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CBSE Questions for Class 11 Engineering Maths Binomial Theorem Quiz 11 - MCQExams.com

The value of x in the expression (x+xlog10x)5, if the third term in the expansion is 10,00,000, is
  • 101
  • 101
  • 105/2
  • 105/2
The total number of terms which are dependent on the value of x in the expansion of (x22+1x2)n is equal to   
  • 2n+1
  • 2n
  • n
  • n+1
If c0,c1,c2cn are binomial coefficients in (1+x)n, then the value of c1+c5+c9+c13+ equals
  • 2n1+2n2sin(nπ4)
  • 2n1+2n2cos(nπ4)
  • 12(2n1+2n2sinnπ4)
  • 12(2n12n2sinnπ4)
The expresion
45C8+7k=152kC7+5i=157iC50i
  • 55C7
  • 57C8
  • 57C7
  • None of these
The coefficient of xn2 in the polynomial (x1)(x2)(x3)....(xn) is 
  • n(n2+2)(3n+1)24
  • n(n21)(3n+2)24
  • n(n2+1)(3n+4)24
  • None of these
The value of the expression 1+4.343+7.4+2.3.49+7.34316+26.31+25.33+26.33+24.34 equal
  • 1
  • 2
  • 4
  • 3
The value of B=0rsn (CrCs)2 is
  • (n+1)n22n
  • (n+1)2nCn2n
  • (n+1)2nCn22n
  • 22n2n
If C0,C1,C2....,Cn denote the binomial coefficients in the expansion of (1+x)n, then C1C0+2C2C1++3C3C2+.....+nCnCn1 equals
  • n2
  • n+12
  • n(n1)2
  • n(n+1)2
If the fourth term of (x(11+logx)+12x)6 is equal to 200 and x>1, then x is equal to
  • 102
  • 10
  • 104
  • 10/2
The number of irrational terms in the expansion of (85+62)100 is
  • 97
  • 98
  • 96
  • 99
The value of the expression
C20C21+C22......+(1)n×C2n is
  • 0, if n is odd
  • (1)n, if n is odd
  • (1)n/2 nCn/2, if n is even
  • (1)n1 nCn1, if n is even
Value of P=0r<snCrCs is
  • 22n12(2nCn)
  • 22n112(2nCn)
  • 22n12(2nCn)
  • None of these
11th term in the expansion of
(3174+32)20 is
  • an irrational number
  • a rational number
  • a positive integer
  • a negative integer
If n is even, then value of the expression
C012C21+13C22.....+(1)nn+1C2n
where
Cr=nCr is
  • (1)nn!(n+1)(n/2)!2
  • (1)n1n!(n+1)(n/2)!2
  • (1)(n+1)(n/2)!2
  • (1)n/2n!(n+1)(n/2)!2
Let
S=C1(1+12)C2+(1+12+13)C3........+.(1)n1(1+12+....+1n)Cn
then
  • nS=1
  • 1S is an integer
  • 1S2 is an integer
  • S is independent of n
values of x for which the sixth term of the expansion of
E=(3log39|x2|+7(15)log7[(4).3|x2|9])7 is 567, are
  • 1
  • 2
  • 3
  • none of these
Sum of the series
nk=0nkr=0(nk)(nkr) is
  • 2n
  • 3n
  • nr=0(1)rCr4r
  • nr=0nCr2r
If in the expansion of (x31x2)n,
nN, sum of coefficient of x5 and x10 is 0, then value of n is
  • 5
  • 10
  • 15
  • none of these
Value of
S=nCr+3(n1Cr)+5(n2Cr)+...+ upto (nr+1)terms
  • n+2Cr+2
  • n+2Cr+2+n+1Cr+2
  • n+2Cr+1
  • n+2Cr+2+n+1Cr
If Sn=1+q+q2+q3+...+qn and Sn=1+(q+12)+(q+12)2+...+(q+12)n,q1 then n+1C1+n+1C2.S1+n+1C3.S2+...+n+1Cn+1.Sn=
  • 2n1.Sn
  • 2n.Sn
  • 2n+1.Sn
  • None of these
The third term from the end in the expansion of (4x3y3y2x)9 is
  • 9C73523y5x5
  • 9C73523y5x5
  • 9C73523y5x3
  • none of these
If the second ,third and fourth terms in the expansion of (x+y)n are 240,720 and 1080 respectively, then the value of x,y,n is
  • x=2,y=3,n=5
  • x=3,y=3,n=5
  • x=2,y=3,n=3
  • x=2,y=2,n=5

Maximum sum of the coefficients in the expansion of (1xsinθ+x2)n is
  • 1
  • 2n
  • 3n
  • 0
C0+3.C1+3.2C2+...+3.nCn=5n.
