8666 + Mcqs in Mathematics Page 94 McqOptions

4651.	The greatest coefficient in the expansion of \[{{(1+x)}^{2n+2}}\] is [BIT Ranchi 1992]
A.	\[\frac{(2n)!}{{{(n!)}^{2}}}\]
B.	\[\frac{(2n+2)!}{{{\{(n+1)!\}}^{2}}}\]
C.	\[\frac{(2n+2)!}{n!(n+1)!}\]
D.	\[\frac{(2n)!}{n!(n+1)!}\]
Answer» C. \[\frac{(2n+2)!}{n!(n+1)!}\]

Discussion

4652.	The middle term in the expansion of \[{{(1+x)}^{2n}}\] is [DCE 2002]
A.	\[\frac{(2n)!}{n!}{{x}^{2}}\]
B.	\[\frac{(2n)!}{n!(n-1)!}{{x}^{n+1}}\]
C.	\[\frac{(2n)!}{{{(n!)}^{2}}}{{x}^{n}}\]
D.	\[\frac{(2n)!}{(n+1)!(n-1)!}\,{{x}^{n}}\]
Answer» D. \[\frac{(2n)!}{(n+1)!(n-1)!}\,{{x}^{n}}\]

Discussion

4653.	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
B.	150000
C.	150090
D.	153180
Answer» B. 150000

Discussion

4654.	The coefficient of middle term in the expansion of \[{{(1+x)}^{10}}\] is [UPSEAT 2001]
A.	\[\frac{10!}{5!\,6!}\]
B.	\[\frac{10\,!}{{{(5\,!)}^{2}}}\]
C.	\[\frac{10\,!}{5\,!\,7\,!}\]
D.	None of these
Answer» C. \[\frac{10\,!}{5\,!\,7\,!}\]

Discussion

4655.	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
B.	8
C.	9
D.	None of these
Answer» D. None of these

Discussion

4656.	If the middle term in the expansion of \[{{\left( {{x}^{2}}+\frac{1}{x} \right)}^{n}}\]is \[924{{x}^{6}}\], then \[n=\]
A.	10
B.	12
C.	14
D.	None of these
Answer» C. 14

Discussion

4657.	In the expansion of \[{{\left( x-\frac{3}{{{x}^{2}}} \right)}^{9}},\] the term independent of x is [Karnataka CET 2001]
A.	Non existent
B.	\[^{9}{{C}_{2}}\]
C.	2268
D.	-2268
Answer» E.

Discussion

4658.	The term independent of x in the expansion of \[{{\left( 2x-\frac{3}{x} \right)}^{6}}\] is [Pb. CET 1999]
A.	4320
B.	216
C.	-216
D.	-4320
Answer» E.

Discussion

4659.	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.	\[\frac{28}{81}\]
B.	\[\frac{28}{243}\]
C.	\[-\frac{28}{243}\]
D.	\[-\frac{28}{81}\]
Answer» C. \[-\frac{28}{243}\]

Discussion

4660.	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
B.	-1
C.	-48
D.	None of these
Answer» E.

Discussion

4661.	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.	\[^{15}{{C}_{6}}{{2}^{6}}\]
B.	\[^{15}{{C}_{5}}{{2}^{5}}\]
C.	\[^{15}{{C}_{4}}{{2}^{4}}\]
D.	\[^{15}{{C}_{8}}{{2}^{8}}\]
Answer» C. \[^{15}{{C}_{4}}{{2}^{4}}\]

Discussion

4662.	The term independent of x in \[{{\left( 2x-\frac{1}{2{{x}^{2}}} \right)}^{12}}\]is [RPET 1985]
A.	-7930
B.	-495
C.	495
D.	7920
Answer» E.

Discussion

4663.	\[{{16}^{th}}\] term in the expansion of \[{{(\sqrt{x}-\sqrt{y})}^{17}}\] is
A.	\[136x{{y}^{7}}\]
B.	\[136xy\]
C.	\[-136x{{y}^{15/2}}\]
D.	\[-136x{{y}^{2}}\]
Answer» D. \[-136x{{y}^{2}}\]

Discussion

4664.	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.	\[^{9}{{C}_{3}}.\frac{1}{{{6}^{3}}}\]
B.	\[^{9}{{C}_{3}}{{\left( \frac{3}{2} \right)}^{3}}\]
C.	\[^{9}{{C}_{3}}\]
D.	None of these
Answer» B. \[^{9}{{C}_{3}}{{\left( \frac{3}{2} \right)}^{3}}\]

