\[\frac{n}{2}(3n-1)\] done
clear
B)
\[\frac{n}{2}(3n+1)\] done
clear
C)
\[\frac{n}{2}(3n-3)\] done
clear
D)
\[\frac{n}{2}(2n-1)\] done
clear
E)
None of these done
clear
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question_answer4)
If \[{{\mathbf{S}}_{\mathbf{n}}}\]of a series is \[\frac{\mathbf{35n}}{\mathbf{2}}\mathbf{-}\frac{\mathbf{7}{{\mathbf{n}}^{\mathbf{2}}}}{\mathbf{2}}\] then find its 7th term.
A)
-21 done
clear
B)
35 done
clear
C)
18 done
clear
D)
-28 done
clear
E)
None of these done
clear
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question_answer5)
The sum of the first three terms \[\mathbf{(}{{\mathbf{S}}_{\mathbf{3}}}\mathbf{)}\] of on A.P. is 108 and if it is given that \[{{\mathbf{a}}_{\mathbf{1}}}{{\mathbf{a}}_{\mathbf{2}}}+\text{ }{{\mathbf{S}}_{\mathbf{3}}}\]= 0 then find the value of its seventh term where \[{{a}_{1}},\text{ }{{a}_{2}}\] are first and second term of the A.P.
A)
225 done
clear
B)
231 done
clear
C)
216 done
clear
D)
229 done
clear
E)
None of these done
clear
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question_answer6)
The trees of a row of a garden are numbered consecutively from 1 to 49. There is a value of p such that the sum of the numbers of trees preceding the tree numbered p is equal to the sum of the numbers of the houses following it, then value of p is:
A)
25 done
clear
B)
35 done
clear
C)
28 done
clear
D)
22 done
clear
E)
None of these done
clear
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question_answer7)
Find the sum of all three-digit numbers which are divisible by 3.
A)
165150 done
clear
B)
195240 done
clear
C)
199950 done
clear
D)
201750 done
clear
E)
None of these done
clear
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question_answer8)
The sum of the 7th and 9th term of an A.P. is 82 and the 10th term is 56. The first term of this A.P. is _______
A)
7.5 done
clear
B)
\[-\]7.5 done
clear
C)
\[-\]11.5 done
clear
D)
15 done
clear
E)
None of these done
clear
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question_answer9)
Split 312 into three distinct parts such that these are in A.P. and the product of its smeller parts is 9880. Find the value of its largest part.
A)
102 done
clear
B)
109 done
clear
C)
113 done
clear
D)
108 done
clear
E)
None of these done
clear
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question_answer10)
If \[\mathbf{1}{{\mathbf{2}}^{\mathbf{th}}}\]term of an A.P. is zero then its \[\mathbf{2}{{\mathbf{2}}^{\mathbf{nd}}}\] term is one third of its ________
A)
\[{{45}^{th}}\] term done
clear
B)
\[{{36}^{th}}term\] done
clear
C)
\[{{44}^{th}}term\] done
clear
D)
\[{{42}^{nd}}term\] done
clear
E)
None of these done
clear
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question_answer11)
Find the sum of those numbers, which lie between 400 and 900 (including both) and leave a remainder 4 on dividing by 7.
A)
41302 done
clear
B)
46609 done
clear
C)
46908 done
clear
D)
48708 done
clear
E)
None of these done
clear
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question_answer12)
If\[\frac{{{\mathbf{p}}^{\mathbf{n-1}}}\mathbf{+}{{\mathbf{q}}^{\mathbf{n-1}}}}{{{\mathbf{p}}^{\mathbf{n-2}}}\mathbf{+}{{\mathbf{q}}^{\mathbf{n-2}}}}\]is the arithmetic mean between p and q then find the value of n.
A)
0 done
clear
B)
1 done
clear
C)
2 done
clear
D)
3 done
clear
E)
None of these done
clear
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question_answer13)
The sum of first eight terms of an A.P. is 66 and the ratio of its \[\mathbf{1}{{\mathbf{3}}^{\mathbf{th}}}\]term to its \[\mathbf{2}{{\mathbf{1}}^{\mathbf{st}}}\]term is 7:11. Find the sum of first 31 terms of this A.P.
