Multinomial Expansion
Trending Questions
Q. If sum of the coefficients in the expansion of (x+3y−2z)n is 128, then greatest coefficient in the expansion (1+x)n is ____
- 7C3
- 8C5
- 9C3
- 5C3
Q. The expression (√2x2+1+√2x2−1)6+(2√2x2+1+√2x2−1)6 is a polynomial of degree
- 6
- 8
- 10
- 12
Q. The coefficient of x28 in the expansion of (1+x3−x6)30 is
- 1
- 0
- 30C6
- 30C3
Q. If the number of terms in the expansion of (x+y+z)n is 231, then the value of n is
- 20
- 30
- 31
- 21
Q. If |4x2−16x+16|−7|x−2|=−3, then the value(s) of x is/are
- 1
- 3
- 114
- 54
Q. If x∈(−2, 6], then (x2−2) lies in
- [−2, 34]
- [2, 34]
- (−2, 34]
- (2, 34]
Q. Let f(x)=20∑r=0arxr and g(x)=9∑r=0brxr+20∑r=10xr. If f(x)=g(x+1), then the value of a10 is
- 21C11
- 19C9
- 19C11
- 21C9
Q. If the coefficient of x1274 in the expansion of (x+1)(x−2)2(x+3)3(x−4)4⋯⋯(x+49)49(x−50)50 is −k, then the value of k is
Q. The coefficient of x11 in the expansion of (1+2x+2x2)6 is
- 144
- 288
- 216
- 384
Q.
In the term , what is the coefficient of ?
Q. If |x2+1|=2x, then x=
- 1
- −1
- 2
- −2
Q. Number of terms in the expansion of (x1 + x2 + x3 + ... +xr)n is equal ton+r−1 Cr−1
- False
- True
Q. Consider the equation x+y+z=16 where x, y, z>0. Let m and n denote the number of positive integral solutions of the equation when x is even and y is odd, respectively. Then the value of m+n is
- 49
- 77
- 105
- 93
Q. If the number of terms in the expansion of (1−2x+4x2)n, x≠0, is 28, then the sum of the coefficients of all the terms in this expansion, is:
- 243
- 729
- 64
- 2187
Q. The coefficient of x10 in the expansion of [1+x2(1−x)]8 is
- 470
- 400
- 476
- 576
Q. The number of distinct terms in the expansion of (x+1x+x2+1x2)15 is
(Different power of x means different terms)
(Different power of x means different terms)
- 60
- 61
- 30
- 31
Q. Which of the is/are true for the coefficient of x2y3zr in the expansion of (x−y+z)12?
- When r=7, then the coefficient is −12!2!3!7!
- When r=6, then the coefficient is −12!2!3!6!
- When r=8, then the coefficient is −12!2!3!8!
- When r=5, then the coefficient is −12!2!3!5!
Q. If the number of distinct terms in expansion of (x+y+z+1xy+1yz+1zx)2 and (x+y+z+1x+1y+1z)2 is m and n respectively, then the value of m+n is
Q. If (1+2x+3x2)10=k1+k2x+…+k21x20, then which of the following is/are correct?
- k2=20
- k3=30
- k3=210
- k2=21
Q. If fundamental period of f(x)=|sec4πx|+|cosec 6πx| is P, then coefficient of x−24P in the expansion (x+bx3)32P is
- 16C1b
- 16C9b9
- 12C3b3
- 16C7b7
Q. If x=111……1(20 digits), y=333……3(10 digits) and z=222……2(10 digits), then x−z is equal to
- y2
- 2y2
- y3
- 3y3
Q. The coefficient of a8b4c9d9 in (abc+abd+acd+bcd)10 is
- 10!
- 1260
- 5040
- 2520
Q. If A(i, j) be the coefficient of ai bj c2010−i−j in the expansion of (a+b−c)2010 then
- Ai, i is defined for i ?1010
- Ai, j=Aj, i
- A.2i, 3i is defined for i ?405
- A0, 1=2000
Q. If x=111……1(20 digits), y=333……3(10 digits) and z=222……2(10 digits), then x−z is equal to
- y2
- 2y2
- y3
- 3y3
Q. The degree of the polynomial 1√4x+1⎡⎣(1+√4x+12)7−(1−√4x+12)7⎤⎦ is
Q. The number of terms in the expansion of (x+y+z)10 is
- 88
- 55
- 66
- 77
Q.
Write the coefficient of in the following.
Q. If x=111……1(20 digits), y=333……3(10 digits) and z=222……2(10 digits), then x−z is equal to
- y3
- y2
- 3y3
- 2y2
Q. Sum of coefficients of the following expansion (x+2y+3z)8 is ____
- 39
- 68
- 38
- 69
Q. Coefficient of a5b4c7 in the expansion of (bc+ca+ab)8 is _____
- 180
- 280
- 360
- 300