Discussion

4665.	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.	44230
B.	44291
C.	44232
D.	None of these
Answer» C. 44232

Discussion

4666.	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
B.	10
C.	11
D.	12
Answer» C. 11

Discussion

4667.	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.	\[^{15}{{C}_{4}}\]
B.	\[^{15}{{C}_{3}}\]
C.	\[^{15}{{C}_{2}}\]
D.	\[^{15}{{C}_{5}}\]
Answer» B. \[^{15}{{C}_{3}}\]

Discussion

4668.	The coefficient of \[{{x}^{5}}\] in the expansion of \[{{(x+3)}^{6}}\] is [DCE 2002]
A.	18
B.	6
C.	12
D.	10
Answer» B. 6

Discussion

4669.	Coefficient of \[{{x}^{2}}\] in the expansion of \[{{\left( x-\frac{1}{2x} \right)}^{8}}\] is [UPSEAT 2002]
A.	\[\frac{1}{7}\]
B.	\[\frac{-1}{7}\]
C.	-7
D.	7
Answer» D. 7

Discussion

4670.	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.	\[n+3\]
B.	\[n+1\]
C.	\[n+2\]
D.	\[n\]
Answer» C. \[n+2\]

Discussion

4671.	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
B.	20
C.	10
D.	5
Answer» E.

Discussion

4672.	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.	\[-\frac{7}{9}\]
B.	\[-\frac{9}{7}\]
C.	\[\frac{7}{9}\]
D.	\[\frac{9}{7}\]
Answer» E.

Discussion

4673.	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
B.	-512
C.	521
D.	251
Answer» C. 521

Discussion

4674.	\[{{r}^{th}}\]term in the expansion of \[{{(a+2x)}^{n}}\]is
A.	\[\frac{n(n+1)....(n-r+1)}{r!}{{a}^{n-r+1}}{{(2x)}^{r}}\]
B.	\[\frac{n(n-1)....(n-r+2)}{(r-1)\,!}{{a}^{n-r+1}}{{(2x)}^{r-1}}\]
C.	\[\frac{n(n+1)....(n-r)}{(r+1)!}{{a}^{n-r}}{{(x)}^{r}}\]
D.	None of these
Answer» C. \[\frac{n(n+1)....(n-r)}{(r+1)!}{{a}^{n-r}}{{(x)}^{r}}\]

Discussion

4675.	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
B.	0
C.	1
D.	44230
Answer» C. 1

Discussion

4676.	The coefficient of \[{{x}^{5}}\] in the expansion of \[{{(1+x)}^{21}}+{{(1+x)}^{22}}+..........+{{(1+x)}^{30}}\] is [UPSEAT 2001]
A.	\[^{51}{{C}_{5}}\]
B.	\[^{9}{{C}_{5}}\]
C.	\[^{31}{{C}_{6}}{{-}^{21}}{{C}_{6}}\]
D.	\[^{30}{{C}_{5}}{{+}^{20}}{{C}_{5}}\]
Answer» D. \[^{30}{{C}_{5}}{{+}^{20}}{{C}_{5}}\]

Discussion

4677.	The coefficient of \[{{x}^{39}}\] in the expansion of \[{{\left( {{x}^{4}}-\frac{1}{{{x}^{3}}} \right)}^{15}}\] is [MP PET 2001]
A.	-455
B.	-105
C.	105
D.	455
Answer» B. -105

Discussion

4678.	If the coefficient of 4th term in the expansion of \[{{(a+b)}^{n}}\] is 56, then n is [AMU 2000]
A.	12
B.	10
C.	8
D.	6
Answer» D. 6

Discussion

4679.	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
B.	15
C.	13
D.	16
Answer» B. 15

Discussion

4680.	In the expansion of \[{{(1+x+{{x}^{3}}+{{x}^{4}})}^{10}},\] the coefficient of \[{{x}^{4}}\] is [MP PET 2000]
A.	\[^{40}{{C}_{4}}\]
B.	\[^{10}{{C}_{4}}\]
C.	210
D.	310
Answer» E.

