Binomial Theorem · JEE Main previous year questions

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2021 14 questions

Q302021 · 1 Sept 2021 · Shift 2· Numerical answer
If the sum of the coefficients in the expansion of $(x + y)^{n}$ is 4096, then the greatest coefficient in the expansion is ___________.
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Answer: 924
Q242021 · 25 Jul 2021 · Shift 1· Numerical answer
The ratio of the coefficient of the middle term in the expansion of $(1 + x)^{20}$ and the sum of the coefficients of two middle terms in expansion of $(1 + x)^{19}$ is ____.
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Answer: 1
Q272021 · 25 Jul 2021 · Shift 1· Numerical answer
The term independent of 'x' in the expansion of $(\frac{x + 1}{x ^{2/3} - x ^{1/3} + 1} - \frac{x - 1}{x - x ^{1/2}})^{10}$ , where $x \neq = 0, 1$ is equal to ____.
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Answer: 210
Q12021 · 25 Jul 2021 · Shift 2
The sum of all those terms which are rational numbers in the expansion of $(2^{1/3} + 3^{1/4})^{12}$ is :
1. A.89
2. B.27
3. C.35
4. D.43
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Answer: D
Q42021 · 25 Jul 2021 · Shift 2
If the greatest value of the term independent of 'x' in the expansion of $(x sin α + a \frac{c o s α}{x})^{10}$ is $\frac{10 !}{( 5 ! ) ^{2}}$ , then the value of 'a' is equal to :
1. A. $- 1$
2. B.1
3. C. $- 2$
4. D.2
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Answer: D
Q162021 · 25 Jul 2021 · Shift 2
If $^{n} P_{r} =^{n} P_{r + 1}$ and $^{n} C_{r} =^{n} C_{r - 1}$ , then the value of r is equal to :
1. A.1
2. B.4
3. C.2
4. D.3
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Answer: C
Q262021 · 25 Jul 2021 · Shift 2· Numerical answer
If the co-efficient of $x^{7}$ and $x^{8}$ in the expansion of $(2 + \frac{x}{3})^{n}$ are equal, then the value of n is equal to ____.
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Answer: 55
Q282021 · 22 Jul 2021 · Shift 2· Numerical answer
If the constant term, in binomial expansion of $(2 x^{r} + \frac{1}{x ^{2}})^{10}$ is 180, then r is equal to ________.
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Answer: 8
Q182021 · 20 Jul 2021 · Shift 1
The coefficient of $x^{256}$ in the expansion of $(1 - x)^{101} (x^{2} + x + 1)^{100}$ is :
1. A. $^{100} C_{16}$
2. B. $^{100} C_{15}$
3. C. $-^{100} C_{16}$
4. D. $-^{100} C_{15}$
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Answer: B
Q232021 · 20 Jul 2021 · Shift 1· Numerical answer
The number of rational terms in the binomial expansion of $(4^{\frac{1}{4}} + 5^{\frac{1}{6}})^{120}$ is ________.
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Answer: 21
Q232021 · 18 Mar 2021 · Shift 2· Numerical answer
The term independent of x in the expansion of $[\frac{x + 1}{x ^{2/3} - x ^{1/3} + 1} - \frac{x - 1}{x - x ^{1/2}}]^{10}, x \neq = 1$ , is equal to ____.
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Answer: 210
Q302021 · 18 Mar 2021 · Shift 2· Numerical answer
Let $^{n} C_{r}$ denote the binomial coefficient of $x^{r}$ in the expansion of $(1 + x)^{n}$ . If $\sum_{k = 0}^{10} (2^{2} + 3 k)^{10} C_{k} = α \cdot 3^{10} + β \cdot 2^{10}, α, β \in R$ , then $α + β$ is equal to ____.
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Answer: 19
Q72021 · 16 Mar 2021 · Shift 1
If n is the number of irrational terms in the expansion of $(3^{1/4} + 5^{1/8})^{60}$ , then $(n - 1)$ is divisible by :
1. A.30
2. B.8
3. C.7
4. D.26
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Answer: D
Q12021 · 26 Feb 2021 · Shift 1
The maximum value of the term independent of 't' in the expansion of $(t x^{\frac{1}{5}} + \frac{( 1 - x ) ^{\frac{1}{10}}}{t})^{10}$ where $x \in (0, 1)$ is :
1. A. $\frac{10 !}{3 ( 5 ! ) ^{2}}$
2. B. $\frac{2 \cdot 10 !}{3 3 ( 5 ! ) ^{2}}$
3. C. $\frac{10 !}{3 ( 5 ! ) ^{2}}$
4. D. $\frac{2 \cdot 10 !}{3 ( 5 ! ) ^{2}}$
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Answer: B