This quiz works best with JavaScript enabled. Home > Cbse > Class 11 > Science > Mathematics > Class 11 Mathematics Chapter 8 Binomial Theorem – Quiz 2 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 11 Mathematics Chapter 8 Binomial Theorem Quiz 2 (60 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. What is the value of 7C6 in Pascal's triangle? A) 35. B) 28. C) 21. D) 42. Show Answer Correct Answer: B) 28. 2. Find the 3rd term in the expansion of $(3x-4y)^3$ A) A. $144xy^2$. B) $-64y^3$. C) $-144x^2y$. D) $27x^3$. E) $-36x^2y$. Show Answer Correct Answer: A) A. $144xy^2$. 3. Factor (64x$^{10}$ + 81) A) (32x + 9i)(32x-9i). B) (8x + 9)(8x-9). C) (8x + 9i)(8x-9i). D) (32x$^{5}$$^{}$ + 9)(32x$^{5}$-9). Show Answer Correct Answer: C) (8x + 9i)(8x-9i). 4. Find the coefficient of x$^{3}$ in the expansion of (1 + x)$^{20}$ A) 8000. B) 4845. C) 1140. D) 190. Show Answer Correct Answer: C) 1140. 5. If n is even, then middle term in the expansion (x +y)$^{n}$ is A) (n+1) th term. B) N/2 term. C) (n/2)+1 term. D) (n+1)/2 and (n+3)/2 terms. Show Answer Correct Answer: C) (n/2)+1 term. 6. Factor $27x^3-64$ A) $\left(3x-4\right)\left(9x^2-12x+16\right)$. B) $\left(3x+4\right)\left(9x^2+12x+16\right)$. C) $\left(3x-4\right)\left(9x^2+12x+16\right)$. D) $\left(3x+4\right)\left(9x^2+12x+16\right)$. Show Answer Correct Answer: C) $\left(3x-4\right)\left(9x^2+12x+16\right)$. 7. Factor 2x$^{3}$ + 128 A) (x + 4)(x$^{2}$-4x + 16). B) 2(x$^{3}$ + 64). C) 2(x + 4)(x$^{2}$-4x + 16). D) 2(x-4)(x$^{2}$ + 4x + 16). Show Answer Correct Answer: C) 2(x + 4)(x$^{2}$-4x + 16). 8. Find the sum of the coefficients in the expansion of $(2x-1)^5$ A) 32. B) 243. C) 0. D) 1. Show Answer Correct Answer: C) 0. 9. Expand completely. $\left(2n+m\right)^3$ A) $40n^3+40n^2m+20nm^2+5m^3$. B) $8n^3+12n^2m+6nm^2+m^3$. C) $8n^3+12n^2m+6nm^2+m^3$. D) $32n^3+24n^2m+8nm^2+m^3$. Show Answer Correct Answer: B) $8n^3+12n^2m+6nm^2+m^3$. 10. If you were to flip a coin 20 times, what is the probability you would get exactly 10 heads? A) 41.19%. B) 58.81%. C) 50%. D) 17.62%. Show Answer Correct Answer: D) 17.62%. 11. What is the first term of $\left(2r-s\right)^8$ A) $256r^8$. B) $128r^8$. C) $64r^8$. D) $64r$. Show Answer Correct Answer: A) $256r^8$. 12. If $^{n}$P7= 42 $^{n}$P5, then the value of 'n' is A) 12. B) 10. C) 13. D) 11. Show Answer Correct Answer: A) 12. 13. Find term 6 in (x+8)$^{12}$ A) 25952256x$^{7}$. B) 792x$^{7}$. C) 6336x. D) 30277632x$^{6}$. Show Answer Correct Answer: A) 25952256x$^{7}$. 14. Explain the concept of combinations with an example. A) Combinations are used to calculate the perimeter of a shape. B) Combinations are the selection of items without considering the order. For example, choosing 2 colors out of 5 different colors. C) Combinations only involve selecting one item at a time. D) Combinations involve arranging items in a specific order. Show Answer Correct Answer: B) Combinations are the selection of items without considering the order. For example, choosing 2 colors out of 5 different colors. 