Discussion

4681.	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
B.	7
C.	14
D.	-14
Answer» C. 14

Discussion

4682.	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.	\[\frac{(2n)!}{(m)!\,(2n-m)!}\]
B.	\[\frac{(2n)!\,3!\,3!}{(2n-m)!}\]
C.	\[\frac{(2n)!}{\left( \frac{2n-m}{3} \right)\,!\,\left( \frac{4n+m}{3} \right)\,!}\]
D.	None of these
Answer» D. None of these

Discussion

4683.	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
B.	9
C.	12
D.	24
Answer» D. 24

Discussion

4684.	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
B.	8
C.	9
D.	10
Answer» D. 10

Discussion

4685.	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
B.	55
C.	45
D.	15
Answer» C. 45

Discussion

4686.	The coefficient of \[{{x}^{32}}\]in the expansion of \[{{\left( {{x}^{4}}-\frac{1}{{{x}^{3}}} \right)}^{15}}\] is [MP PET 1994]
A.	\[^{15}{{C}_{5}}\]
B.	\[^{15}{{C}_{6}}\]
C.	\[^{15}{{C}_{4}}\]
D.	\[^{15}{{C}_{7}}\]
Answer» D. \[^{15}{{C}_{7}}\]

Discussion

4687.	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.	\[^{100}{{C}_{47}}\]
B.	\[^{100}{{C}_{53}}\]
C.	\[{{-}^{100}}{{C}_{53}}\]
D.	\[{{-}^{100}}{{C}_{100}}\]
Answer» D. \[{{-}^{100}}{{C}_{100}}\]

Discussion

4688.	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.	\[\frac{462{{a}^{6}}}{{{b}^{5}}}\]
B.	\[\frac{462{{a}^{5}}}{{{b}^{6}}}\]
C.	\[\frac{-462{{a}^{5}}}{{{b}^{6}}}\]
D.	\[\frac{-462{{a}^{6}}}{{{b}^{5}}}\]
Answer» C. \[\frac{-462{{a}^{5}}}{{{b}^{6}}}\]

Discussion

4689.	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
B.	14 only
C.	7 or 14
D.	None of these
Answer» D. None of these

Discussion

4690.	.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.	\[\frac{405}{256}\]
B.	\[\frac{504}{259}\]
C.	\[\frac{450}{263}\]
D.	None of these
Answer» B. \[\frac{504}{259}\]

Discussion

4691.	In the expansion of \[{{\left( x-\frac{1}{x} \right)}^{6}}\], the constant term is [AMU 1982; MP PET 1984; MNR 1979]
A.	-20
B.	20
C.	30
D.	-30
Answer» B. 20

Discussion

4692.	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
B.	16
C.	12
D.	-10
Answer» E.

Discussion

4693.	If the expansion of \[{{\left( {{y}^{2}}+\frac{c}{y} \right)}^{5}}\], the coefficient of y will be [MNR 1983]
A.	\[20c\]
B.	\[10c\]
C.	\[10{{c}^{3}}\]
D.	\[20{{c}^{2}}\]
Answer» D. \[20{{c}^{2}}\]

Discussion

4694.	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.	\[A=B\]
B.	\[A=2B\]
C.	\[2A=B\]
D.	None of these
Answer» C. \[2A=B\]

Discussion

4695.	In the expansion of \[{{\left( \frac{a}{x}+bx \right)}^{12}}\],the coefficient of x-10 will be
A.	\[12{{a}^{11}}\]
B.	\[12{{b}^{11}}a\]
C.	\[12{{a}^{11}}b\]
D.	\[12{{a}^{11}}{{b}^{11}}\]
Answer» D. \[12{{a}^{11}}{{b}^{11}}\]

Discussion

4696.	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.	\[{{n}^{2}}-2np+4{{p}^{2}}=0\]
B.	\[{{n}^{2}}-n\,(4p+1)+4{{p}^{2}}-2=0\]
C.	\[{{n}^{2}}-n\,(4p+1)+4{{p}^{2}}=0\]
D.	None of these
Answer» C. \[{{n}^{2}}-n\,(4p+1)+4{{p}^{2}}=0\]

Discussion

4697.	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
B.	7
C.	8
D.	9
Answer» E.

Discussion

4698.	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
B.	3 and 2
C.	2/3 and 9
D.	3/2 and \[6\]
Answer» D. 3/2 and \[6\]

Discussion

4699.	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
B.	\[1/2\]
C.	3
D.	4
Answer» C. 3

Discussion

4700.	\[{{6}^{th}}\]term in expansion of \[{{\left( 2{{x}^{2}}-\frac{1}{3{{x}^{2}}} \right)}^{10}}\] is
A.	\[\frac{4580}{17}\]
B.	\[-\frac{896}{27}\]
C.	\[\frac{5580}{17}\]
D.	None of these
Answer» C. \[\frac{5580}{17}\]

Discussion

Explore topic-wise MCQs in Joint Entrance Exam - Main (JEE Main).