A)
885 done
clear
B)
765 done
clear
C)
668 done
clear
D)
826 done
clear
E)
None of these done
clear
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question_answer14)
If the \[{{\mathbf{p}}^{\mathbf{th}}}\]term of an A.P. is \[\frac{\mathbf{1}}{\mathbf{q}}\] and \[{{\mathbf{q}}^{\mathbf{th}}}\]term is \[\frac{\mathbf{1}}{\mathbf{p}}\] then sum of its pq terms is
A)
\[\frac{1}{2}(p+q)\] done
clear
B)
\[\frac{1}{2}(pq+1)\] done
clear
C)
\[\frac{1}{2}pq\] done
clear
D)
\[\frac{1}{2}q\] done
clear
E)
None of these done
clear
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question_answer15)
If the ratio of the sums of \[{{\mathbf{m}}^{\mathbf{2}}}\] and \[{{\mathbf{n}}^{\mathbf{2}}}\] of an AP is \[{{\mathbf{m}}^{\mathbf{3}}}:\text{ }{{\mathbf{n}}^{\mathbf{3}}}\], the of its \[{{\mathbf{m}}^{\mathbf{2}}}\] and \[{{\mathbf{n}}^{\mathbf{2}}}\] terms is ______
A)
\[\frac{2{{m}^{2}}+mn}{2{{n}^{2}}+mn}\] done
clear
B)
\[\frac{2{{m}^{2}}+mn-1}{2{{n}^{2}}+mn-1}\] done
clear
C)
\[\frac{{{m}^{2}}+mn-2}{{{n}^{2}}+mn-2}\] done
clear
D)
\[\frac{2{{m}^{2}}+mn+1}{2{{n}^{2}}+mn+1}\] done
clear
E)
None of these done
clear
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question_answer16)
If there are (2n - 1) terms in an A.P., the of the of its terms to its even terms is _____
A)
\[\frac{n+1}{n}\] done
clear
B)
\[\frac{n-1}{n}\] done
clear
C)
\[\frac{n}{n-1}\] done
clear
D)
\[\frac{n}{n+1}\] done
clear
E)
None of these done
clear
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question_answer17)
315 workers were engaged to finish a piece of work in a fixed number of days. Four workers were dropped the second day, four more workers were dropped the third day and so on. Thus, it took 8 more days to complete the work. Find the number of days in which the work was completed.
A)
33 done
clear
B)
42 done
clear
C)
36 done
clear
D)
39 done
clear
E)
None of these done
clear
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question_answer18)
The ratio of the sum of n terms of two arithmetic progressions is (5n + 1): (2n + 15). Find the ratio of their \[{{\mathbf{m}}^{\mathbf{th}}}\]terms.
A)
\[\frac{10m-4}{4m+13}\] done
clear
B)
\[\frac{5m+3}{7m+11}\] done
clear
C)
\[\frac{7m-3}{5m+13}\] done
clear
D)
\[\frac{4m-5}{3n+11}\] done
clear
E)
None of these done
clear
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question_answer19)
In an A.P., the sum of its first n terms is \[\frac{\mathbf{5}{{\mathbf{n}}^{\mathbf{2}}}}{\mathbf{3}}\mathbf{+}\frac{\mathbf{13n}}{\mathbf{5}}\]. Find its \[{{\mathbf{n}}^{\mathbf{th}}}\]terms.
A)
\[\frac{50n-14}{15}\] done
clear
B)
\[\frac{50n+14}{15}\] done
clear
C)
\[\frac{64(2n-1)}{15}\] done
clear
D)
\[\frac{64(2n+1)}{15}\] done
clear
E)
None of these done
clear
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question_answer20)
If the sum of m, 2m, 3m terms of an A.P. are \[{{\mathbf{S}}_{\mathbf{1}}},{{\mathbf{S}}_{\mathbf{2}}},{{\mathbf{S}}_{\mathbf{3}}}\] respectively, then (\[{{\mathbf{S}}_{\mathbf{2}}}-{{\mathbf{S}}_{\mathbf{1}}}\]) equals to __
A)
2\[{{S}_{3}}\] done
clear
B)
3\[{{S}_{3}}\] done
clear
C)
\[\frac{{{s}_{3}}}{2}\] done
clear
D)
\[\frac{{{s}_{3}}}{3}\] done
clear
E)
None of these done
clear
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question_answer21)
If the sum of the first m, n, r terms of an A.P. are a, b, c respectively, then\[\frac{\mathbf{a}}{\mathbf{3}}\mathbf{(n-r)+}\frac{\mathbf{b}}{\mathbf{n}}\mathbf{(r-m)+}\frac{\mathbf{c}}{\mathbf{r}}\mathbf{(m-n)}\] equals to ________
A)
0 done
clear
B)
1 done
clear
C)
m + n + r done
clear
D)
2 done
clear
E)
None of these done
clear
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question_answer22)
If sum of first p terms of an A.P. is equal to q and the sum of first q terms of it is equal to p, then find the sum of (p + q) terms of this A.P.