15. What is the Binomial expansion of (a-b)$^{7}$? A) A$^{7}$ + 7a$^{6}$b + 21a$^{5}$b$^{2}$ + 35a$^{4}$b$^{3}$ + 35a$^{3}$b$^{4}$ + 21a$^{2}$b$^{5}$ + 7ab$^{6}$ + b$^{7}$. B) A$^{7}$ + 7a$^{6}$b-21a$^{5}$b$^{2}$ + 35a$^{4}$b$^{3}$-35a$^{3}$b$^{4}$ + 21a$^{2}$b$^{5}$-7ab$^{6}$ + b$^{7}$. C) A$^{7}$-b$^{7}$. D) A$^{7}$-7a$^{6}$b + 21a$^{5}$b$^{2}$-35a$^{4}$b$^{3}$ + 35a$^{3}$b$^{4}$-21a$^{2}$b$^{5}$ + 7ab$^{6}$-b$^{7}$. Show Answer Correct Answer: D) A$^{7}$-7a$^{6}$b + 21a$^{5}$b$^{2}$-35a$^{4}$b$^{3}$ + 35a$^{3}$b$^{4}$-21a$^{2}$b$^{5}$ + 7ab$^{6}$-b$^{7}$. 16. The 3rd term in row 6 of Pascal's Triangle is A) 15. B) 50. C) 20. D) 24. Show Answer Correct Answer: A) 15. 17. $\left(3r-5\right)^3$ A) $27r^3-135r^2+225r-125$. B) $27r^3-125$. C) $27r^3-45r^2+75r-125$. D) $27r^3+135r^2+225r+125$. Show Answer Correct Answer: A) $27r^3-135r^2+225r-125$. 18. What is the Pascal triangle used for in binomial theorems? A) To find the area of a circle. B) To determine prime numbers in a sequence. C) To calculate square roots of numbers. D) To determine coefficients of terms in binomial expansions. Show Answer Correct Answer: D) To determine coefficients of terms in binomial expansions. 19. Write the general term rule for this arithmetic sequence:25, 21, 17, 13, ..... A) A$_{n}$ = 4n + 25. B) A$_{n}$ = 4n + 29. C) A$_{n }$=-4n + 29. D) A$_{n}$ =-4n + 25. Show Answer Correct Answer: C) A$_{n }$=-4n + 29. 20. $\left(4-3x\right)^7$ A) -193563. B) -20412. C) -86016. D) -240920. Show Answer Correct Answer: C) -86016. 21. How do you create Pascal's Triangle? A) The first row is all 1's, 2nd all 2's, third all 3's, etc. B) 1's all the way down on the outside of both right and left sides, then add the two numbers above each space to complete the triangle. C) Use the perfect square numbers. D) Count by twos. Show Answer Correct Answer: B) 1's all the way down on the outside of both right and left sides, then add the two numbers above each space to complete the triangle. 22. A normally distributed data set of 500 values has a mean of 35 and a standard deviation of 7. Which is closest to the probability that a value in the data set will fall between 42 and 46? (The answer is given as a decimal and not a percent). A) 0.10. B) 50. C) 0.04. D) 10. Show Answer Correct Answer: A) 0.10. 23. Find the 12th term in the expansion of (x-5)$^{13}$. A) -3808593750. B) -3808593750x$^{2}$. C) -48828125x$^{9}$. D) -48828125. Show Answer Correct Answer: B) -3808593750x$^{2}$. 24. According to the empirical rule, approximately what percentage of data falls within three standard deviations of the mean? A) 99.7%. B) 68%. C) 95%. D) 100%. Show Answer Correct Answer: A) 99.7%. 25. True or False:When something is a factor, the remainder is 0. A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: A) True. 26. Which of the following is the correct expansion of $(x-3)^2$ A) $x^2-9x + 9$. B) $x^2-6x + 9$. C) $x^2-3x + 9$. D) $x^2 + 6x + 9$. Show Answer Correct Answer: B) $x^2-6x + 9$. 27. What is the 4th row of Pascal's Triangle? A) 1 4 8 4 1. B) 1 4 6 4 1. C) 1 3 3 1. D) 1 2 1. Show Answer Correct Answer: B) 1 4 6 4 1. 28. Expand Completely. (Using Pascal's Triangle) $\left(2n+m\right)^4$ A) $16n^4+32n^3m+24n^2m^2+8nm^3+m^4$. B) $16n^4-32n^3m-24n^2m^2-8nm^3-m^4$. C) $16n^4-32n^3m+24n^2m^2-8nm^3-m^4$. D) None of the above. Show Answer Correct Answer: A) $16n^4+32n^3m+24n^2m^2+8nm^3+m^4$. 