-
question_answer1)
\[{{6}^{th}}\]term in expansion of \[{{\left( 2{{x}^{2}}-\frac{1}{3{{x}^{2}}} \right)}^{10}}\] is
A)
\[\frac{4580}{17}\] done
clear
B)
\[-\frac{896}{27}\] done
clear
C)
\[\frac{5580}{17}\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer2)
If the ratio of the coefficient of third and fourth term in the expansion of \[{{\left( x-\frac{1}{2x} \right)}^{n}}\] is 1 : 2, then the value of n will be
A)
18 done
clear
B)
16 done
clear
C)
12 done
clear
D)
- 10 done
clear
View Solution play_arrow
-
question_answer3)
If the coefficients of \[{{r}^{th}}\]term and \[{{(r+4)}^{th}}\]term are equal in the expansion of \[{{(1+x)}^{20}}\], then the value of r will be [RPET 1985, 97; Kerala (Engg.) 2001; MP PET 2002]
A)
7 done
clear
B)
8 done
clear
C)
9 done
clear
D)
10 done
clear
View Solution play_arrow
-
question_answer4)
\[{{r}^{th}}\]term in the expansion of \[{{(a+2x)}^{n}}\]is
A)
\[\frac{n(n+1)....(n-r+1)}{r!}{{a}^{n-r+1}}{{(2x)}^{r}}\] done
clear
B)
\[\frac{n(n-1)....(n-r+2)}{(r-1)\,!}{{a}^{n-r+1}}{{(2x)}^{r-1}}\] done
clear
C)
\[\frac{n(n+1)....(n-r)}{(r+1)!}{{a}^{n-r}}{{(x)}^{r}}\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer5)
\[{{16}^{th}}\] term in the expansion of \[{{(\sqrt{x}-\sqrt{y})}^{17}}\] is
A)
\[136x{{y}^{7}}\] done
clear
B)
\[136xy\] done
clear
C)
\[-136x{{y}^{15/2}}\] done
clear
D)
\[-136x{{y}^{2}}\] done
clear
View Solution play_arrow
-
question_answer6)
In \[{{\left( \sqrt[3]{2}+\frac{1}{\sqrt[3]{3}} \right)}^{n}}\] if the ratio of \[{{7}^{th}}\] term from the beginning to the \[{{7}^{th}}\] term from the end is \[\frac{1}{6}\], then \[n=\]
A)
7 done
clear
B)
8 done
clear
C)
9 done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer7)
If coefficient of \[{{(2r+3)}^{th}}\] and \[{{(r-1)}^{th}}\] terms in the expansion of \[{{(1+x)}^{15}}\] are equal, then value of r is [RPET 1995, 2003; UPSEAT 2001]
A)
5 done
clear
B)
6 done
clear
C)
4 done
clear
D)
3 done
clear
View Solution play_arrow
-
question_answer8)
If \[{{x}^{4}}\] occurs in the \[{{r}^{th}}\] term in the expansion of \[{{\left( {{x}^{4}}+\frac{1}{{{x}^{3}}} \right)}^{15}}\], then \[r=\] [MP PET 1995; Pb. CET 2002]
A)
7 done
clear
B)
8 done
clear
C)
9 done
clear
D)
10 done
clear
View Solution play_arrow
-
question_answer9)
If the \[{{(r+1)}^{th}}\] term in the expansion of \[{{\left( \sqrt[3]{\frac{a}{\sqrt{b}}}+\sqrt{\frac{b}{\sqrt[3]{a}}} \right)}^{21}}\] has the same power of a and b, then the value of r is
A)
9 done
clear
B)
10 done
clear
C)
8 done
clear
D)
6 done
clear
View Solution play_arrow
-
question_answer10)
If the third term in the binomial expansion of \[{{(1+x)}^{m}}\] is \[-\frac{1}{8}{{x}^{2}}\], then the rational value of m is
A)
2 done
clear
B)
\[1/2\] done
clear
C)
3 done
clear
D)
4 done
clear
