Multinomial Theorem

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JEE Main 2016

LEVELBoard

If the number of terms in the expansion of $(1 - \frac{2}{x} + \frac{4}{x ^{2}})^{n}, x \neq = 0$ , is 28, then the sum of the coefficients of all the terms in this expansion, is

Coefficient of $x^{11}$ in the expansion of $(1 + x^{2})^{4} (1 + x^{3})^{7} (1 + x^{4})^{12}$ is

JEE Main 2020 (9 January Shift 1)

LEVELJEE Main

The coefficient of $x^{4}$ in the expansion of $(1 + x + x^{2})^{10}$ is:

JEE Main 2020 - 9 Jan (Morning)

LEVELJEE Main

Find the coefficient of $x^{4}$ in $(1 + x + x^{2})^{10}$

JEE Main 2020 - 4 Sep (Morning)

LEVELJEE Advanced

Let $(2 x^{2} + 3 x + 4)^{10} = \sum_{r = 0}^{20} a_{r} x^{r}$ . Then $\frac{a _{7}}{a _{13}}$ is equal to

JEE Main 2021 (31 Aug Shift 2)

LEVELJEE Main

If the coefficient of $a^{7} b^{8}$ in the expansion of $(a + 2 b + 4 ab)^{10}$ is $K \cdot 2^{16}$ , then $K$ is equal to .

JEE Main 2022 (29 June Shift 1)

LEVELJEE Main

If the constant term in the expansion of $(3 x^{3} - 2 x^{2} + \frac{5}{x ^{5}})^{10}$ is $2^{k} \cdot l$ , where $l$ is an odd integer, then the value of $k$ is equal to :

JEE Main 2023 (10 Apr Shift 1)

LEVELJEE Main

The coefficient of $x^{7}$ in $(1 - x + 2 x^{3})^{10}$ is —————————— .

JEE Main 2023 (15 Apr Shift 1)

LEVELJEE Main

Let $(a + b x + c x^{2})^{10} = \sum_{i = 0}^{20} p_{i} x^{i}, a, b, c \in N$ . If $p_{1} = 20$ and $p_{2} = 210$ , then $2 (a + b + c)$ is equal to

JEE Main 2023 (25 January Shift 1)

LEVELJEE Main

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If the number of terms in the expansion of (1−x2​+x24​)n,x=0, is 28, then the sum of the coefficients of all the terms in this expansion, is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Coefficient of x11 in the expansion of (1+x2)4(1+x3)7(1+x4)12 is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The coefficient of x4 in the expansion of (1+x+x2)10 is:

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Find the coefficient of x4 in (1+x+x2)10

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Let (2x2+3x+4)10=∑r=020​ar​xr. Then a13​a7​​ is equal to

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If the coefficient of a7b8 in the expansion of (a+2b+4ab)10 is K⋅216, then K is equal to .

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If the constant term in the expansion of (3x3−2x2+x55​)10 is 2k⋅l, where l is an odd integer, then the value of k is equal to :

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The coefficient of x7 in (1−x+2x3)10 is —————————— .

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Let (a+bx+cx2)10=∑i=020​pi​xi,a,b,c∈N. If p1​=20 and p2​=210, then 2(a+b+c) is equal to

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The constant term in the expansion of (2x+x71​+3x2)5 is ______.

If the number of terms in the expansion of $(1 - \frac{2}{x} + \frac{4}{x ^{2}})^{n}, x \neq = 0$ , is 28, then the sum of the coefficients of all the terms in this expansion, is

Coefficient of $x^{11}$ in the expansion of $(1 + x^{2})^{4} (1 + x^{3})^{7} (1 + x^{4})^{12}$ is

The coefficient of $x^{4}$ in the expansion of $(1 + x + x^{2})^{10}$ is:

Find the coefficient of $x^{4}$ in $(1 + x + x^{2})^{10}$

Let $(2 x^{2} + 3 x + 4)^{10} = \sum_{r = 0}^{20} a_{r} x^{r}$ . Then $\frac{a _{7}}{a _{13}}$ is equal to

If the coefficient of $a^{7} b^{8}$ in the expansion of $(a + 2 b + 4 ab)^{10}$ is $K \cdot 2^{16}$ , then $K$ is equal to .

If the constant term in the expansion of $(3 x^{3} - 2 x^{2} + \frac{5}{x ^{5}})^{10}$ is $2^{k} \cdot l$ , where $l$ is an odd integer, then the value of $k$ is equal to :

The coefficient of $x^{7}$ in $(1 - x + 2 x^{3})^{10}$ is —————————— .

Let $(a + b x + c x^{2})^{10} = \sum_{i = 0}^{20} p_{i} x^{i}, a, b, c \in N$ . If $p_{1} = 20$ and $p_{2} = 210$ , then $2 (a + b + c)$ is equal to

The constant term in the expansion of $(2 x + \frac{1}{x ^{7}} + 3 x^{2})^{5}$ is ______.