This quiz works best with JavaScript enabled. Home > Cbse > Class 11 > Science > Mathematics > Class 11 Mathematics Chapter 8 Binomial Theorem – Quiz 8 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 11 Mathematics Chapter 8 Binomial Theorem Quiz 8 (60 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. What is the relationship between the Binomial Theorem and combinatorics? A) Combinatorics only deals with permutations, not combinations. B) The Binomial Theorem is primarily used in calculus. C) The Binomial Theorem is closely related to combinatorics through binomial coefficients, which count combinations. D) The Binomial Theorem is unrelated to combinatorics. Show Answer Correct Answer: C) The Binomial Theorem is closely related to combinatorics through binomial coefficients, which count combinations. 2. $\left(4+ax\right)^6$ $x^4$ $x^5$ A) 2. B) 3. C) 4. D) 5. Show Answer Correct Answer: A) 2. 3. Find the 3rd term in the expansion of $\left(x+4\right)^5$ A) $4x^5$. B) $64x^3$. C) $160x^3$. D) $640x^2$. Show Answer Correct Answer: C) $160x^3$. 4. Add or Subtract to Simplify:(4x$^{2}$+ x)-(x$^{2}$+ 2x) A) 3x$^{2}$ + 2x. B) 3x$^{2}$ + 3x. C) 4x$^{2 }$+ 2x. D) 3x$^{2 }$-x. Show Answer Correct Answer: D) 3x$^{2 }$-x. 5. What is the third term in the expansion of (x + 4)$^{5}$? A) 640 x$^{2}$. B) 64 x$^{3}$. C) 4 x$^{5}$. D) 160 x$^{3}$. Show Answer Correct Answer: D) 160 x$^{3}$. 6. Use the binomial theorem to expand $\left(4-2z\right)^3$ A) $64+96z+48z^2+8z^3$. B) $64-64z+144z^2-8z^3$. C) $64-96z+48z^2-8z^3$. D) $64-96z+48z^2+8z^3$. Show Answer Correct Answer: C) $64-96z+48z^2-8z^3$. 7. Find the positive value of m for which the coefficient of $x^2$ $\left(1+x\right)^m$ A) $m=6$. B) $m=4$. C) $m=5$. D) $m=3$. Show Answer Correct Answer: B) $m=4$. 8. The formula to find greatest coefficient, when n is even A) (n+1)|x| / |x|+1. B) $^{n}$Cn/2. C) $^{n}$Cr/2. D) None. Show Answer Correct Answer: B) $^{n}$Cn/2. 9. $\left(2x-6\right)^3$ A) $8x^3-72x^2+216x-36$. B) $8x^3-72x^2+216x-216$. C) $6x^3-42x^2+72x-216$. D) None of the above. Show Answer Correct Answer: B) $8x^3-72x^2+216x-216$. 10. How many ways can you choose 3 items out of 5? A) 7. B) 15. C) 6. D) 10. Show Answer Correct Answer: D) 10. 11. What is the second term in the binomial expansion of $\left(2r-3s\right)^{12}$ A) $608256r^{10}s^2$. B) $-73728r^{11}s$. C) $73728r^{11}s$. D) $-608256r^{10}s^2$. Show Answer Correct Answer: B) $-73728r^{11}s$. 12. Expand:$\left(x+5\right)^5$ A) $x^5+ +1250x^2+3025x$. B) $x^5+ +3025x+3025$. C) $x^5+ +1250x^2+3125x$. D) $x^5+ +3125x+3125$. Show Answer Correct Answer: D) $x^5+ +3125x+3125$. 13. If the 4th term in the expansion of $(2x + 3)^5$ $T_4$ $T_4$ A) $C(5, 2)\cdot (2x)^2\cdot 3^3$. B) $C(5, 3)\cdot (2x)^2\cdot 3^3$. C) $C(5, 3)\cdot (2x)^3\cdot 3^2$. D) $C(5, 2)\cdot (2x)^3\cdot 3^2$. Show Answer Correct Answer: C) $C(5, 3)\cdot (2x)^3\cdot 3^2$. 14. If $f\left(x\right)=2x^4-3x^3+2x^2-x+17$ $f\left(-2\right)$ A) $83$. B) 83 Mathematical EquivalenceON. C) All the above. D) None of the above. Show Answer Correct Answer: A) $83$. 15. What is the common ratio for the sequence:3, 15, 75 ..... A) 12. B) 1/5. C) 5. D) None of the above. Show Answer Correct Answer: C) 5. 