View Solution play_arrow
-
question_answer11)
The first 3 terms in the expansion of \[{{(1+ax)}^{n}}\] \[(n\ne 0)\] are 1, 6x and 16x2. Then the value of a and n are respectively [Kerala (Engg.) 2002]
A)
2 and 9 done
clear
B)
3 and 2 done
clear
C)
2/3 and 9 done
clear
D)
3/2 and \[6\] done
clear
View Solution play_arrow
-
question_answer12)
If the coefficients of \[{{T}_{r}},\,{{T}_{r+1}},\,{{T}_{r+2}}\] terms of \[{{(1+x)}^{14}}\] are in A.P., then r = [Pb. CET 2002]
A)
6 done
clear
B)
7 done
clear
C)
8 done
clear
D)
9 done
clear
View Solution play_arrow
-
question_answer13)
Coefficient of x in the expansion of \[{{\left( {{x}^{2}}+\frac{a}{x} \right)}^{5}}\] is [Orissa JEE 2004]
A)
\[9{{a}^{2}}\] done
clear
B)
\[10{{a}^{3}}\] done
clear
C)
\[10{{a}^{2}}\] done
clear
D)
\[10a\] done
clear
View Solution play_arrow
-
question_answer14)
If the coefficients of \[{{p}^{th}}\], \[{{(p+1)}^{th}}\] and \[{{(p+2)}^{th}}\]terms in the expansion of \[{{(1+x)}^{n}}\]are in A.P., then [AIEEE 2005]
A)
\[{{n}^{2}}-2np+4{{p}^{2}}=0\] done
clear
B)
\[{{n}^{2}}-n\,(4p+1)+4{{p}^{2}}-2=0\] done
clear
C)
\[{{n}^{2}}-n\,(4p+1)+4{{p}^{2}}=0\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer15)
In the expansion of \[{{\left( \frac{a}{x}+bx \right)}^{12}}\],the coefficient of x-10 will be
A)
\[12{{a}^{11}}\] done
clear
B)
\[12{{b}^{11}}a\] done
clear
C)
\[12{{a}^{11}}b\] done
clear
D)
\[12{{a}^{11}}{{b}^{11}}\] done
clear
View Solution play_arrow
-
question_answer16)
The ratio of the coefficient of terms \[{{x}^{n-r}}{{a}^{r}}\]and \[{{x}^{r}}{{a}^{n-r}}\] in the binomial expansion of \[{{(x+a)}^{n}}\]will be
A)
\[x:a\] done
clear
B)
\[n:r\] done
clear
C)
\[x:n\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer17)
If A and B are the coefficients of \[{{x}^{n}}\] in the expansions of \[{{(1+x)}^{2n}}\] and \[{{(1+x)}^{2n-1}}\]respectively, then [MP PET 1999; Pb. CET 2004]
A)
\[A=B\] done
clear
B)
\[A=2B\] done
clear
C)
\[2A=B\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer18)
If the expansion of \[{{\left( {{y}^{2}}+\frac{c}{y} \right)}^{5}}\], the coefficient of y will be [MNR 1983]
A)
\[20c\] done
clear
B)
\[10c\] done
clear
C)
\[10{{c}^{3}}\] done
clear
D)
\[20{{c}^{2}}\] done
clear
View Solution play_arrow
-
question_answer19)
If p and q be positive, then the coefficients of \[{{x}^{p}}\] and \[{{x}^{q}}\] in the expansion of \[{{(1+x)}^{p+q}}\]will be [MNR 1983; AIEEE 2002]
A)
Equal done
clear
B)
Equal in magnitude but opposite in sign done
clear
C)
Reciprocal to each other done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer20)
In the expansion of \[{{\left( x-\frac{1}{x} \right)}^{6}}\], the constant term is [AMU 1982; MP PET 1984; MNR 1979]
A)
- 20 done
clear
B)
20 done
clear
C)
30 done
clear
D)
- 30 done
