JEE Main - Simple applications of the binomial theorem One Line Questions & Answers

1. The sum of the binomial coefficients of (x+y)^n is equivalent to the expansion of: — (1+1)^n

2. The sum of the binomial coefficients of (a + b)^n is equal to: — (a+b)^n

3. What is the sum of the coefficients of the terms with odd powers of x in the expansion of (1 + x)^n? — 2^(n-1)

4. The sum of the coefficients of the terms with even powers of x in the expansion of (1 + x)^n is: — 2^(n-1)

5. What is the sum of the coefficients of the expansion of (2x - 3y)^4? — -1

6. The sum of the coefficients in the expansion of (3x - 2y)^3 is: — 1

7. The expansion of (1 - x)^n is: — 1 - nx + (n(n-1)/2!)x^2 - ...

8. The binomial expansion of (1 + x)^n is given by: — 1 + nx + (n(n-1)/2!)x^2 + ...

9. What is the value of (1.01)^5 approximated to three decimal places? — 1.051

10. What is the coefficient of x^2y^3 in the expansion of (x + y)^5? — 10

11. What is the value of C(5, 2)? — 10

12. What is the value of (10)^4? — 10000

13. Find the term containing x^3 in the expansion of (x + 2)^5. — 80x^3

14. What is the numerical value of C(10, 3)? — 120

15. What is the coefficient of x^4y^2 in the expansion of (x + y)^6? — 15

16. What is the sum of the coefficients in the binomial expansion of (x + y)^n? — 2^n

17. What is the value of C(n, 0) + C(n, 1) + C(n, 2) + ... + C(n, n)? — 2^n

18. Find the constant term in the expansion of (x - 1/x)^6. — 20

19. Find the coefficient of x^2 in (x + y + z)^3. — 3

20. Find the term independent of x in the expansion of (x^2 - 3/x)^6. — -405

21. What is the coefficient of the second term in the expansion of (a + b)^5? — 5

22. What is the coefficient of x^5 in the expansion of (x + 3)^8? — 8C5 * 3^5

23. In the expansion of (x + y)^9, what is the position of the middle term? — 5th term

24. What is the coefficient of x^3 in the expansion of (3 + 2x)^5? — 1080

25. Find the coefficient of the 4th term in the expansion of (x - 2y)^5. — -80

26. Using the binomial theorem, what is the value of 99^3? — 970299

27. The expansion of (a - b)^n is an alternating series if: — a is positive and b is negative

28. The expansion of (1 + x)^n is valid for: — Any real value of x

29. What is the coefficient of x^7 in the expansion of (x + 1/x)^15? — 0

30. What is the coefficient of x^4 in the expansion of (2 - x)^7? — C(7, 4) * 2^3 * (-1)^4

31. The expansion of (a + b)^n has how many terms? — n+1

32. What is the value of C(n, 1)? — n

33. If the coefficient of the (r)th term in the expansion of (1 + x)^n is equal to the coefficient of the (r+1)th term, then: — n = 2r - 1

34. The expansion of (x + y)^n is symmetric with respect to x and y if: — The coefficients are equal

35. For the expansion of (x + y)^n, when n is even, how many terms are there and what is the position of the middle term? — n+1 terms, (n/2 + 1)th term

36. If the expansion of (x + a)^n contains a term with x^k, then the term is given by: — nCk * a^k * x^(n-k)

37. The coefficient of x^r in the binomial expansion of (1 + x)^n is given by: — nCr

38. What is the coefficient of x^r in the expansion of (x + a)^n? — nCr * a^r

39. What is the general term in the binomial expansion of (a + x)^n? — nCr * a^(n-r) * x^r

40. The general term in the expansion of (x + iy)^n is given by: — nCr * x^(n-r) * (iy)^r

41. In the expansion of (x + y)^n, what is the (r+1)th term? — nCr * x^(n-r) * y^r

42. In the expansion of (x + a)^n, the (r)th term is given by: — nCr-1 * x^(n-r+1) * a^(r-1)

43. What is the sign of the middle term in the expansion of (x - y)^10? — Positive

44. The expansion of (x + y)^n can be used to approximate values like: — sqrt(2)

45. The value of C(n, r) is equal to C(n, n-r). This property is known as: — Symmetry

46. Which term in the expansion of (2x - 3y)^7 contains x^4? — The 5th term

47. What is the value of the middle term in the expansion of (x + y)^10? — The 6th term

48. Which term in the expansion of (a + b)^12 is the middle term? — The 7th term

49. Find the term independent of x in the expansion of (2x - 3/x^2)^9. — C(9, 6) * 2^3 * (-3)^6

50. To find the sum of coefficients in (ax + by)^n, we substitute: — x = 1, y = 1

Simple applications of the binomial theorem - One Line Questions