29. Find the product:(5x + 2) (x$^{2 }$-3x +6) A) 5x$^{3 }$+ 17x$^{2}$-24x +12. B) 5x$^{3}$-13x$^{2}$ + 24x +12. C) 5x$^{3}$ +13x$^{2}$-24x-12. D) 5x$^{3 }$-17x$^{2 }$+24x +12. Show Answer Correct Answer: B) 5x$^{3}$-13x$^{2}$ + 24x +12. 30. Given the binomial $\left(x^5-y^3\right)^{15}$ A) $455x^{15}y^{36}$. B) $-455x^{15}y^{36}$. C) $455x^8y^{15}$. D) $x^{15}y^{36}$. Show Answer Correct Answer: A) $455x^{15}y^{36}$. 31. Using the Binomial Theorem, what is the constant term in the expansion of $(2x-1)^4$ A) 16. B) 24TagsAZ.MA.9-12.P.A-APR.C.5. C) -8. D) 1. Show Answer Correct Answer: A) 16. 32. If the top row of Pascal's Triangle is row 0, then what is the sum of the numbers in the eighth row? A) 256. B) 264. C) 255. D) 257. E) 260. Show Answer Correct Answer: A) 256. 33. Determine the number of 5 card combinations out of a deck of 52 cards if there is exactly one ace in each combination. A) $_{4}$C$_{1}$ x $_{48}$C$_{4}$. B) $4\times52_{C_3}$. C) 10246. D) $_{52}$C$_{5}$. Show Answer Correct Answer: A) $_{4}$C$_{1}$ x $_{48}$C$_{4}$. 34. Expand the binomial (2x+3)$^{4}$ A) 16x$^{4}$+81. B) 16x$^{4}$+96x$^{3}$+216x$^{2}$+216x+81. C) X$^{4}$+4x$^{3}$+6x$^{2}$+4x+1. D) 16x$^{4}$+186x$^{3}$+398x$^{2}$+312x+81. Show Answer Correct Answer: B) 16x$^{4}$+96x$^{3}$+216x$^{2}$+216x+81. 35. Row 0 on pascal triangle A) 1331. B) 121. C) 11. D) 1. E) 14641. Show Answer Correct Answer: D) 1. 36. Expand (x-1)$^{4}$ A) X$^{4 }$+ 4x$^{3 }$+ 6x$^{2 }$+ 4x + 1. B) X$^{4 }$-4x$^{3 }$+ 6x$^{2 }$-4x + 1. C) X$^{4 }$-4x$^{3 }$+ 6x$^{2 }$-4x + 4. D) X$^{4 }$+ 4x$^{3 }$-6x$^{2 }$+ 4x-1. Show Answer Correct Answer: B) X$^{4 }$-4x$^{3 }$+ 6x$^{2 }$-4x + 1. 37. How many terms are in this expansion? $\left(x+52\right)^5$ A) 6. B) 25. C) 3. D) 50. E) 5. Show Answer Correct Answer: A) 6. 38. 7r$^{3}$-8r$^{2}$+42r-48 A) (r$^{2}$+6)(r$^{2}$+8). B) (r$^{2}$+6)(7r-8). C) (r$^{2}$+6)(7r+8). D) (r$^{2}$+6)(7r+6). Show Answer Correct Answer: B) (r$^{2}$+6)(7r-8). 39. Find the third term in the expansion of $\left(4y-x\right)^4$ A) $95y^2x^2$. B) $96y^2x^2$. C) $-16yx^3$. D) $91y^2x^2$. Show Answer Correct Answer: B) $96y^2x^2$. 40. Find the coefficient of x$^{3 }$in the expansions of (x + 2)$^{5}$. A) 35. B) 30. C) 25. D) 40. Show Answer Correct Answer: D) 40. 41. Kamali has 6 unique bracelets and is trying to decide which 3 to wear on a date. Use Pascal's Triangle to find the number of different combinations of 3 bracelets that Kamali could choose from the6 she owns? A) 15. B) 1. C) 6. D) 20. Show Answer Correct Answer: D) 20. 42. Through $\left(3x-\frac{2}{3}y^2\right)^5$ $xy^8$ A) $\frac{80}{27}$. B) $\frac{85}{27}$. C) $\frac{88}{27}$. D) $\frac{80}{28}$. Show Answer Correct Answer: A) $\frac{80}{27}$. 43. How many ways can 8 cheerleaders be chosen for 3 positions on the cheer team? A) 56. B) 24. C) 128. D) 336. Show Answer Correct Answer: A) 56. 44. What number can always be found at the left side of the triangle? A) 1. B) 0. C) 2. D) 3. E) 4. Show Answer Correct Answer: A) 1. 45. What is the 14th term of the geometric sequence?3, 9, 27, 81, ..... A) 45. B) 4, 782, 969. C) 14, 348, 907. D) 1, 594, 323. Show Answer Correct Answer: B) 4, 782, 969. 46. Which of the following is the correct formula in calculating the binomial coefficient in a binomial expansion? A) $nCr=\frac{r!}{\left(n-r\right)!r!}$. B) $nCr=\frac{n!