clear
View Solution play_arrow
-
question_answer21)
In the expansion of \[{{\left( {{x}^{2}}-2x \right)}^{10}}\], the coefficient of \[{{x}^{16}}\] is [MP PET 1985]
A)
-1680 done
clear
B)
1680 done
clear
C)
3360 done
clear
D)
6720 done
clear
View Solution play_arrow
-
question_answer22)
.In the expansion of \[{{\left( \frac{x}{2}-\frac{3}{{{x}^{2}}} \right)}^{10}}\], the coefficient of \[{{x}^{4}}\]is [IIT 1983; EAMCET 1985; DCE 2000; RPET 2001; UPSEAT 2002; J & K 2005]
A)
\[\frac{405}{256}\] done
clear
B)
\[\frac{504}{259}\] done
clear
C)
\[\frac{450}{263}\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer23)
If the coefficients of \[{{5}^{th}}\], \[{{6}^{th}}\]and \[{{7}^{th}}\] terms in the expansion of \[{{(1+x)}^{n}}\]be in A.P., then n = [Roorkee 1984; Pb. CET 1999]
A)
7 only done
clear
B)
14 only done
clear
C)
7 or 14 done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer24)
The coefficient of \[{{x}^{7}}\] in the expansion of \[{{\left( \frac{{{x}^{2}}}{2}-\frac{2}{x} \right)}^{8}}\] is [MNR 1975]
A)
- 56 done
clear
B)
56 done
clear
C)
- 14 done
clear
D)
14 done
clear
View Solution play_arrow
-
question_answer25)
The coefficient of \[{{x}^{-7}}\] in the expansion of \[{{\left( ax-\frac{1}{b{{x}^{2}}} \right)}^{11}}\] will be [IIT 1967; RPET 1996; Pb. CET 2003]
A)
\[\frac{462{{a}^{6}}}{{{b}^{5}}}\] done
clear
B)
\[\frac{462{{a}^{5}}}{{{b}^{6}}}\] done
clear
C)
\[\frac{-462{{a}^{5}}}{{{b}^{6}}}\] done
clear
D)
\[\frac{-462{{a}^{6}}}{{{b}^{5}}}\] done
clear
View Solution play_arrow
-
question_answer26)
The coefficient of \[{{x}^{53}}\] in the following expansion \[\sum\limits_{m=0}^{100}{{{\,}^{100}}{{C}_{m}}{{(x-3)}^{100-m}}}{{.2}^{m}}\]is
A)
\[^{100}{{C}_{47}}\] done
clear
B)
\[^{100}{{C}_{53}}\] done
clear
C)
\[{{-}^{100}}{{C}_{53}}\] done
clear
D)
\[{{-}^{100}}{{C}_{100}}\] done
clear
View Solution play_arrow
-
question_answer27)
The coefficient of \[{{x}^{32}}\]in the expansion of \[{{\left( {{x}^{4}}-\frac{1}{{{x}^{3}}} \right)}^{15}}\] is [MP PET 1994]
A)
\[^{15}{{C}_{5}}\] done
clear
B)
\[^{15}{{C}_{6}}\] done
clear
C)
\[^{15}{{C}_{4}}\] done
clear
D)
\[^{15}{{C}_{7}}\] done
clear
View Solution play_arrow
-
question_answer28)
If the coefficients of \[{{x}^{7}}\] and \[{{x}^{8}}\]in \[{{\left( 2+\frac{x}{3} \right)}^{n}}\]are equal, then n is [EAMCET 1983; Kurukshetra CEE 1998; DCE 2000; RPET 2001; UPSEAT 2001]
A)
56 done
clear
B)
55 done
clear
C)
45 done
clear
D)
15 done
clear
View Solution play_arrow
-
question_answer29)
The coefficient of \[{{x}^{3}}\] in the expansion of \[{{\left( x-\frac{1}{x} \right)}^{7}}\] is [MP PET 1997; Pb. CET 2001]
A)
14 done
clear
B)
21 done
clear
C)
28 done
clear
D)
35 done
clear
View Solution play_arrow
-
question_answer30)
