Binomial Theorem · JEE Main previous year questions

2019 9 questions

1. Q102019 · 12 Apr 2019 · Shift 1

   The coefficient of $x^{18}$ in the product $(1+x)(1-x{)}^{10}(1+x+x^2{)}^9$ is :

   1. A.126
   2. B.-84
   3. C.-126
   4. D.84
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   Answer: D

2. Q182019 · 12 Apr 2019 · Shift 2

   The term independent of x in the expansion of $\left(\frac{1}{60}-\frac{x^8}{81}\right){\left(2x^2-\frac{3}{x^2}\right)}^6$ is equal to :

   1. A.36
   2. B.-108
   3. C.-36
   4. D.-72
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   Answer: C

3. Q232019 · 10 Apr 2019 · Shift 1

   If the coefficients of $x^2$ and $x^3$ are both zero, in the expansion of the expression $(1+ax+b{x}^2)(1-3x{)}^{15}$ in powers of x, then the ordered pair (a,b) is equal to :

   1. A.(28, 861)
   2. B.(28, 315)
   3. C.(-21, 714)
   4. D.(-54, 315)
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   Answer: B

4. Q82019 · 10 Apr 2019 · Shift 2

   The smallest natural number n, such that the coefficient of x in the expansion of ${\left(x^2+\frac{1}{x^3}\right)}^n$ is ${}^n{\mathrm{C}}_{23}$, is :

   1. A.23
   2. B.58
   3. C.38
   4. D.35
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   Answer: C

5. Q102019 · 9 Apr 2019 · Shift 1

   If the fourth term in the binomial expansion of ${\left(\frac{2}{x}+x^{{\log }_{8}x}\right)}^6$ (x > 0) is $20\times 8^7$, then a value of x is :

   1. A.$8^{-2}$
   2. B.$8^2$
   3. C.$8^3$
   4. D.8
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   Answer: B

6. Q252019 · 9 Apr 2019 · Shift 2

   If some three consecutive coefficients in the binomial expansion of $(x+1{)}^n$ in powers of x are in the ratio $2:15:70$, then the average of these three coefficients is :-

   1. A.625
   2. B.227
   3. C.964
   4. D.232
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   Answer: D

7. Q62019 · 8 Apr 2019 · Shift 2

   If the fourth term in the binomial expansion of ${\left(\sqrt{x^{\left(\frac{1}{1+{\log }_{10}x}\right)}}+x^{\frac{1}{12}}\right)}^6$ is equal to 200, and x > 1, then the value of x is :

   1. A.100
   2. B.$10^3$
   3. C.10
   4. D.$10^4$
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   Answer: C

8. Q62019 · 12 Jan 2019 · Shift 1

   A ratio of the 5th term from the beginning to the 5th term from the end in the binomial expansion of ${\left(2^{1/3}+\frac{1}{2(3{)}^{1/3}}\right)}^{10}$ is :

   1. A.$1:2(6{)}^{1/3}$
   2. B.$1:4(6{)}^{1/3}$
   3. C.$2(36{)}^{1/3}:1$
   4. D.$4(36{)}^{1/3}:1$
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   Answer: D

9. Q212019 · 12 Jan 2019 · Shift 2

   The total number of irrational terms in the binomial expansion of $(7^{1/5}-3^{1/10}{)}^{60}$ is :

   1. A.54
   2. B.55
   3. C.49
   4. D.48
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   Answer: A