This quiz works best with JavaScript enabled. Home > Cbse > Class 11 > Science > Mathematics > Class 11 Mathematics Chapter 8 Binomial Theorem – Quiz 4 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 11 Mathematics Chapter 8 Binomial Theorem Quiz 4 (60 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. Which of the following represents the SUM of a geometric series with 8 TOTAL terms and whose FIRST TERM is 3 and whose COMMON RATIO is 4? A) 32, 756. B) 42, 560. C) 28, 765. D) 65, 535. Show Answer Correct Answer: D) 65, 535. 2. Find the coefficient of $x^{32}$ $\left(x^4-\frac{1}{x^3}\right)^{15}$ A) $-15C_7$. B) $-15C_8$. C) $15C_8$. D) $15C_4$. Show Answer Correct Answer: D) $15C_4$. 3. Which of these is the first step in mathematical induction? A) Prove the statement is true for the first element in the set. B) Show that if the statement is true for the first k elements, then it is true for the (k+1)st case. C) Prove that the problem you are working on is the base to all proofs. D) None of these are correct. Show Answer Correct Answer: A) Prove the statement is true for the first element in the set. 4. What is the fourth term of (n + 2m)$^{5}$ A) 160nm$^{4}$. B) 80n$^{2}$m$^{3}$. C) 80nm$^{4}$. D) 40n$^{2}$m$^{3}$. Show Answer Correct Answer: B) 80n$^{2}$m$^{3}$. 5. What would be the 5th term of the expansion of (n+4)$^{4}$? A) 256. B) 257. C) 259. D) N$^{4}$. Show Answer Correct Answer: A) 256. 6. How do you know what row of Pascal's triangle to use to expand a binomial? A) You use the row that is on the bottom of the triangle. B) You use the row that has the same number of terms as the exponent. C) You use the row that is the same number as the exponent. D) You just guess. Show Answer Correct Answer: C) You use the row that is the same number as the exponent. 7. Which of the following statements about the Binomial Theorem is true? A) It can be generalized for any real exponent. B) It is only valid for two terms in the binomial. C) It cannot be used for negative exponents. D) It can only be used for positive integer exponents. Show Answer Correct Answer: A) It can be generalized for any real exponent. 8. Find term 5 in row 7 A) 21. B) 28. C) 7. D) 35. Show Answer Correct Answer: A) 21. 9. What is the Index of binomial? A) The sum of all coefficients. B) The power of the first coefficient. C) The power of a binomial. D) The Pascal's triangle. Show Answer Correct Answer: C) The power of a binomial. 10. Find the coefficient of $a^5b^7$ $\left(a+b\right)^{12}$ A) 792. B) 786. C) 789. D) 796. Show Answer Correct Answer: A) 792. 11. From the ground, a rubber ball is thrown 20 feet into the air. If its rebound ratio is ($^{7}$/$_{10}$), how far will it have traveled during the first five bounces. A) 55.462. B) 58.139. C) 960, 341.857. D) 110.924. Show Answer Correct Answer: D) 110.924. 12. Use Pascal's Triangle to expand the expression.(2x+5)$^{4}$ A) 2x$^{4}$ + 40x$^{3 }$+ 300x$^{2}$ + 1000x +625. B) 16x$^{4 }$+ 160x$^{3}$ +600x$^{2}$ +1000x + 625. C) 16x$^{4}$ + 1000x$^{3}$ + 600x$^{2 }$+ 160x +625. D) None of the above. Show Answer Correct Answer: B) 16x$^{4 }$+ 160x$^{3}$ +600x$^{2}$ +1000x + 625. 13. What would be the 2nd term of the expansion of (y+4)$^{4}$? A) 96y$^{2}$. B) 253y. C) 64y. D) 16y$^{3}$. Show Answer Correct Answer: D) 16y$^{3}$. 