If in the expansion of \[{{(1+x)}^{m}}{{(1-x)}^{n}}\], the coefficient of x and \[{{x}^{2}}\]are 3 and - 6 respectively, then m is [IIT 1999; MP PET 2000]
A)
6 done
clear
B)
9 done
clear
C)
12 done
clear
D)
24 done
clear
View Solution play_arrow
-
question_answer31)
If \[{{x}^{m}}\]occurs in the expansion of \[{{\left( x+\frac{1}{{{x}^{2}}} \right)}^{2n}},\]then the coefficient of \[{{x}^{m}}\] is [UPSEAT 1999]
A)
\[\frac{(2n)!}{(m)!\,(2n-m)!}\] done
clear
B)
\[\frac{(2n)!\,3!\,3!}{(2n-m)!}\] done
clear
C)
\[\frac{(2n)!}{\left( \frac{2n-m}{3} \right)\,!\,\left( \frac{4n+m}{3} \right)\,!}\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer32)
If coefficients of 2nd, 3rd and 4th terms in the binomial expansion of \[{{(1+x)}^{n}}\] are in A.P., then \[{{n}^{2}}-9n\] is equal to [RPET 1999; UPSEAT 2002]
A)
- 7 done
clear
B)
7 done
clear
C)
14 done
clear
D)
- 14 done
clear
View Solution play_arrow
-
question_answer33)
In the expansion of \[{{(1+x+{{x}^{3}}+{{x}^{4}})}^{10}},\] the coefficient of \[{{x}^{4}}\] is [MP PET 2000]
A)
\[^{40}{{C}_{4}}\] done
clear
B)
\[^{10}{{C}_{4}}\] done
clear
C)
210 done
clear
D)
310 done
clear
View Solution play_arrow
-
question_answer34)
If coefficients of \[{{(2r+1)}^{th}}\] term and \[{{(r+2)}^{th}}\] term are equal in the expansion of \[{{(1+x)}^{43}},\] then the value of r will be [UPSEAT 1999]
A)
14 done
clear
B)
15 done
clear
C)
13 done
clear
D)
16 done
clear
View Solution play_arrow
-
question_answer35)
If the coefficient of 4th term in the expansion of \[{{(a+b)}^{n}}\] is 56, then n is [AMU 2000]
A)
12 done
clear
B)
10 done
clear
C)
8 done
clear
D)
6 done
clear
View Solution play_arrow
-
question_answer36)
The coefficient of \[{{x}^{39}}\] in the expansion of \[{{\left( {{x}^{4}}-\frac{1}{{{x}^{3}}} \right)}^{15}}\] is [MP PET 2001]
A)
- 455 done
clear
B)
- 105 done
clear
C)
105 done
clear
D)
455 done
clear
View Solution play_arrow
-
question_answer37)
The coefficient of \[{{x}^{5}}\] in the expansion of \[{{(1+x)}^{21}}+{{(1+x)}^{22}}+..........+{{(1+x)}^{30}}\] is [UPSEAT 2001]
A)
\[^{51}{{C}_{5}}\] done
clear
B)
\[^{9}{{C}_{5}}\] done
clear
C)
\[^{31}{{C}_{6}}{{-}^{21}}{{C}_{6}}\] done
clear
D)
\[^{30}{{C}_{5}}{{+}^{20}}{{C}_{5}}\] done
clear
View Solution play_arrow
-
question_answer38)
If the coefficients of second, third and fourth term in the expansion of \[{{(1+x)}^{2n}}\] are in A.P., then \[2{{n}^{2}}-9n+7\] is equal to [AMU 2001; MP PET 2004]
A)
- 1 done
clear
B)
0 done
clear
C)
1 done
clear
D)
3/2 done
clear
View Solution play_arrow
-
question_answer39)
The coefficient of \[{{x}^{-9}}\] in the expansion of \[{{\left( \frac{{{x}^{2}}}{2}-\frac{2}{x} \right)}^{9}}\] is [Kerala (Engg.) 2001]
A)
512 done
clear
B)
- 512 done
clear
C)
521 done
clear
D)
251 done
clear
View Solution play_arrow
-
