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question_answer1)
The fourth term in the expansion of \[{{(1-2x)}^{3/2}}\]will be [RPET 1989]
A)
\[-\frac{3}{4}{{x}^{4}}\] done
clear
B)
\[\frac{{{x}^{3}}}{2}\] done
clear
C)
\[-\frac{{{x}^{3}}}{2}\] done
clear
D)
\[\frac{3}{4}{{x}^{4}}\] done
clear
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question_answer2)
Cube root of 217 is
A)
6.01 done
clear
B)
6.04 done
clear
C)
6.02 done
clear
D)
None of these done
clear
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question_answer3)
The expansion of \[\frac{1}{{{(4-3x)}^{1/2}}}\]binomial theorem will be valid, if
A)
\[x<1\] done
clear
B)
\[|x|\,<1\] done
clear
C)
\[-\frac{2}{\sqrt{3}}<x<\frac{2}{\sqrt{3}}\] done
clear
D)
None of these done
clear
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question_answer4)
If \[{{(a+bx)}^{-2}}=\frac{1}{4}-3x+......\], then \[(a,b)\]= [UPSEAT 2002]
A)
(2, 12) done
clear
B)
\[(-2,12)\] done
clear
C)
\[(2,\,\,-12)\] done
clear
D)
None of these done
clear
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question_answer5)
\[\frac{1}{\sqrt[3]{6-3x}}=\]
A)
\[{{6}^{1/3}}\left[ 1+\frac{x}{6}+\frac{2{{x}^{2}}}{{{6}^{2}}}+.... \right]\] done
clear
B)
\[{{6}^{-1/3}}\left[ 1+\frac{x}{6}+\frac{2{{x}^{2}}}{{{6}^{2}}}+.... \right]\] done
clear
C)
\[{{6}^{1/3}}\left[ 1-\frac{x}{6}+\frac{2{{x}^{2}}}{{{6}^{2}}}-.... \right]\] done
clear
D)
\[{{6}^{-1/3}}\left[ 1-\frac{x}{6}+\frac{2{{x}^{2}}}{{{6}^{2}}}-.... \right]\] done
clear
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question_answer6)
\[{{\left( \frac{a}{a+x} \right)}^{\frac{1}{2}}}+{{\left( \frac{a}{a-x} \right)}^{\frac{1}{2}}}=\] [DCE 1994; Pb. CET 2002; AIEEE 2002]
A)
\[2+\frac{3{{x}^{2}}}{4{{a}^{2}}}+....\] done
clear
B)
\[1+\frac{3{{x}^{2}}}{8{{a}^{2}}}+....\] done
clear
C)
\[2+\frac{x}{a}+\frac{3{{x}^{2}}}{4{{a}^{2}}}+....\] done
clear
D)
\[2-\frac{x}{a}+\frac{3{{x}^{2}}}{4{{a}^{2}}}\]+...... done
clear
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question_answer7)
\[{{(r+1)}^{th}}\] term in the expansion of \[{{(1-x)}^{-4}}\]will be
A)
\[\frac{{{x}^{r}}}{r!}\] done
clear
B)
\[\frac{(r+1)(r+2)(r+3)}{6}{{x}^{r}}\] done
clear
C)
\[\frac{(r+2)(r+3)}{2}{{x}^{r}}\] done
clear
D)
None of these done
clear
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question_answer8)
In the expansion of \[{{\left( \frac{1+x}{1-x} \right)}^{2}}\], the coefficient of \[{{x}^{n}}\] will be
A)
\[4n\] done
clear
B)
\[4n-3\] done
clear
C)
\[4n+1\] done
clear
D)
None of these done
clear
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question_answer9)
\[\frac{1}{{{(2+x)}^{4}}}=\]
A)
\[\frac{1}{2}\left( 1-2x+\frac{5}{2}{{x}^{2}}-.... \right)\] done
clear
B)
\[\frac{1}{16}\left( 1-2x+\frac{5}{2}{{x}^{2}}-.... \right)\] done
clear
C)
\[\frac{1}{16}\left( 1+2x+\frac{5}{2}{{x}^{2}}+.... \right)\] done
clear
D)
\[\frac{1}{2}\left( 1+2x+\frac{5}{2}{{x}^{2}}+.... \right)\] done
clear
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question_answer10)
\[\frac{1}{{{\left( {{x}^{2}}+\frac{1}{x} \right)}^{\frac{4}{3}}}}\] can be expanded by binomial theorem, if
A)
\[x<1\] done
clear
B)
\[|x|<1\] done
clear
C)
\[x>1\] done
clear
D)
\[|x|>1\] done
clear
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question_answer11)
The coefficient of \[{{x}^{3}}\] in the expansion of \[\frac{{{(1+3x)}^{2}}}{1-2x}\] will be
A)
8 done
clear
B)
32 done
clear
C)
50 done
clear
D)
None of these done
clear
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question_answer12)
If \[|x|<1\]then the coefficient of \[{{x}^{n}}\] in the expansion of \[{{(1+x+{{x}^{2}}+....)}^{2}}\]will be [Pb. CET 1989]