16. For Mrs. V:mean = 55 and standard deviation = 19For Mr. T:mean = 33 and standard deviation = 10.5Mary Beth is very proud of the score of 80 that she earned in Mrs. V's class. Albert is equally proud of the score of 42 he earned in Mr. T's class. Who has the better score? A) Mary Beth. B) Albert. C) All the above. D) None of the above. Show Answer Correct Answer: A) Mary Beth. 17. Factor completely $4x^4-5x^2+1$ A) $\left(4x^2-1\right)\left(x^2+1\right)$. B) $\left(4x^2-1\right)\left(x^2-1\right)$. C) $\left(2x+1\right)\left(2x+1\right)\left(x-1\right)\left(x+1\right)$. D) $\left(2x-1\right)\left(2x+1\right)\left(x-1\right)\left(x+1\right)$. Show Answer Correct Answer: D) $\left(2x-1\right)\left(2x+1\right)\left(x-1\right)\left(x+1\right)$. 18. What is the first term in the expansion of $\left(2x+10y\right)^{15}$ A) $10y^{15}$. B) $10^{15}y^{15}$. C) $2^{15}x^{15}$. D) $2x^{15}$. Show Answer Correct Answer: C) $2^{15}x^{15}$. 19. The term independent of x in the expansion of $\left(x^3+\frac{3}{x^2}\right)^{15}$ A) $15_{C_9}\left(3\right)^9$. B) $15_{C_9}\left(3\right)^7$. C) $15_{C_9}\left(3\right)^4$. D) $15_{C_6}\left(3\right)^6$. Show Answer Correct Answer: A) $15_{C_9}\left(3\right)^9$. 20. Describe a real-world application of the Binomial Theorem. A) Determining the average speed of a moving object in physics experiments. B) Analyzing the stock market trends using linear regression. C) Calculating probabilities in binomial experiments, such as product launches or quality control. D) Calculating the area of geometric shapes using the Pythagorean theorem. Show Answer Correct Answer: C) Calculating probabilities in binomial experiments, such as product launches or quality control. 21. Whichanswer bvelow has the Sigma Symbol in it, which means "sum up" ? A) $\frac{\partial x}{\partial y}$. B) $\log_xy$. C) $\sum_x^y$. D) $\prod_x^y$. Show Answer Correct Answer: C) $\sum_x^y$. 22. Expand:$\left(a+b\right)^2$ A) $a^2-ab+b^2$. B) $a^2+2ab+b^2$. C) $a^2+ab+b^2$. D) $a^2-2ab+b^2$. Show Answer Correct Answer: B) $a^2+2ab+b^2$. 23. Simplify expression and write in standard form.(2w-5)$^{3}$ A) 8w$^{3}$-125. B) 8w$^{3}$-40w$^{2}$ + 150w-125. C) 2w$^{3}$-15. D) 8w$^{3}$-60w$^{2}$ + 150w-125. Show Answer Correct Answer: D) 8w$^{3}$-60w$^{2}$ + 150w-125. 24. Find the coefficient of x$^{3 }$in the expansions of (1-x)$^{15}$. A) 455. B) -500. C) -455. D) 500. Show Answer Correct Answer: C) -455. 25. Find the 5th term of the expansion:(5x + 2)$^{7}$ A) 16800x$^{2}$. B) 70000x$^{3}$. C) 175000x$^{4}$. D) 175000x$^{3}$. Show Answer Correct Answer: B) 70000x$^{3}$. 26. Evaluate:(24/6)! A) 24. B) 6. C) 720. D) 12. Show Answer Correct Answer: A) 24. 27. Find the 6th term in the expansion of (3x+2)$^{8}$ A) 48384x$^{5}$. B) 108864x$^{5}$. C) 48384x$^{3}$. D) 108864x$^{3}$. Show Answer Correct Answer: C) 48384x$^{3}$. 28. Which row of Pascal's triangle would you use to expand $\left(2x+10y\right)^{15}$ A) Row 12. B) Row 10. C) Row 15. D) Row 25. Show Answer Correct Answer: C) Row 15. 