question_answer40)
If the coefficients of \[{{x}^{2}}\]and \[{{x}^{3}}\]in the expansion of \[{{(3+ax)}^{9}}\] are the same, then the value of a is [DCE 2001]
A)
\[-\frac{7}{9}\] done
clear
B)
\[-\frac{9}{7}\] done
clear
C)
\[\frac{7}{9}\] done
clear
D)
\[\frac{9}{7}\] done
clear
View Solution play_arrow
-
question_answer41)
If the second, third and fourth term in the expansion of \[{{(x+a)}^{n}}\] are 240, 720 and 1080 respectively, then the value of n is [Kurukshetra CEE 1991; DCE 1995, 2001]
A)
15 done
clear
B)
20 done
clear
C)
10 done
clear
D)
5 done
clear
View Solution play_arrow
-
question_answer42)
In the expansion of \[{{(1+x)}^{n}}\]the coefficient of pth and \[{{(p+1)}^{th}}\] terms are respectively p and q. Then \[p+q=\] [EAMCET 2002]
A)
\[n+3\] done
clear
B)
\[n+1\] done
clear
C)
\[n+2\] done
clear
D)
\[n\] done
clear
View Solution play_arrow
-
question_answer43)
Coefficient of \[{{x}^{2}}\] in the expansion of \[{{\left( x-\frac{1}{2x} \right)}^{8}}\] is [UPSEAT 2002]
A)
\[\frac{1}{7}\] done
clear
B)
\[\frac{-1}{7}\] done
clear
C)
- 7 done
clear
D)
7 done
clear
View Solution play_arrow
-
question_answer44)
The coefficient of \[{{x}^{5}}\] in the expansion of \[{{(x+3)}^{6}}\] is [DCE 2002]
A)
18 done
clear
B)
6 done
clear
C)
12 done
clear
D)
10 done
clear
View Solution play_arrow
-
question_answer45)
The coefficient of \[{{x}^{32}}\] in the expansion of \[{{\left( {{x}^{4}}-\frac{1}{{{x}^{3}}} \right)}^{15}}\] is [Karnataka CET 2003; Pb. CET 2000]
A)
\[^{15}{{C}_{4}}\] done
clear
B)
\[^{15}{{C}_{3}}\] done
clear
C)
\[^{15}{{C}_{2}}\] done
clear
D)
\[^{15}{{C}_{5}}\] done
clear
View Solution play_arrow
-
question_answer46)
If in the expansion of \[{{(1+x)}^{21}}\], the coefficients of \[{{x}^{r}}\] and \[{{x}^{r+1}}\] be equal, then r is equal to [UPSEAT 2004]
A)
9 done
clear
B)
10 done
clear
C)
11 done
clear
D)
12 done
clear
View Solution play_arrow
-
question_answer47)
The term independent of x in the expansion of \[{{\left( \sqrt{\frac{x}{3}}+\frac{3}{2{{x}^{2}}} \right)}^{10}}\] will be [IIT 1965; BIT Ranchi 1993; KCET 2000; UPSEAT 2001]
A)
3/2 done
clear
B)
5/4 done
clear
C)
5/2 done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer48)
The term independent of x in the expansion of \[{{\left( \frac{1}{2}{{x}^{1/3}}+{{x}^{-1/5}} \right)}^{8}}\] will be [Roorkee 1985]
A)
5 done
clear
B)
6 done
clear
C)
7 done
clear
D)
8 done
clear
View Solution play_arrow
-
question_answer49)
In the expansion of \[{{\left( \frac{3{{x}^{2}}}{2}-\frac{1}{3x} \right)}^{9}}\],the term independent of x is [MNR 1981; AMU 1983; JMI EEE 2001]
A)
\[^{9}{{C}_{3}}.\frac{1}{{{6}^{3}}}\] done
clear
B)
\[^{9}{{C}_{3}}{{\left( \frac{3}{2} \right)}^{3}}\] done
clear
C)
\[^{9}{{C}_{3}}\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer50)