The greatest coefficient in the expansion of \[{{(1+x)}^{2n+2}}\] is [BIT Ranchi 1992]

The middle term in the expansion of \[{{(1+x)}^{2n}}\] is [DCE 2002]

The term independent of x in the expansion of \[{{\left( {{x}^{2}}-\frac{3\sqrt{3}}{{{x}^{3}}} \right)}^{10}}\] is [RPET 1999]

The coefficient of middle term in the expansion of \[{{(1+x)}^{10}}\] is [UPSEAT 2001]

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 \[n=\]

If the middle term in the expansion of \[{{\left( {{x}^{2}}+\frac{1}{x} \right)}^{n}}\]is \[924{{x}^{6}}\], then \[n=\]

In the expansion of \[{{\left( x-\frac{3}{{{x}^{2}}} \right)}^{9}},\] the term independent of x is [Karnataka CET 2001]

The term independent of x in the expansion of \[{{\left( 2x-\frac{3}{x} \right)}^{6}}\] is [Pb. CET 1999]

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]

The term independent of x in the expansion of \[{{\left( {{x}^{2}}-\frac{1}{x} \right)}^{9}}\] is [EAMCET 1982; MP PET 2003]

In the expansion of \[{{\left( x+\frac{2}{{{x}^{2}}} \right)}^{15}}\], the term independent of \[x\] is [MP PET 1993; Pb. CET 2002]

The term independent of x in \[{{\left( 2x-\frac{1}{2{{x}^{2}}} \right)}^{12}}\]is [RPET 1985]

\[{{16}^{th}}\] term in the expansion of \[{{(\sqrt{x}-\sqrt{y})}^{17}}\] is

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]

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]

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]

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]

The coefficient of \[{{x}^{5}}\] in the expansion of \[{{(x+3)}^{6}}\] is [DCE 2002]

Coefficient of \[{{x}^{2}}\] in the expansion of \[{{\left( x-\frac{1}{2x} \right)}^{8}}\] is [UPSEAT 2002]

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]

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]

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]

The coefficient of \[{{x}^{-9}}\] in the expansion of \[{{\left( \frac{{{x}^{2}}}{2}-\frac{2}{x} \right)}^{9}}\] is [Kerala (Engg.) 2001]

\[{{r}^{th}}\]term in the expansion of \[{{(a+2x)}^{n}}\]is

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]

The coefficient of \[{{x}^{5}}\] in the expansion of \[{{(1+x)}^{21}}+{{(1+x)}^{22}}+..........+{{(1+x)}^{30}}\] is [UPSEAT 2001]

The coefficient of \[{{x}^{39}}\] in the expansion of \[{{\left( {{x}^{4}}-\frac{1}{{{x}^{3}}} \right)}^{15}}\] is [MP PET 2001]

If the coefficient of 4th term in the expansion of \[{{(a+b)}^{n}}\] is 56, then n is [AMU 2000]

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]

In the expansion of \[{{(1+x+{{x}^{3}}+{{x}^{4}})}^{10}},\] the coefficient of \[{{x}^{4}}\] is [MP PET 2000]

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]

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]

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]

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]

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]

The coefficient of \[{{x}^{32}}\]in the expansion of \[{{\left( {{x}^{4}}-\frac{1}{{{x}^{3}}} \right)}^{15}}\] is [MP PET 1994]

The coefficient of \[{{x}^{53}}\] in the following expansion \[\sum\limits_{m=0}^{100}{{{\,}^{100}}{{C}_{m}}{{(x-3)}^{100-m}}}{{.2}^{m}}\]is

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]

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]

.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]

In the expansion of \[{{\left( x-\frac{1}{x} \right)}^{6}}\], the constant term is [AMU 1982; MP PET 1984; MNR 1979]

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

If the expansion of \[{{\left( {{y}^{2}}+\frac{c}{y} \right)}^{5}}\], the coefficient of y will be [MNR 1983]

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]

In the expansion of \[{{\left( \frac{a}{x}+bx \right)}^{12}}\],the coefficient of x-10 will be

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]

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]

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]

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

\[{{6}^{th}}\]term in expansion of \[{{\left( 2{{x}^{2}}-\frac{1}{3{{x}^{2}}} \right)}^{10}}\] is