14. Find the z-score.Mean = 25Standard Deviation:7x = 9.6 A) -2.2. B) -36. C) 5.2. D) 23.46. Show Answer Correct Answer: A) -2.2. 15. Find the 32nd term of the arithmetic sequence:9, 4, -1, -6, -11, ..... A) 81. B) -225. C) -146. D) -34. Show Answer Correct Answer: C) -146. 16. Describe the signs ( + and-) in the expanded form of (x + 5)$^{4}$ . A) All +. B) All-. C) Alternating ending in-. D) Alternating ending in +. Show Answer Correct Answer: A) All +. 17. An algebra 2 test has 6 multiple choice questions with four choices with one correct answer each. If we just randomly guess on each of the 6 questions, what is the probability that you get exactly 3 questions correct? A) 0.962. B) 0.831. C) 0.132. D) 0.250. Show Answer Correct Answer: C) 0.132. 18. A method of expanding a binomial. A) Binomial Theorem. B) Pascal's Triangle. C) Combination. D) Permutation. Show Answer Correct Answer: A) Binomial Theorem. 19. Expand (x+4)$^{8}$ A) X$^{8}$ + 8 x$^{7}$ + 28 x$^{6}$ + 56x$^{5}$ + 70x$^{4}$ + 56x$^{3}$ + 28x$^{2}$ + 8x +1. B) X$^{8}$ + 32 x$^{7}$ + 448 x$^{6}$ + 3584 x$^{5}$ + 17920 x$^{4}$ + 57344 x$^{3}$ + 114688 x$^{2}$ + 131072 x + 65536. C) X$^{7}$ + 28 x$^{6}$ + 336 x$^{5}$ + 2240 x$^{4}$ + 8960 x$^{3}$ + 21504 x$^{2}$ + 28672 x + 16384. D) X$^{8}$-32 x$^{7}$ + 448 x$^{6}$-3584 x$^{5}$ + 17920 x$^{4}$-57344 x$^{3}$ + 114688 x$^{2}$-131072 x + 65536. Show Answer Correct Answer: B) X$^{8}$ + 32 x$^{7}$ + 448 x$^{6}$ + 3584 x$^{5}$ + 17920 x$^{4}$ + 57344 x$^{3}$ + 114688 x$^{2}$ + 131072 x + 65536. 20. When using mathematical induction to prove:$\sum_{i=1}^ni^2=\frac{n\left(n+1\right)\left(2n+1\right)}{6}$ A) $S_{k+1}=\frac{k\left(k+1\right)\left(2k+1\right)}{6}$. B) $\sum_{i=1}^{k+1}i^2=\frac{\left(k\right)\left(k+1\right)\left(2k+1\right)}{6}+\left(k+1\right)^2$. C) $S_{k+1}=\left(k+1\right)^2$. D) $\sum_{k=1}^n\left(k+1\right)^2=\frac{\left(k+1\right)\left(k+2\right)\left(2k+3\right)}{6}$. Show Answer Correct Answer: D) $\sum_{k=1}^n\left(k+1\right)^2=\frac{\left(k+1\right)\left(k+2\right)\left(2k+3\right)}{6}$. 21. C0+C1+C2+C3+ ..... Cn= A) 2$^{n}$. B) 0. C) 1. D) None. Show Answer Correct Answer: A) 2$^{n}$. 22. Find the coefficient of x$^{4}$ in the expansion of (1-x)$^{14}$ A) 364. B) -1001. C) 1001. D) -364. Show Answer Correct Answer: C) 1001. 23. What is the sum of the coefficients in the expansion of $(2x-3)^5$ A) $-1$. B) $-25$. C) $-243$. D) $-32$. Show Answer Correct Answer: C) $-243$. 24. Given an investment of $ 1, 500:Which investment would have a larger balance after 5 years?Option 1-4% compounded monthlyOption 2-3.9% compounded daily. A) Option 1. B) Option 2. C) All the above. D) None of the above. Show Answer Correct Answer: A) Option 1. 25. In the expansion of $(x^4-\frac{1}{x^3})^6$ $x^{-4}$ A) 2. B) 5. C) 3. D) 4. Show Answer Correct Answer: D) 4. 26. Find the sum.(2x$^{2}$ + 5x-7) + ( 3-4x$^{2}$ + 6x) A) -2x$^{2}$ + 11x-4. B) 2x$^{2}$ $_{}$+ 5x-7. C) 2x$^{2 }$+ 3x +1. D) -2x$^{2 }$-11x-4. Show Answer Correct Answer: A) -2x$^{2}$ + 11x-4. 27. The number of permutations using the letters of the word LOOPHOLE is: A) 3520. B) 3360. C) 4630. D) 4000. Show Answer Correct Answer: B) 3360. 