Binomial Theorem: JEE Main Mathematics Previous Year Questions

391 previous year questions from Binomial Theorem. Here are the 25 most important ones; open any question for the correct answer and a full step-by-step solution.

1. $The coefficient of x^{3} in the expansion of (1 - x)^{3/2}, (| x | < 1) is$
2. $If A denotes the sum of all the coefficients in the expansion of (1 - 3 x + 10 x^{2})^{n} and B denotes the sum of all the coefficients in the expansion of\dots$
3. $If the ratio of the 7th term from the beginning to the 7 th term from the end in the expansion of (32 + \frac{1}{3 3})^{n} is \frac{1}{6}, then\dots$
4. $The remainder when ((64)^{(64)})^{(64)} is divided by 7 is equal to$
5. $Let m = (9 n^{2} + 54 n + 80) (9 n^{2} + 45 n + 54) (9 n^{2} + 36 n + 35) . The greatest positive integer which divides m, for all positive integers n, is$
6. $The term independent of x in the expansion of (\frac{x + 1}{x ^{2/3} - x ^{1/3} + 1} - \frac{x - 1}{x - x ^{1/2}})^{10}, x \neq = 1, is equal to$
7. $Let S = {x : x ϵ R and (3 + 2)^{x^{2} - 4} + (3 - 2)^{x^{2} - 4} - 10} Then n (S) eqaual to$
8. $The sum of all rational terms in the expansion of (2 + 3)^{8} is:$
9. $In the expansion of (3^{\frac{- x}{4}} + 3^{\frac{5 x}{4}})^{n}, the sum of the binomial coefficients is 256 and four times the term with greatest binomial coefficie\dots$
10. $The sum of the real values of x for which the middle term in the binomial expansion of (\frac{x ^{3}}{3} + \frac{3}{x})^{8} equals 5670 is :$
11. $The sum of the coefficients in the expansion of (1 + \frac{x}{2})^{12} is$
12. $If \sum \frac{( - 1 ) ^{r} . C _{r}}{( r + 1 ) ( r + 2 ) ( r + 3 )} = \frac{1}{a ( n + b )}, then a + b is$
13. $For x = \frac{5}{7}, if t_{k} is the first negative term in the expansion of (1 + x)^{7/5}, then t_{1} + t_{2} + \dots t_{k} =$
14. $In the third term in binomial expansion of (1 + x^{log_{2} x})^{5} equals 2560, then a possible value of x is :$
15. $If (1 - x + x^{2})^{10} = a_{0} + a_{1} x + a_{2} x^{2} + \dots + a_{20} x^{20}, then 2 a_{2} + 3 a_{3} + 4 a_{4} + \dots + 20 a_{20} =$
16. $If the 4^{th} term in the expansion of (\frac{x}{2} - \frac{2 y}{3})^{6} is -20 , then xy =$
17. $If x is so small that x3 and higher powers of x may be neglected, then \frac{( 1 + x ) ^{3/2} - ( 1 + \frac{1}{2} x ) ^{3}}{( 1 - x ) ^{1/2}} may be ap\dots$
18. $The product of the last two digits of (1919)^{1919} is$
19. $If \sum K^{2} (1 0_{C_{K}})^{2} = 22000 L, then L is equal to___.$
20. $The sum of coefficients of integral powers of x in the binomial expansion of (1 - 2 x)^{50} is$
21. $The value of the numerically greatest term in the expansion of (2 x + 3 y)^{11}, when x = \frac{1}{2} and y = \frac{1}{3} is$
22. $If \sum_{r = 0}^{10} (\frac{10 ^{r + 1} - 1}{10 ^{r}}) \cdot^{11} C_{r + 1} = \frac{α 11 - 11 ^{11}}{10 ^{10}}, then\dots$
23. $The coefficients of x^{50} in (1 + x)^{101} (1 - x + x^{2})^{100} is \dots \dots \dots$
24. $If the second, third and fourth terms in the expansion of (x + y)^{n} are 135,30 and \frac{10}{3}, respectively, then 6 (n^{3} + x^{2} + y) is equal\dots$
25. $If P (n) : 2^{n} < n! then the smallest positive integer for which P (n) is true, is$

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Binomial Theorem: JEE Main Mathematics Previous Year Questions

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