  • True
  • False
(mC0+mC1mC2mC3)+(mC4+mC5mC6mC7)+...=0 if and only if for some positive integer k,m=
  • 4k
  • 4k+1
  • 4k1
  • 4k+2
In the expansion of (512+718)1024, the number of integral terms is
  • 128
  • 129
  • 130
  • 131
If the expansion of (x3+1x2)n contains a term independent of x, then the value of n can be
  • 18
  • 20
  • 24
  • 22
In the expansion of (3x25+53x2)10 mid term is
  • 291
  • 242
  • 252
  • 284
If (1+x)^{2n} =a_0+a_1x....+a_{2n}x^{2n}, then
  • a_1+a_2+a_4.....=\dfrac 12 (a_0+a_1+a_2.....)
  • a_{n+1}=a_n
  • a_{n-3}=a_{n+3}
  • a_{n-3}>a_{n+3}
If ac>b^2 then the sum of the coefficients in the expansion of (a\alpha ^2x^2+2b\alpha x+c)^n,(a,b,c,\alpha \in R, n\in N) is
  • Positive if a>0.
  • Positive if c>0.
  • Negative if a<0, n is odd.
  • Positive if c<0,n is even.
If the sum of the coefficients in the expansion of (l^2x^2-2lx+1)^{50} vanishes then l is equal to:
  • -1
  • -2
  • 1
  • 2
Find the value(s) of k such that the term independent of x in \displaystyle\left(3x^2+\frac{k}{2x}\right)^6 is 135.
  • \pm2
  • \pm1
  • \pm3
  • \pm4
Find the coefficient of x^4 in the expansion of \left(2x^2+\frac{3}{x^3}\right)^7
  • ^7C_22^53^3
  • ^7C_22^53^2
  • ^7C_23^52^2
  • ^7C_32^53^2
The sum of the series \frac{1}{1\times 2}^{25}C_0 + \frac{1}{2\times 3}^{23}C_1+\frac{1}{3\times 4}^{25}C_2+...... + \frac{1}{26\times 27}^{25}C_{25}
  • \dfrac{2^{27}-1}{26\times 27}
  • \dfrac{2^{27}-28}{26\times 27}
  • \dfrac{1}{2}\left(\frac{2^{26}+1}{26\times 27}\right)
  • \dfrac{2^{26}-1}{52}
The number of rational terms in the expansion of \left(x^{\displaystyle\frac{1}{5}}+y^{\displaystyle\frac{1}{10}}\right)^{45} is
  • 5
  • 6
  • 4
  • 7
The value of x in the expression { \left( x+{ x }^{ \log _{ 10 }{ x }  } \right)  }^{ 5 }, if the third term in the expansion is 1,000,000, is
  • 10,{ 10 }^{ { -3 }/{ 2 } }
  • 100 or { 10 }^{ { -3 }/{ 2 } }
  • 10 or { 10 }^{ { -5 }/{ 2 } }
  • None of these
Sum of the last 30 coefficients in the expansion of { \left( 1+x \right)  }^{ 59 }, when expanded in ascending power of x is
  • { 2 }^{ 59 }
  • { 2 }^{ 58 }
  • { 2 }^{ 30 }
  • { 2 }^{ 29 }
If there is a term containing x^{2r} in \left( x + \dfrac{1}{x^2} \right )^{n - 3}, then
  • n - 2r is a positive integral multiple of 3.