29. (2x + 5y-z) + (-6x-4y + 7z) A) -4x +6y + 6z. B) 4x + y + 6z. C) -4x-y + 6z. D) -4x + y + 6z. E) None of these. Show Answer Correct Answer: D) -4x + y + 6z. 30. How many distinguishable ways exist to arrange the letters in the word ELEMENTAL? A) 90, 720. B) 30, 240. C) 362, 880. D) 60, 480. Show Answer Correct Answer: B) 30, 240. 31. Which row of Pascal's Triangle would you use to expand (x+y)$^{3}$? A) 1 2 1. B) 1 1. C) 1. D) 1 3 3 1. Show Answer Correct Answer: D) 1 3 3 1. 32. Expand $\left(u^2-2\right)^3$ A) $u^6-6u^4+12u^2-8$. B) $u^6-16u^4+12u^2-8$. C) $u^6-24u^4+12u^2-8$. D) $5u^6-20u^4+40u^2-40$. Show Answer Correct Answer: A) $u^6-6u^4+12u^2-8$. 33. How can the binomial theorem be applied in probability? A) The binomial theorem helps calculate probabilities in binomial experiments. B) The binomial theorem is irrelevant in statistical analysis. C) The binomial theorem applies only to algebraic expressions. D) The binomial theorem is used to calculate the area of shapes. Show Answer Correct Answer: A) The binomial theorem helps calculate probabilities in binomial experiments. 34. Describe the signs ( + and-) in the expanded form of (x-3)$^{4}$ . A) All +. B) All-. C) Alternating ending in +. D) Alternating ending in-. Show Answer Correct Answer: C) Alternating ending in +. 35. What kind of sequence is illustrated below? 16, 8, 4, 2, ..... A) Recursive. B) Arithmetic. C) Geometric. D) None of the Above. Show Answer Correct Answer: C) Geometric. 36. Fin the coefficient of the term in $x^2$ $\left(x^2+\frac{1}{x^3}\right)^6$ A) 6. B) 15. C) 30. D) 20. E) 10. Show Answer Correct Answer: B) 15. 37. Does this sequence converge or diverge? $\left\{\frac{10n-6}{2n-3}\right\}$ A) Converges to 5. B) Converges to 0. C) Converges to 2. D) Diverges. Show Answer Correct Answer: A) Converges to 5. 38. A geometric sum has g$_{2}$=18 and g$_{5}$=486. Find the sum of the first 9 terms. A) 1, 536. B) 59, 046. C) 177, 156. D) None of these. Show Answer Correct Answer: B) 59, 046. 39. Factor. $216x^3+125$ A) $6\left(x+5\right)^3$. B) $\left(6x+5\right)\left(36x^2-30x+25\right)$. C) $\left(6x+5\right)^3$. D) $\left(6x+5\right)\left(6x^2-30x+25\right)$. Show Answer Correct Answer: B) $\left(6x+5\right)\left(36x^2-30x+25\right)$. 40. Expand $\left(x-y\right)^4$ A) $x^4-4x^3y+6x^2y^2-4xy^3+y^4$. B) $x^4+4x^3y^3+6x^2y^2+4xy+1$. C) $x^4+4x^3y+6x^2y^2+4xy^3+y^4$. D) $x^4+4x^3+6x^2+4x+1$. Show Answer Correct Answer: A) $x^4-4x^3y+6x^2y^2-4xy^3+y^4$. 41. Which row of Pascal's Triangle would you use to expand (x+y)$^{6}$? A) 1 6 15 20 20 15 6 1. B) 1 6 15 20 15 6 1. C) 1 6 15 6 1. D) 1 6 10 10 6 1. Show Answer Correct Answer: B) 1 6 15 20 15 6 1. 42. 1 kilometer is equal to (a) meters. A) 1500 meters. B) 2000 meters. C) A. 1000 meters. D) 500 meters. Show Answer Correct Answer: C) A. 1000 meters. 43. Find the 2nd term in expansion of (3b + 4a)$^{4}$. A.APR.5 A) 864b$^{2}$a$^{2}$. B) 81b$^{4}$. C) 435b$^{3}$a. D) 432b$^{3}$a. Show Answer Correct Answer: D) 432b$^{3}$a. 44. Row 4 on pascal triangle A) 1331. B) 11. C) 1. D) 14641. E) 121. Show Answer Correct Answer: D) 14641. 45. Find the 6th term of the expansion:(4x-9)$^{5}$ A) 131220x. B) -59049x. C) 131220. D) -59049. Show Answer Correct Answer: D) -59049. 