The term independent of x in \[{{\left( 2x-\frac{1}{2{{x}^{2}}} \right)}^{12}}\]is [RPET 1985]
A)
- 7930 done
clear
B)
- 495 done
clear
C)
495 done
clear
D)
7920 done
clear
View Solution play_arrow
-
question_answer51)
In the expansion of \[{{\left( x+\frac{2}{{{x}^{2}}} \right)}^{15}}\], the term independent of \[x\] is [MP PET 1993; Pb. CET 2002]
A)
\[^{15}{{C}_{6}}{{2}^{6}}\] done
clear
B)
\[^{15}{{C}_{5}}{{2}^{5}}\] done
clear
C)
\[^{15}{{C}_{4}}{{2}^{4}}\] done
clear
D)
\[^{15}{{C}_{8}}{{2}^{8}}\] done
clear
View Solution play_arrow
-
question_answer52)
The term independent of x in the expansion of \[{{\left( {{x}^{2}}-\frac{1}{x} \right)}^{9}}\] is [EAMCET 1982; MP PET 2003]
A)
1 done
clear
B)
-1 done
clear
C)
- 48 done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer53)
The term independent of x in the expansion of \[{{\left( 2x+\frac{1}{3x} \right)}^{6}}\]is [MNR 1995]
A)
\[\frac{160}{9}\] done
clear
B)
\[\frac{80}{9}\] done
clear
C)
\[\frac{160}{27}\] done
clear
D)
\[\frac{80}{3}\] done
clear
View Solution play_arrow
-
question_answer54)
The term independent of x in the expansion \[{{\left( {{x}^{2}}-\frac{1}{3x} \right)}^{9}}\]is [Roorkee 1981; RPET 1990, 95; Pb. CET 2000]
A)
\[\frac{28}{81}\] done
clear
B)
\[\frac{28}{243}\] done
clear
C)
\[-\frac{28}{243}\] done
clear
D)
\[-\frac{28}{81}\] done
clear
View Solution play_arrow
-
question_answer55)
The term independent of x in the expansion of \[{{\left( 2x-\frac{3}{x} \right)}^{6}}\] is [Pb. CET 1999]
A)
4320 done
clear
B)
216 done
clear
C)
- 216 done
clear
D)
- 4320 done
clear
View Solution play_arrow
-
question_answer56)
In the expansion of \[{{\left( 2{{x}^{2}}-\frac{1}{x} \right)}^{12}}\], the term independent of x is [MP PET 2001]
A)
10th done
clear
B)
9th done
clear
C)
8th done
clear
D)
7th done
clear
View Solution play_arrow
-
question_answer57)
In the expansion of \[{{\left( x-\frac{3}{{{x}^{2}}} \right)}^{9}},\] the term independent of x is [Karnataka CET 2001]
A)
Non existent done
clear
B)
\[^{9}{{C}_{2}}\] done
clear
C)
2268 done
clear
D)
- 2268 done
clear
View Solution play_arrow
-
question_answer58)
If the middle term in the expansion of \[{{\left( {{x}^{2}}+\frac{1}{x} \right)}^{n}}\]is \[924{{x}^{6}}\], then \[n=\]
A)
10 done
clear
B)
12 done
clear
C)
14 done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer59)
The middle term in the expansion of \[{{\left( x+\frac{1}{x} \right)}^{10}}\] is [BIT Ranchi 1991; RPET 2002; Pb. CET 1991]
A)
\[^{10}{{C}_{4}}\frac{1}{x}\] done
clear
B)
\[^{10}{{C}_{5}}\] done
clear
C)
\[^{10}{{C}_{5}}x\] done
clear
D)
\[^{10}{{C}_{7}}{{x}^{4}}\] done
clear
View Solution play_arrow
-
question_answer60)
The term independent of x in the expansion of \[{{\left( {{x}^{2}}-\frac{3\sqrt{3}}{{{x}^{3}}} \right)}^{10}}\] is [RPET 1999]