28. The population of a city is decreasing by 3% every year. If the population is 125, 000 in the 1st year, how many will remain in the 10th year? A) 95, 029 people. B) 92, 178 people. C) 167, 990 people. D) 163, 096 people. Show Answer Correct Answer: A) 95, 029 people. 29. The coefficient $x^{12}$ $(x^2+2x)^{10}$ A) 23040. B) 16520. C) 11520. D) 13410. Show Answer Correct Answer: C) 11520. 30. Given the binomial $\left(5x^4+3y^5\right)^8$ A) $6561y^{13}$. B) $3y^{40}$. C) $6561y^{40}$. D) $3y^{13}$. Show Answer Correct Answer: C) $6561y^{40}$. 31. Expand (3 + i)$^{5}$, where i is the imaginary number, using the Binomial Theorem. (Note:i$^{0}$ = 1, i$^{1}$ = i, i$^{2}$ =-1, and i$^{3}$ =-i) A) 28 + 96i. B) -12 + 316i. C) -3 + 79i. D) 7 + 24i. Show Answer Correct Answer: B) -12 + 316i. 32. What does the p stand for in the binomial probability formula? A) Probability of Failures. B) Number of trials. C) Number of Successes. D) Probability of Successes. Show Answer Correct Answer: D) Probability of Successes. 33. $\left(p+q\right)^6$ A) 1, 5, 10, 5, 1. B) 1, 4, 6, 4, 1. C) 1, 6, 15, 20, 15, 6, 1. D) 1, 8, 28, 56, 70, 56, 28, 8, 1. Show Answer Correct Answer: C) 1, 6, 15, 20, 15, 6, 1. 34. Find the third term of $\left(3x+y\right)^4$ A) $54x^2y^2$. B) $54x^3y$. C) $6x^2y^2$. D) $549xy^3$. Show Answer Correct Answer: A) $54x^2y^2$. 35. Expand:$\left(a-b\right)^5$ A) $a^5+5a^4b+10a^3b^2+10a^2b^3+5ab^4+b^5$. B) $a^5-5a^4b-10a^3b^2-10a^2b^3-5ab^4-b^5$. C) $a^5-5a^4b+10a^3b^2-10a^2b^3+5ab^4-b^5$. D) $a^5-5a^4b+10a^2b^3-10a^3b^2+5ab^4-b^5$. Show Answer Correct Answer: C) $a^5-5a^4b+10a^3b^2-10a^2b^3+5ab^4-b^5$. 36. What is the relationship between the binomial coefficients and combinations? A) Binomial coefficients are used only in probability calculations. B) Combinations are a type of binomial coefficient. C) Binomial coefficients are unrelated to combinations. D) Binomial coefficients are the mathematical representation of combinations. Show Answer Correct Answer: D) Binomial coefficients are the mathematical representation of combinations. 37. Find term 3 in row 8 A) 56. B) 3. C) 28. D) 8. Show Answer Correct Answer: A) 56. 38. In the expansion of $(x + 2)^4$ $x^2$ A) 6. B) 24. C) 12. D) 16. Show Answer Correct Answer: B) 24. 39. Find the product:(3x-5) ( 4x$^{2}$-2x-3) A) 12x$^{3}$-20x$^{2}$-6x + 15. B) 12x$^{3}$-26x$^{2}$-25x + 15. C) 12x$^{3}$-20x$^{2}$-5x + 15. D) 12x$^{3}$-26x$^{2}$ + x + 15. Show Answer Correct Answer: D) 12x$^{3}$-26x$^{2}$ + x + 15. 40. $^{n}$Cr +$^{n}$Cr-1 = A) $^{n}$Cr+1. B) $^{n+1}$Cr. C) $^{2n}$Cr. D) None. Show Answer Correct Answer: B) $^{n+1}$Cr. 41. Find the product:(x-2) (3x$^{2 }$+ 2x-4) A) 3x$^{2 }$-4x +8. B) 3x$^{3 }$-4x$^{2}$-8x +8. C) 3x$^{3 }$-x$^{2 }$+8x +8. D) 3x$^{3 }$+4x$^{2 }$-8x-8. Show Answer Correct Answer: B) 3x$^{3 }$-4x$^{2}$-8x +8. 42. The term independent of X in (x+1/x)$^{2}$ is equal to A) 4. B) 2. C) 2x. D) 1/2. Show Answer Correct Answer: B) 2. 43. An unbiased coin is tossed 10 times. Which of these will not give the probability that there are fewer than 3 heads tossed? A) (1/2)$^{10}$ + (1/2)$^{9}$(1/2) + (1/2)$^{8}$(1/2)$^{2}$. B) P(0) + P(1) + P(2). C) $_{10}$C$_{0}$(1/2)$^{10}$ + $_{10}$C$_{1}$(1/2)$^{9}$(1/2) + $_{10}$C$_{2}$(1/2)$^{8}$(1/2)$^{2}$. D) 1-[P(3) + P(4) + + P(10)]. Show Answer Correct Answer: A) (1/2)$^{10}$ + (1/2)$^{9}$(1/2) + (1/2)$^{8}$(1/2)$^{2}$. 