A)
\[p+q\] done
clear
B)
\[-\left( p\text{ }+\text{ }q \right)\] done
clear
C)
\[\text{ }p+q\] done
clear
D)
1 done
clear
E)
None of these done
clear
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question_answer23)
If \[\mathbf{1}{{\mathbf{9}}^{\mathbf{th}}}\] term of an A.P. is 544 and \[\mathbf{54}{{\mathbf{4}}^{\mathbf{th}}}\] term is 19 then find the term which is equal to zero?
A)
525 done
clear
B)
563 done
clear
C)
562 done
clear
D)
544 done
clear
E)
None of these done
clear
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question_answer24)
Sum of n terms of the series \[\sqrt{\mathbf{80}}\mathbf{,}\sqrt{\mathbf{45}}\mathbf{,}\sqrt{\mathbf{20}}\mathbf{,}.......\] is ______
A)
\[\frac{\sqrt{5n}}{2}(9-n)\] done
clear
B)
\[4\sqrt{5}(9-n)\] done
clear
C)
\[2\sqrt{5}(9-n)\] done
clear
D)
\[3\sqrt{5}(3-n)\] done
clear
E)
None of these done
clear
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question_answer25)
If p, q, r are in A.P., then q + r, r + p and p + q are in __
A)
arithmetic progression done
clear
B)
geometric progression done
clear
C)
harmonic progression done
clear
D)
arithmetic-geometric progression done
clear
E)
None of these done
clear
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question_answer26)
If \[{{\mathbf{a}}^{\mathbf{th}}},\text{ }{{\mathbf{b}}^{\mathbf{th}}}\mathbf{and}\text{ }{{\mathbf{c}}^{\mathbf{th}}}\]terms of an H.P. are p, q and r respectively, the value of \[\mathbf{qr}\,\,\left( \mathbf{b}-\mathbf{c} \right)+\mathbf{pr}\,\,\left( \mathbf{c}-\mathbf{a} \right)+\mathbf{pq}\text{ }\left( \mathbf{a}-\mathbf{b} \right)\]
A)
-1 done
clear
B)
1 done
clear
C)
0 done
clear
D)
2q done
clear
E)
None of these done
clear
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question_answer27)
If (a + 1), (b + 1), (c + 1), (d + 1) are in G.P., then \[{{\left( \mathbf{b}+\mathbf{c}+\mathbf{2} \right)}^{\mathbf{2}}}=\]_________
A)
(a + b + 2) (b + c + 2) done
clear
B)
\[\left( a\text{ }+\text{ }b\text{ }+\text{ }1 \right)\text{ }{{\left( c\text{ }+\text{ }d\text{ }+\text{ }1 \right)}^{2}}\] done
clear
C)
(a+b+2) (b+c+2) done
clear
D)
(a + b + 1) (b + c + 1) done
clear
E)
None of these done
clear
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question_answer28)
Find the value of P, if P = 1+ (1 + 2) + (1 + 2 + 3) + (1 + 2 + 3 + 4) +..... + (1 + 2+3+.....+25)
A)
2715 done
clear
B)
2925 done
clear
C)
3055 done
clear
D)
2655 done
clear
E)
None of these done
clear
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question_answer29)
Find the sum to n terms of the following series. 3 + 33 + 333 + .........
A)
\[\frac{10}{27}({{10}^{n}}-1)\] done
clear
B)
\[\frac{50}{81}({{10}^{n}}-1)-\frac{5n}{9}\] done
clear
C)
\[\frac{10}{27}({{10}^{n}}-1)-\frac{n}{3}\] done
clear
D)
\[\frac{50}{81}({{10}^{n}}-1)\] done
clear
E)
None of these done
clear
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question_answer30)
If the first and 10th terms of a G.P. are \[\frac{{{\mathbf{q}}^{\mathbf{6}}}}{{{\mathbf{q}}^{\mathbf{5}}}}\] and \[\frac{{{\mathbf{p}}^{\mathbf{4}}}}{{{\mathbf{q}}^{\mathbf{3}}}}\] , then find the ratio between its 6th to 7th term.