A)
153090 done
clear
B)
150000 done
clear
C)
150090 done
clear
D)
153180 done
clear
View Solution play_arrow
-
question_answer61)
The coefficient of middle term in the expansion of \[{{(1+x)}^{10}}\] is [UPSEAT 2001]
A)
\[\frac{10!}{5!\,6!}\] done
clear
B)
\[\frac{10\,!}{{{(5\,!)}^{2}}}\] done
clear
C)
\[\frac{10\,!}{5\,!\,7\,!}\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer62)
The middle term in the expansion of \[{{(1+x)}^{2n}}\] is [DCE 2002]
A)
\[\frac{(2n)!}{n!}{{x}^{2}}\] done
clear
B)
\[\frac{(2n)!}{n!(n-1)!}{{x}^{n+1}}\] done
clear
C)
\[\frac{(2n)!}{{{(n!)}^{2}}}{{x}^{n}}\] done
clear
D)
\[\frac{(2n)!}{(n+1)!(n-1)!}\,{{x}^{n}}\] done
clear
View Solution play_arrow
-
question_answer63)
The greatest coefficient in the expansion of \[{{(1+x)}^{2n+2}}\] is [BIT Ranchi 1992]
A)
\[\frac{(2n)!}{{{(n!)}^{2}}}\] done
clear
B)
\[\frac{(2n+2)!}{{{\{(n+1)!\}}^{2}}}\] done
clear
C)
\[\frac{(2n+2)!}{n!(n+1)!}\] done
clear
D)
\[\frac{(2n)!}{n!(n+1)!}\] done
clear
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question_answer64)
The greatest term in the expansion of \[\sqrt{3}{{\left( 1+\frac{1}{\sqrt{3}} \right)}^{20}}\]is
A)
\[\frac{25840}{9}\] done
clear
B)
\[\frac{24840}{9}\] done
clear
C)
\[\frac{26840}{9}\] done
clear
D)
None of these done
clear
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question_answer65)
If n is even positive integer, then the condition that the greatest term in the expansion of \[{{(1+x)}^{n}}\]may have the greatest coefficient also, is
A)
\[\frac{n}{n+2}<x<\frac{n+2}{n}\] done
clear
B)
\[\frac{n+1}{n}<x<\frac{n}{n+1}\] done
clear
C)
\[\frac{n}{n+4}<x<\frac{n+4}{4}\] done
clear
D)
None of these done
clear
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question_answer66)
The interval in which x must lie so that the greatest term in the expansion of \[{{(1+x)}^{2n}}\]has the greatest coefficient, is
A)
\[\left( \frac{n-1}{n},\frac{n}{n-1} \right)\] done
clear
B)
\[\left( \frac{n}{n+1},\frac{n+1}{n} \right)\] done
clear
C)
\[\left( \frac{n}{n+2},\frac{n+2}{n} \right)\] done
clear
D)
None of these done
clear
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question_answer67)
The greatest coefficient in the expansion of \[{{(1+x)}^{2n+1}}\] is [RPET 1997]
A)
\[\frac{(2n+1)\,!}{n!(n+1)!}\] done
clear
B)
\[\frac{(2n+2)!}{n!(n+1)!}\] done
clear
C)
\[\frac{(2n+1)!}{{{[(n+1)!]}^{2}}}\] done
clear
D)
\[\frac{(2n)!}{{{(n!)}^{2}}}\] done
clear
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question_answer68)
The coefficient of \[{{x}^{4}}\] in the expansion of \[{{(1+x+{{x}^{2}}+{{x}^{3}})}^{n}}\] is [MNR 1993; RPET 2001; DCE 1998]
A)
\[^{n}{{C}_{4}}\] done
clear
B)
\[^{n}{{C}_{4}}{{+}^{n}}{{C}_{2}}\] done
clear
C)
