Binomial Theorem · JEE Main previous year questions

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2020 7 questions

Q52020 · 6 Sept 2020 · Shift 2
If the constant term in the binomial expansion of $(x - \frac{k}{x ^{2}})^{10}$ is 405, then $∣ k ∣$ equals :
1. A.3
2. B.9
3. C.1
4. D.2
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Answer: A
Q72020 · 3 Sept 2020 · Shift 2
If the term independent of x in the expansion of $(\frac{3}{2} x^{2} - \frac{1}{3 x})^{9}$ is k, then 18 k is equal to :
1. A.5
2. B.9
3. C.7
4. D.11
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Answer: C
Q12020 · 2 Sept 2020 · Shift 1
Let $α > 0$ , $β > 0$ be such that $α^{3} + β^{2} = 4$ . If the maximum value of the term independent of x in the binomial expansion of $(α x^{\frac{1}{9}} + β x^{- \frac{1}{6}})^{10}$ is 10k, then k is equal to :
1. A.176
2. B.336
3. C.352
4. D.84
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Answer: B
Q212020 · 9 Jan 2020 · Shift 1· Numerical answer
The coefficient of $x^{4}$ is the expansion of $(1 + x + x^{2})^{10}$ is _______.
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Answer: 615
Q142020 · 9 Jan 2020 · Shift 2
In the expansion of $(\frac{x}{c o s θ} + \frac{1}{x s i n θ})^{16}$ , if $ℓ_{1}$ is the least value of the term independent of x when $\frac{π}{8} \leq θ \leq \frac{π}{4}$ and $ℓ_{2}$ is the least value of the term independent of x when $\frac{π}{16} \leq θ \leq \frac{π}{8}$ , then the ratio $ℓ_{2} : ℓ_{1}$ is equal to :
1. A. $8 : 1$
2. B. $16 : 1$
3. C. $1 : 8$
4. D. $1 : 16$
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Answer: B
Q82020 · 8 Jan 2020 · Shift 2
If $α$ and $β$ be the coefficients of $x^{4}$ and $x^{2}$ respectively in the expansion of $(x + x^{2} - 1)^{6} + (x - x^{2} - 1)^{6}$ , then
1. A. $α + β = 60$
2. B. $α - β = 60$
3. C. $α + β = - 30$
4. D. $α - β = - 132$
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Answer: D
Q32020 · 7 Jan 2020 · Shift 2
The coefficient of $x^{7}$ in the expression $(1 + x)^{10} + x (1 + x)^{9} + x^{2} (1 + x)^{8} + \dots + x^{10}$ is:
1. A.120
2. B.330
3. C.420
4. D.210
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Answer: B