44. What is the coefficient of y in the expansion of (2y +1)$^{4}$ A) 24. B) 4. C) 32. D) 6. Show Answer Correct Answer: C) 32. 45. 30x$^{3}$+15x$^{2}$-18x-9 A) (5x$^{2}$-3)(6x+3). B) 3(5x$^{2}$-3)(2x+1). C) 3(5x$^{2}$+3)(2x-1). D) (5x$^{2}$-3)(6x+1). Show Answer Correct Answer: B) 3(5x$^{2}$-3)(2x+1). 46. The probability that Tim will sink a foul shot is 70%. If Tim attempts 30 foul shots, what is the probability that he sinks between 19 and 23 shots, inclusive? A) .232 or 23.2%. B) $_{30}$C$_{19}$(.70)$^{19}$(.30)$^{11}$ + $_{30}$C$_{23}$(.70)$^{23}$(.30)$^{7}$. C) .681 or 68.1%. D) 1-[P(0) + P(1) + P(2) + + P(18)]. Show Answer Correct Answer: C) .681 or 68.1%. 47. What does the C in nCr stand for? A) Component. B) Permutation. C) Composite. D) Combination. Show Answer Correct Answer: D) Combination. 48. Which correctly shows 5! A) 5*4*3*2*1*0. B) 4*3*2*1. C) 5*4*3*2*1. D) 5*5*5*5*5. Show Answer Correct Answer: C) 5*4*3*2*1. 49. One of the terms of the binomial (Ax + y)$^{n}$ is 13440x$^{6}$y$^{4}$. What is the value of A? A) 4. B) 2. C) 10. D) 12. E) 8. Show Answer Correct Answer: B) 2. 50. How many terms are the in the expansion of (1+b)$^{4}$ A) 5. B) 6. C) 3. D) 4. E) 2. Show Answer Correct Answer: A) 5. 51. What is the 7th term of the expansion (9h + 3j)$^{6}$? A) 729j$^{6}$. B) 729j$^{7}$. C) 531441h$^{7}$. D) 531441h$^{6}$. E) 13122hj$^{5}$. Show Answer Correct Answer: A) 729j$^{6}$. 52. $\left(y+2\right)^2+4\left(y+2\right)+3$ A) $\left(y+2\right)\left(y+2\right)$. B) $\left(y+3\right)\left(y+1\right)$. C) $\left(y+6\right)\left(y+1\right)$. D) $\left(y+5\right)\left(y+3\right)$. Show Answer Correct Answer: D) $\left(y+5\right)\left(y+3\right)$. 53. Given the expression $\left(x^2-2y\right)^7$ $x^{10}y^2$ A) 74. B) 88. C) 84. D) 82. Show Answer Correct Answer: C) 84. 54. Expand the expression.(2x+5)$^{4}$ A) 2x$^{4}$ + 40x$^{3 }$+ 300x$^{2}$ + 1000x +625. B) 16x$^{4 }$+ 160x$^{3}$ +600x$^{2}$ +1000x + 625. C) 16x$^{4}$ + 1000x$^{3}$ + 600x$^{2 }$+ 160x +625. D) None of the above. Show Answer Correct Answer: B) 16x$^{4 }$+ 160x$^{3}$ +600x$^{2}$ +1000x + 625. 55. If $^{n}$Ca= $^{n}$Cb then A) N=a+b or a=b. B) N=a*b or a=b. C) N=a-b or a=b. D) None. Show Answer Correct Answer: A) N=a+b or a=b. 56. If the area of a rectangle is x$^{2}$-100, what could be the length and width of the rectangle? A) (x + 50) and (x-50). B) (x + 10) and (x-10). C) (x + 10i) and (x-10i). D) (x + 10) and (x + 10). Show Answer Correct Answer: B) (x + 10) and (x-10). 57. Factor:x$^{3 }$+ 1 A) (x+1)(x$^{2 }$-x + 1). B) (x + 1)$^{3}$. C) (x-1) (x$^{2}$ + x-1). D) (x + 1)(x$^{2}$-2x + 1). Show Answer Correct Answer: A) (x+1)(x$^{2 }$-x + 1). 58. From a deck of 52 cards, how many 5 card hands have at most 3 kings? A) 2, 598, 908. B) 2, 598, 912. C) 2, 598, 904. D) 2, 598, 916. Show Answer Correct Answer: B) 2, 598, 912. 59. What is the coefficient of x$^{2}$ in the expansion of (4x-1)$^{6}$ A) 60. B) 240. C) 15. D) 320. Show Answer Correct Answer: B) 240. 60. True or False:The coefficients of the 3rd and the 7th terms in the expansion of $\left(x+y\right)^8$ A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: A) True. ← 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 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