\[^{n}{{C}_{4}}+{{\,}^{n}}{{C}_{2}}+\,{{\,}^{n}}{{C}_{4}}{{.}^{n}}{{C}_{2}}\] done
clear
D)
\[^{n}{{C}_{4}}+{{\,}^{n}}{{C}_{2}}+{{\,}^{n}}{{C}_{1}}.{{\,}^{n}}{{C}_{2}}\] done
clear
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question_answer69)
The coefficient of \[\frac{1}{x}\] in the expansion of \[{{(1+x)}^{n}}{{\left( 1+\frac{1}{x} \right)}^{n}}\]is
A)
\[\frac{n!}{(n-1)!(n+1)!}\] done
clear
B)
\[\frac{(2n)\,!}{(n-1)!(n+1)!}\] done
clear
C)
\[\frac{n!}{(n-1)!(n+1)!}\] done
clear
D)
None of these done
clear
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question_answer70)
The term independent of x in the expansion of \[{{(1+x)}^{n}}{{\left( 1+\frac{1}{x} \right)}^{n}}\] is [EAMCET 1989]
A)
\[C_{0}^{2}+2C_{1}^{2}+....+(n+1)C_{n}^{2}\] done
clear
B)
\[{{({{C}_{0}}+{{C}_{1}}+....+{{C}_{n}})}^{2}}\] done
clear
C)
\[C_{0}^{2}+C_{1}^{2}+.....+C_{n}^{2}\] done
clear
D)
None of these done
clear
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question_answer71)
The coefficient of \[{{t}^{24}}\] in the expansion of \[{{(1+{{t}^{2}})}^{12}}(1+{{t}^{12}})\,(1+{{t}^{24}})\] is [IIT Screening 2003]
A)
\[^{12}{{C}_{6}}+2\] done
clear
B)
\[^{12}{{C}_{5}}\] done
clear
C)
\[^{12}{{C}_{6}}\] done
clear
D)
\[^{12}{{C}_{7}}\] done
clear
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question_answer72)
The coefficient of \[{{x}^{5}}\] in the expansion of \[{{({{x}^{2}}-x-2)}^{5}}\] is [EAMCET 2003]
A)
- 83 done
clear
B)
- 82 done
clear
C)
- 81 done
clear
D)
0 done
clear
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question_answer73)
The coefficient of \[{{x}^{n}}\]in expansion of \[(1+x)\,{{(1-x)}^{n}}\] is [AIEEE 2004]
A)
\[{{(-1)}^{n-1}}n\] done
clear
B)
\[{{(-1)}^{n}}(1-n)\] done
clear
C)
\[{{(-1)}^{n-1}}{{(n-1)}^{2}}\] done
clear
D)
\[(n-1)\] done
clear
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question_answer74)
The middle term in the expansion of \[{{\left( x+\frac{1}{2x} \right)}^{2n}}\], is [MP PET 1995]
A)
\[\frac{1.3.5....(2n-3)}{n!}\] done
clear
B)
\[\frac{1.3.5....(2n-1)}{n!}\] done
clear
C)
\[\frac{1.3.5....(2n+1)}{n!}\] done
clear
D)
None of these done
clear
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question_answer75)
In the expansion of \[{{(1+3x+2{{x}^{2}})}^{6}}\]the coefficient of \[{{x}^{11}}\] is [Kerala (Engg.) 2005]
A)
144 done
clear
B)
288 done
clear
C)
216 done
clear
D)
576 done
clear
E)
(3)(211) done
clear
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question_answer76)
The middle term in the expression of \[{{\left( x-\frac{1}{x} \right)}^{18}}\] is [Karnataka CET 2005]
A)
\[^{18}{{C}_{9}}\] done
clear
B)
\[{{-}^{18}}{{C}_{9}}\] done
clear
C)
\[^{18}{{C}_{0}}\] done
clear
D)
\[{{-}^{18}}{{C}_{10}}\] done
clear
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