A)
1 done
clear
B)
n done
clear
C)
\[n+1\] done
clear
D)
None of these done
clear
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question_answer13)
If \[|x|>1\], then \[{{(1+x)}^{-2}}\] =
A)
\[1-2x+3{{x}^{2}}-....\] done
clear
B)
\[1+2x+3{{x}^{2}}+\].... done
clear
C)
\[1-\frac{2}{x}+\frac{3}{{{x}^{2}}}-....\] done
clear
D)
\[\frac{1}{{{x}^{2}}}-\frac{2}{{{x}^{3}}}+\frac{3}{{{x}^{4}}}-\]... done
clear
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question_answer14)
If \[|x|<1\], then in the expansion of \[{{(1+2x+3{{x}^{2}}+4{{x}^{3}}+....)}^{1/2}},\] the coefficient of \[{{x}^{n}}\]is
A)
n done
clear
B)
\[n+1\] done
clear
C)
1 done
clear
D)
- 1 done
clear
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question_answer15)
The approximate value of \[{{(7.995)}^{1/3}}\]correct to four decimal places is [MNR 1991; UPSEAT 2000]
A)
1.9995 done
clear
B)
1.9996 done
clear
C)
1.9990 done
clear
D)
1.9991 done
clear
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question_answer16)
If \[|x|<1\], then the value of\[1+n\left( \frac{2x}{1+x} \right)+\frac{n(n+1)}{2!}{{\left( \frac{2x}{1+x} \right)}^{2}}+.....\infty \]will be [AMU 1983]
A)
\[{{\left( \frac{1+x}{1-x} \right)}^{n}}\] done
clear
B)
\[{{\left( \frac{2x}{1+x} \right)}^{n}}\] done
clear
C)
\[{{\left( \frac{1+x}{2x} \right)}^{n}}\] done
clear
D)
\[{{\left( \frac{1-x}{1+x} \right)}^{n}}\] done
clear
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question_answer17)
The sum of \[1+n\left( 1-\frac{1}{x} \right)+\frac{n(n+1)}{2!}\text{ }{{\left( 1-\frac{1}{x} \right)}^{2}}+.....\infty ,\] will be [Roorkee 1975]
A)
\[{{x}^{n}}\] done
clear
B)
\[{{x}^{-n}}\] done
clear
C)
\[{{\left( 1-\frac{1}{x} \right)}^{n}}\] done
clear
D)
None of these done
clear
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question_answer18)
The first four terms in the expansion of \[{{(1-x)}^{3/2}}\] are [RPET 1989]
A)
\[1-\frac{3}{2}x+\frac{3}{8}{{x}^{2}}-\frac{1}{16}{{x}^{3}}\] done
clear
B)
\[1-\frac{3}{2}x-\frac{3}{8}{{x}^{2}}-\frac{{{x}^{3}}}{16}\] done
clear
C)
\[1-\frac{3}{2}x+\frac{3}{8}{{x}^{2}}+\frac{{{x}^{3}}}{16}\] done
clear
D)
None of these done
clear
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question_answer19)
The coefficient of \[{{x}^{n}}\] in \[\frac{{{(1+x)}^{2}}}{{{(1-x)}^{3}}}\]is
A)
\[3{{n}^{2}}+2n+1\] done
clear
B)
\[2{{n}^{2}}+2n+1\] done
clear
C)
\[{{n}^{2}}+n+1\] done
clear
D)
\[2{{n}^{2}}-2n+1\] done
clear
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question_answer20)
\[1+\frac{1}{3}x+\frac{1.4}{3.6}{{x}^{2}}+\frac{1.4.7}{3.6.9}{{x}^{3}}+....\]is equal to
A)
x done
clear
B)
\[{{(1+x)}^{1/3}}\] done
clear
C)
\[{{(1-x)}^{1/3}}\] done
clear
D)
\[{{(1-x)}^{-1/3}}\] done
clear
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question_answer21)
\[1-\frac{1}{8}+\frac{1}{8}.\frac{3}{16}-\frac{1.3.5}{8.16.24}+.....\]= [EAMCET 1990]
A)
\[\frac{2}{5}\] done
clear
B)
\[\frac{\sqrt{2}}{5}\] done
clear
C)
\[\frac{2}{\sqrt{5}}\] done
clear
D)
None of these done
clear
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question_answer22)
If \[{{(r+1)}^{th}}\] term is the first negative term in the expansion of \[{{(1+x)}^{7/2}}\], then the value of r is
A)
5 done
clear
B)
6 done
clear
C)
4 done
clear
D)
7 done
clear
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question_answer23)
The coefficient of \[{{x}^{n}}\] in the expansion of \[{{(1-2x+3{{x}^{2}}-4{{x}^{3}}+.....)}^{-n}}\]is
A)
\[\frac{(2n)!}{n!}\] done
clear
B)
\[\frac{(2n)!}{{{(n!)}^{2}}}\] done
clear
C)