A)
\[\frac{{{q}^{2}}}{{{p}^{3}}}\] done
clear
B)
\[\frac{q}{{{p}^{2}}}\] done
clear
C)
\[\frac{q}{p}\] done
clear
D)
\[\frac{{{p}^{2}}}{q}\] done
clear
E)
None of these done
clear
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question_answer31)
If \[\mathbf{A=5+}\frac{\mathbf{5}}{\mathbf{B}}\mathbf{+}\frac{\mathbf{5}}{{{\mathbf{B}}^{\mathbf{2}}}}\mathbf{+}\frac{\mathbf{5}}{{{\mathbf{B}}^{\mathbf{3}}}}\mathbf{+}.....\infty \]then the value of B is________
A)
\[\frac{-A}{A-5}\] done
clear
B)
\[\frac{A}{A-5}\] done
clear
C)
\[\frac{A}{A+5}\] done
clear
D)
\[\frac{-A}{A+5}\] done
clear
E)
None of these done
clear
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question_answer32)
If \[\mathbf{Q=}\frac{\mathbf{3}}{\sqrt{\mathbf{3}}}\mathbf{+1+}\frac{\mathbf{1}}{\sqrt{\mathbf{3}}}\mathbf{+}\frac{\mathbf{1}}{\mathbf{3}}\mathbf{+}......\]\[\infty \]then find the value of \[\mathbf{Q}-\frac{\mathbf{1}}{\mathbf{Q}}\]
A)
\[\frac{3\sqrt{3}-1}{6}\] done
clear
B)
\[\frac{7\sqrt{3}+11}{6}\] done
clear
C)
\[\frac{3\sqrt{3}+1}{6}\] done
clear
D)
\[\frac{7\sqrt{3}-11}{6}\] done
clear
E)
None of these done
clear
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question_answer33)
Find the value of x (where \[\mathbf{o}{}^\circ <\mathbf{x}<\mathbf{90}{}^\circ )\]if \[\mathbf{3}{{\mathbf{2}}^{\mathbf{1}+\,\,\mathbf{sinx}\,+\,\,\mathbf{s}i{{\mathbf{n}}^{\mathbf{2}}}\mathbf{x}\,+\,\,......\infty }}\] =1024
A)
\[30{}^\circ \] done
clear
B)
\[45{}^\circ \] done
clear
C)
\[60{}^\circ \] done
clear
D)
\[15{}^\circ \] done
clear
E)
None of these done
clear
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question_answer34)
Find the value of 7th term of the series.
A)
\[\frac{-12}{11}\] done
clear
B)
\[-\]24 done
clear
C)
\[-\]16 done
clear
D)
\[\frac{-12}{7}\] done
clear
E)
None of these done
clear
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question_answer35)
If p, q and r are in Harmanic Progression, then, \[\frac{\mathbf{p}}{\mathbf{q+r}}\mathbf{,}\frac{\mathbf{q}}{\mathbf{p+r}}\] and \[\frac{\mathbf{r}}{\mathbf{p+q}}\] are in ______
A)
arithmetic progression done
clear
B)
geometric progression done
clear
C)
harmonic progression done
clear
D)
arithmetic-geometric progression done
clear
E)
None of these done
clear
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question_answer36)
If A, G and H are respectively arithmetic, geometric and harmonic means between two distinct positive real numbers p and q, then which one of the following is incorrect?
A)
\[{{G}^{2}}=AH\] done
clear
B)
\[A-G>0\] done
clear
C)
\[G-H>0\] done
clear
D)
\[A<G<H\] done
clear
E)
None of these done
clear
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question_answer37)
If p, q and r are the \[{{\mathbf{a}}^{\mathbf{th}}},\text{ }{{\mathbf{b}}^{\mathbf{th}}}\mathbf{and}\text{ }{{\mathbf{c}}^{\mathbf{th}}}\] terms respectively of an A.P. as well as G.P., then the value of \[{{\mathbf{p}}^{\mathbf{q}-\mathbf{r}}},\text{ }{{\mathbf{q}}^{\mathbf{r}-\mathbf{p}}},\text{ }{{\mathbf{r}}^{\mathbf{p}-\mathbf{q}}}\] equals to ______
A)
0 done
clear
B)
1 done
clear
C)
\[-\,1\] done
clear
D)
2 done
clear
E)
None of these done
clear
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question_answer38)
On inserting 5 Arithmetic means between 3 and 27, the sum of these five terms is equal to ______
A)
six times the A.M. between 3 and 27 done
clear
B)
five times the A.M. between 3 and 27 done
clear
C)
105 done
clear
D)
72 done
clear
E)
None of these done
clear
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question_answer39)
The Arithmetic Mean of two numbers is 5 more than geometric Mean and 9.8 more than harmonic mean. Find the numbers.
A)
20, 80 done
clear
B)
30, 120 done
clear
C)
90, 160 done
clear
D)
160, 250 done
clear
E)
None of these done
clear
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question_answer40)
If third and eighth terms of a Geometric progression are\[\frac{\mathbf{3}}{\mathbf{16}}\] and 6 respectively, then find the \[\mathbf{1}{{\mathbf{0}}^{\mathbf{th}}}\] term of the series.
A)
16 done
clear
B)
\[\frac{1}{8}\] done
clear
C)
\[\frac{1}{12}\] done
clear
D)
24 done
clear
E)
None of these done
clear
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