}{\left(n-r\right)!n!}$. C) $nCr=\frac{n!}{\left(n-r\right)!r!}$. D) $nCr=\frac{r!}{\left(r-n\right)!n!}$. Show Answer Correct Answer: C) $nCr=\frac{n!}{\left(n-r\right)!r!}$. 47. The coefficient of y$^{4}$ in th expansion of (y$^{4}$+3)$^{3}$ A) 9. B) 26. C) 25. D) 27. Show Answer Correct Answer: D) 27. 48. Find term 6 in row 9 A) 84. B) 9. C) 36. D) 126. Show Answer Correct Answer: A) 84. 49. Which row of the Pascal's Triangle is the number 6 first found in? A) 3rd. B) 6th. C) 4th. D) 5th. E) 2nd. Show Answer Correct Answer: D) 5th. 50. $\frac{\frac{x+1}{x^2}}{\frac{1}{x}+\frac{x+1}{x}}$ A) $\frac{\frac{x+1}{x^2}}{\frac{x+2}{x}}$. B) $\frac{x+1}{x\left(x+2\right)}$. C) $\frac{1}{x}$. D) $\frac{2x+2}{x\left(x+2\right)}$. Show Answer Correct Answer: B) $\frac{x+1}{x\left(x+2\right)}$. 51. If n is even in the expansion of (a+b)$^{n}$, the middle term is: A) (n/2)$^{th}$ term. B) [(n/2)-1]$^{th}$ term. C) [(n/2)+1]$^{th}$ term. D) N$^{th}$ term. Show Answer Correct Answer: C) [(n/2)+1]$^{th}$ term. 52. In how many ways can you arrange the letters of the word EDUCATION such that the vowels are always together? A) 120 ways. B) 14400 ways. C) 362880 ways. D) 6547234 ways. Show Answer Correct Answer: B) 14400 ways. 53. From $\left(x^2-2y\right)^7$ A) $560x^6y^4$. B) $550x^6y^5$. C) $560x^4y^6$. D) $566x^6y^4$. Show Answer Correct Answer: A) $560x^6y^4$. 54. Expand $\left(x-7\right)^2$ A) X$^{2}$ + 14x-49. B) X$^{2}$-14x + 49. C) 49x$^{2}$. D) -x$^{2}$-14x-49. Show Answer Correct Answer: B) X$^{2}$-14x + 49. 55. If 1 1 is first row, 1 2 1 is second row then what is 4$^{th}$$^{}$ row? A) 1 4 6 4 1. B) 1 5 7 5 1. C) 1 2 3 4 3 2 1. D) 1 4 10 4 1. Show Answer Correct Answer: A) 1 4 6 4 1. 56. Use Pascal's Triangle to find the 4th term in the expansion of (4x-3)$^{5}$. A) 5760x$^{3}$. B) -4320. C) -4320x$^{2}$. D) 5760. Show Answer Correct Answer: C) -4320x$^{2}$. 57. Multiply. $-3x^2\left(7x^2-x+4\right)$ A) $^{ }$ $7x^2-x+4\left(-3x^2\right)$. B) $-21x^4+3x^3-12x^2$. C) $21x^4+3x^3+12x^2$. D) $-21x^2+3x^3-21x^4$. Show Answer Correct Answer: B) $-21x^4+3x^3-12x^2$. 58. Select the correct expansion of(1-x)$^{5}$ A) -1 + 5x-10x$^{2}$ + 10x$^{3}$-5x$^{4}$ + x$^{5}$. B) 1 + 5x + 10x$^{2}$ + 10x$^{3}$ + 5x$^{4}$ + x$^{5}$. C) 1-5x + 10x$^{2}$ + 10x$^{3}$ + 5x$^{4}$-x$^{5}$. D) 1-5x + 10x$^{2}$-10x$^{3}$ + 5x$^{4}$-x$^{5}$. Show Answer Correct Answer: D) 1-5x + 10x$^{2}$-10x$^{3}$ + 5x$^{4}$-x$^{5}$. 59. The sign of the z-score indicates whether the location is above(positive) or below(negative) the mean. A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: A) True. 60. If the coefficients of $x^7$ $x^8$ $(2+\frac{x}{3})^n$ A) 15. B) 56. C) 55. D) 45. Show Answer Correct Answer: C) 55. ← PreviousNext →Related QuizzesScience QuizzesClass 11 QuizzesClass 11 Mathematics Chapter 8 Binomial Theorem Quiz 1Class 11 Mathematics Chapter 8 Binomial Theorem Quiz 3Class 11 Mathematics Chapter 8 Binomial Theorem Quiz 4Class 11 Mathematics Chapter 8 Binomial Theorem Quiz 5Class 11 Mathematics Chapter 8 Binomial Theorem Quiz 6Class 11 Mathematics Chapter 8 Binomial Theorem Quiz 7Class 11 Mathematics Chapter 8 Binomial Theorem Quiz 8Class 11 Mathematics Chapter 8 Binomial Theorem Quiz 9 🏠 Back to Homepage 📘 Download PDF Books 📕 Premium PDF Books