\[\frac{1}{2}\frac{(2n)!}{{{(n!)}^{2}}}\] done
clear
D)
None of these done
clear
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question_answer24)
The coefficient of \[{{x}^{n}}\]in the expansion of \[{{(1-9x+20{{x}^{2}})}^{-1}}\] is
A)
\[{{5}^{n}}-{{4}^{n}}\] done
clear
B)
\[{{5}^{n+1}}-{{4}^{n+1}}\] done
clear
C)
\[{{5}^{n-1}}-{{4}^{n-1}}\] done
clear
D)
None of these done
clear
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question_answer25)
The coefficient of \[{{x}^{n}}\] in the expansion of \[\frac{1}{(1-x)(3-x)}\] is
A)
\[\frac{{{3}^{n+1}}-1}{{{2.3}^{n+1}}}\] done
clear
B)
\[\frac{{{3}^{n+1}}-1}{{{3}^{n+1}}}\] done
clear
C)
\[\left( \frac{{{3}^{n+1}}-1}{{{3}^{n+1}}} \right)\] done
clear
D)
None of these done
clear
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question_answer26)
The coefficient of \[{{x}^{n}}\] in the expansion of \[{{(1+x+{{x}^{2}}+....)}^{-n}}\] is
A)
1 done
clear
B)
\[{{(-1)}^{n}}\] done
clear
C)
n done
clear
D)
\[n+1\] done
clear
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question_answer27)
If \[y=3x+6{{x}^{2}}+10{{x}^{3}}+....,\]then the value of x in terms of y is
A)
\[1-{{(1-y)}^{-1/3}}\] done
clear
B)
\[1-{{(1+y)}^{1/3}}\] done
clear
C)
\[1+{{(1+y)}^{-1/3}}\] done
clear
D)
\[1-{{(1+y)}^{-1/3}}\] done
clear
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question_answer28)
The coefficient of \[x\] in the expansion of \[{{[\sqrt{1+{{x}^{2}}}-x]}^{-1}}\]in ascending powers of x, when \[|x|<1\], is [MP PET 1996]
A)
0 done
clear
B)
\[\frac{1}{2}\] done
clear
C)
\[-\frac{1}{2}\] done
clear
D)
1 done
clear
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question_answer29)
\[1+\frac{1}{4}+\frac{1.3}{4.8}+\frac{1.3.5}{4.8.12}+...........=\] [RPET 1996; EAMCET 2001]
A)
\[\sqrt{2}\] done
clear
B)
\[\frac{1}{\sqrt{2}}\] done
clear
C)
\[\sqrt{3}\] done
clear
D)
\[\frac{1}{\sqrt{3}}\] done
clear
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question_answer30)
If x is positive, the first negative term in the expansion of \[{{(1+x)}^{27\,/\,5}}\] is [AIEEE 2003]
A)
7th term done
clear
B)
5th term done
clear
C)
8th term done
clear
D)
6th term done
clear
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question_answer31)
Coefficient of \[{{x}^{r}}\] in the expansion of \[{{(1-2x)}^{-1/2}}\] is [Kurukshetra CEE 2001]
A)
\[\frac{(2r)\,!}{{{(r\,!)}^{2}}}\] done
clear
B)
\[\frac{(2r)\,!}{{{2}^{r}}{{(r!)}^{2}}}\] done
clear
C)
\[\frac{(2r)!}{{{(r!)}^{2}}{{2}^{2r}}}\] done
clear
D)
\[\frac{(2r)!}{{{2}^{r}}.(r+1)!.(r-1)!}\] done
clear
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question_answer32)
\[{{\sum\limits_{k=1}^{n}{k\left( 1+\frac{1}{n} \right)}}^{k-1}}=\] [EAMCET 2002; Pb. CET 2002]
A)
\[n(n-1)\] done
clear
B)
\[n(n+1)\] done
clear
C)
\[{{n}^{2}}\] done
clear
D)
\[{{(n+1)}^{2}}\] done
clear
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question_answer33)
The expression \[{{[x+{{({{x}^{3}}-1)}^{1/2}}]}^{5}}+{{[x-{{({{x}^{3}}-1)}^{1/2}}]}^{5}}\] is a polynomial of degree [Pb. CET 2000]
A)
5 done
clear
B)
6 done
clear
C)
7 done
clear
D)
8 done
clear
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question_answer34)
If x is so small that \[{{x}^{3}}\] and higher powers of x may be neglected, then \[\frac{{{(1+x)}^{\frac{3}{2}}}-{{\left( 1+\frac{1}{2}x \right)}^{3}}}{{{(1-x)}^{\frac{1}{2}}}}\] may be approximated as [AIEEE 2005]
A)
\[-\frac{3}{8}{{x}^{2}}\] done
clear
B)
\[\frac{x}{2}-\frac{3}{8}{{x}^{2}}\] done
clear
C)
\[1-\frac{3}{8}{{x}^{2}}\] done
clear
D)
\[3x+\frac{3}{8}{{x}^{2}}\] done
clear
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