46. Find the 3rd term in the expansion of $\left(2y+x\right)^4$ A) $24y^2x^2$. B) $48y^2x^2$. C) $24yx$. D) $24y^2x$. Show Answer Correct Answer: A) $24y^2x^2$. 47. The coefficient of x$^{3}$y$^{4}$ in (2x+3y$^{2}$)$^{5}$ is A) 360. B) 240. C) 720. D) 1080. Show Answer Correct Answer: C) 720. 48. How many terms are in this expansion? A) 25. B) 50. C) 3. D) 6. E) 5. Show Answer Correct Answer: D) 6. 49. At a company, the data set containing the ages of applicants for a particular job was 30 years old, and the standard deviation of the data set was 3.5 years. Which is closest to the percent of applicants that were 21 years old or younger? A) 2.0%. B) 0.5%. C) 2.57%. D) 9.0%. Show Answer Correct Answer: B) 0.5%. 50. (4x-y$^{2}$)$^{4}$ A) 256x$^{4}$-64x$^{3}$y$^{2}$ + 16x$^{2}$y$^{4}$-4xy$^{6}$ + y$^{8}$. B) 256x$^{4}$-256x$^{3}$y$^{2}$ + 96x$^{2}$y$^{4}$-20xy$^{6}$-4y$^{8}$. C) All the above. D) None of the above. Show Answer Correct Answer: A) 256x$^{4}$-64x$^{3}$y$^{2}$ + 16x$^{2}$y$^{4}$-4xy$^{6}$ + y$^{8}$. 51. Identify the leading coefficient in the polynomial.7x$^{2}$+4x-5x$^{6}$$^{}$-15 A) 7. B) 4. C) -15. D) -5. Show Answer Correct Answer: D) -5. 52. For a certain type of computer, the length of time between charges of the battery is normally distributed with a mean of 50 hours and a standard deviation of 15 hours. John owns one of these computers and wants to know the probability that the length of time will be between 50 and 70 hours. A) 0.4087. B) 0.5000. C) 0.9082. D) 0.8989. Show Answer Correct Answer: A) 0.4087. 53. What is the second term of $\left(3x-y\right)^5$ A) $243x^4$. B) $81x^4y$. C) $243x^4y$. D) $243x^2y^2$. Show Answer Correct Answer: C) $243x^4y$. 54. How many terms would be in the expanded form of (x-3)$^{5}$? A) 6. B) 8. C) 5. D) 7. Show Answer Correct Answer: A) 6. 55. To complete the 23th degree binomial expansion, which row of pascal's triangle would you need to use? A) 22ndTagsAII.9-12.7.BP.9-12.5.F. B) 24th. C) The triangle doesn't go that high. D) 23rd. Show Answer Correct Answer: D) 23rd. 56. Find the coefficient of $y^2$ $\left(y-2\right)^5$ A) 320. B) 80. C) -320. D) -80. Show Answer Correct Answer: D) -80. 57. $\left(x+3y\right)^5$ A) $405x^5y^5$. B) $-405xy$. C) $405xy$. D) $405xy^5$. Show Answer Correct Answer: D) $405xy^5$. 58. When x=5/2, numerically greatest term in the expansion of (3 +2x)$^{15}$ is A) 8th. B) 6th. C) 12th. D) 10th. Show Answer Correct Answer: C) 12th. 59. Given the binomial $\left(5x^4+3y^5\right)^8$ $x^{20}$ A) $4725000x^{20}y^{15}$. B) $4725000x^9y^{15}$. C) $175000x^9y^8$. D) $175000x^{20}y^{15}$. Show Answer Correct Answer: A) $4725000x^{20}y^{15}$. 60. Approximately what interest rate would be needed in order to grow an investment of $ 1, 400 to $ 2, 500 in 10 years if the interest was compound monthly? A) 5.81%. B) 5.88%. C) 5.96%. D) 5.84%. Show Answer Correct Answer: A) 5.81%. ← PreviousNext →Related QuizzesScience QuizzesClass 11 QuizzesClass 11 Mathematics Chapter 8 Binomial Theorem Quiz 1Class 11 Mathematics Chapter 8 Binomial Theorem Quiz 2Class 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 9 🏠 Back to Homepage 📘 Download PDF Books 📕 Premium PDF Books