  • n - 2r is even
  • n - 2r is odd
  • None of the above
The term independent of x in the expansion of \left [\sqrt {\dfrac {x}{3}} + \sqrt {\dfrac {3}{2x^{2}}} \right ]^{10} is
  • 1
  • ^{10}C_{1}
  • \dfrac {5}{12}
  • None of these
Coefficient of x^n in the expansion of \left(\displaystyle 1+\frac{x}{1!}+\frac{x^2}{2!}+...+\frac{x^n}{n!}\right)^2 is?
  • \displaystyle\frac{2^n}{n!}
  • \displaystyle\frac{2^{n-1}}{n!}
  • \displaystyle\frac{2^{n+1}}{n!}
  • None of these
\sum { { \left( -1 \right)  }^{ r } } ~ { _{  }^{ n }{ C } }_{ r }\cfrac { 1+r\log _{ e }{ 10 }  }{ { \left( 1+\log _{ e }{ { 10 }^{ n } }  \right)  }^{ r } }
  • 1
  • -1
  • n
  • none of these
If \sum _{ r=0 }^{ n-1 }{ { \left( \cfrac { { _{  }^{ n }{ C } }_{ r } }{ { _{  }^{ n }{ C } }_{ r }+{ _{  }^{ n }{ C } }_{ r+1 } }  \right)  }^{ 3 } } =\cfrac { 4 }{ 5 } then n=
  • 4
  • 6
  • 8
  • None of these
If (1+x)^{10} = a_0 + a_1x + a_2x^2 + ..... + a_{10}x^{10}, then value of (a_0 -a_2 + a_4 - a_6 + a_8 - a_{10})^2 + (a_1 -a_3 + a_5 - a_7 + a_9)^2 is
  • 2^{10}
  • 2
  • 2^{20}
  • 2^{30}
If \left\{ x \right\}  denotes the fraction part of 'x', then \left\{ \dfrac { { 3 }^{ 1001 } }{ 82 }  \right\} =
  • \dfrac { 9 }{ 82 }
  • \dfrac { 81 }{ 82 }
  • \dfrac { 3 }{ 82 }
  • \dfrac { 1 }{ 82 }
The coefficient of x^{160} in the expansion of \displaystyle (x^8 + 1)^{60} \left( x^{12} + 3x^4 + \frac{3}{x^4} + \frac{1}{x^{12}} \right)^{-10} is
  • \displaystyle ^{30}C_6
  • \displaystyle ^{30}C_5
  • divisible by 189
  • divisible by 203
The value of \sum _{ r=1 }^{ 10 }{ \left( \sin { \cfrac { 2nr }{ 11 }  } -i\cos { \cfrac { 2nr }{ 11 }  }  \right)  } is
  • 0
  • -1
  • -i
  • i
The co-efficient of {x^{53}} in the expression \sum\limits_{m = 0}^{100} {{}^{100}} {c_m}{(x - 3)^{100 - m}}{2^m}\, is
  • {}^{100}{c_{53}}
  • {}^{98}{c_{53}}
  • {}^{65}{c_{53}}
  • {}^{100}{c_{65}}
In the expression of \left( {{2^x} + \frac{1}{{{4^x}}}} \right)^n\, ratio  of 2nd and third terms is given by\,{t_3}/{t_2} = 7 and the sum of the co-efficients of 2nd and 3rd term is 36, then the value of x is 
  • \dfrac{-1}{3}
  • \dfrac{-1}{2}
  • \dfrac{1}{3}
  • \dfrac{1}{2}
The sum of the binomial coefficients in the expansion of { \left( { x }^{ -3/4 }+a{ x }^{ 5/4 } \right)  }^{ n } lies between 200 and 400 and the term independent of x equals 448. The value of a is
  • 1
  • 2
  • 1/2
  • for no value of a
The coefficient {x^n} in the expression of {\left( {1 + x} \right)^{2n}} and {\left( {1 + x} \right)^{2n - 1}} are in the ratio.
  • 1:2
  • 1:3
  • 3:1
  • 2:1
0:0:2


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