This quiz works best with JavaScript enabled. Home > Cbse > Class 11 > Science > Mathematics > Class 11 Mathematics Chapter 8 Binomial Theorem – Quiz 6 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 11 Mathematics Chapter 8 Binomial Theorem Quiz 6 (60 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. $\sum_{k=1}^{\infty}\left(\frac{2}{5}\right)^k$ A) $\infty$. B) $\frac{2}{5}$. C) $\frac{2}{3}$. D) 0. Show Answer Correct Answer: C) $\frac{2}{3}$. 2. Kamali has 7 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 the 7 she owns? A) 21. B) 35. C) 7. D) 1. Show Answer Correct Answer: B) 35. 3. Find the term containing $x^5$ $\left(2y+x\right)^7$ A) $672y^2x^5$. B) $14y^3x^5$. C) $84y^2x^5$. D) $280y^3x^5$. Show Answer Correct Answer: C) $84y^2x^5$. 4. (2x$^{3}$ + 1)$^{5}$ A) 32x $^{15}$ + 80x $^{12}$ + 80x $^{9}$ + 40x $^{6}$ + 10x $^{3}$ + 1. B) X $^{20}$-5x + 10x$^{2}$-8y$^{3}$ + 5x$^{4}$-y $^{5}$. C) All the above. D) None of the above. Show Answer Correct Answer: A) 32x $^{15}$ + 80x $^{12}$ + 80x $^{9}$ + 40x $^{6}$ + 10x $^{3}$ + 1. 5. Expand Correctly (Using Pascal's Triangle) $\left(2x-y\right)^4$ A) $y^4-8xy^3+24x^2y^2-32x^3y+16x^4$. B) $16-32xy^3+24x^2y^2-8+y^4$. C) $16x^4-32x^3y+24x^2y^2-8xy^3+y^4$. D) None of the above. Show Answer Correct Answer: C) $16x^4-32x^3y+24x^2y^2-8xy^3+y^4$. 6. The probability that Tim will sink a foul shot is 70%. If Tim attempts 30 foul shots, what is the probability he sinks exactly 21 foul shots? A) ~72.4%. B) ~15.7%. C) ~68.1%. D) 70%. Show Answer Correct Answer: B) ~15.7%. 7. Amir has a biscuit tin containing 3 bourbons and 5 custard creams. He chooses a biscuit at random, eats it, then chooses another and eats that too. Draw a tree diagram and use it to find the probability that Amir has eaten at least one custard cream. A) $\frac{25}{28}$. B) $\frac{30}{56}$. C) $\frac{15}{56}$. D) None of the above. Show Answer Correct Answer: A) $\frac{25}{28}$. 8. Find the coefficient of the term containing $u^2$ $\left(u-3\right)^5$ A) $90$. B) $-270$. C) $405$. D) $-27$. Show Answer Correct Answer: B) $-270$. 9. Find the coefficient of y$^{3}$ in the expansion of (1-3y)$^{14 }$by using combination A) 364. B) -9828. C) 9828. D) -364. Show Answer Correct Answer: B) -9828. 10. $\left(x+y\right)^2=$ A) $xy^2$. B) $x^2+xy+y^2$. C) $x^2+y^2$. D) $xy+x+y$. Show Answer Correct Answer: B) $x^2+xy+y^2$. 11. If $^{n}$Pr= 5040 and $^{n}$Cr=210, then the values of 'n' and 'r' are A) 14, 10. B) 4, 10. C) 10, 14. D) 10, 4. Show Answer Correct Answer: D) 10, 4. 12. Simplify $\left(x-4\right)^3.$ A) $x^3-12x^2+48x-64$. B) $x^3+12x^2-16x-4$. C) $x^3+12x^2+48x-64$. D) $64-48x+12x^2-x^3$. Show Answer Correct Answer: A) $x^3-12x^2+48x-64$. 13. Open the link, Binomial Theorem, from the Google Document, and use the notes from the link to answer the questions. You have 5 minutes to locate the link. Are you ready? Click yes! A) Yes. B) . C) All the above. D) None of the above. Show Answer Correct Answer: A) Yes. 14. What is Ms. Arruda's Cat's Name? A) Moxy. B) Diane. C) Roxy. D) Foxy. Show Answer Correct Answer: C) Roxy. 15. The coefficient of the middle term in the expansion of (2+3x)$^{4 }$is: A) 216. B) 5!. C) 6. D) 8!. Show Answer Correct Answer: A) 216. 16. If n is the positive integer, then 2$^{3n}$-7n-1 is divisible by A) 49. B) 7. C) 81. D) 10. Show Answer Correct Answer: A) 49. 17. Write the explicit formula for the geometric sequence.3, -12, 48, -192, ..... A) A$_{n}$ = 3(4)$^{n-1}$. B) A$_{n}$ = 4(3)$^{n-1}$. C) A$_{n}$ = 3(-4)$^{n-1}$. D) A$_{n}$ =-4(3)$^{n-1}$. Show Answer Correct Answer: C) A$_{n}$ = 3(-4)$^{n-1}$. 18. Using the Binomial Theorem expand:$\left(x-5\right)^4$ A) $x^4-20x^3+150x^2-500x+625$. B) X4-20x3+150x2-500x+625 Mathematical EquivalenceON. C) All the above. D) None of the above. Show Answer Correct Answer: A) $x^4-20x^3+150x^2-500x+625$. 19. Use the binomial expansion to expand $\left(u^2-2\right)^3$ A) $u^6-24u^4+12u^2-8$. B) $u^6-16u^4+12u^2-8$. C) $5u^6-20u^4+40u^2-40$. D) $u^6-6u^4+12u^2-8$. Show Answer Correct Answer: D) $u^6-6u^4+12u^2-8$. 20. If $_{n}$C$_{2 }$= 28, then what is the value of n? A) 7. B) 8. C) 6. D) 5. Show Answer Correct Answer: B) 8. 21. Using Binomial Theorem, find the coefficient of $x^2y^6$ $\left(2x-3y^2\right)^5$ A) -1081. B) -1080. C) -1088. D) 1080. Show Answer Correct Answer: B) -1080. 22. In a city, it is estimated that the maximum temperature for the thirty days of June is normally distributed with a mean of 23 degrees and a standard deviation of 5 degrees. Calculate the number of days in this month in which it is expected to reach a maximum temperature between 21 and 27 degrees. A) 13 days. B) 4 days. C) 10 days. D) 8 days. Show Answer Correct Answer: A) 13 days. 23. $\left(2-5x\right)^7$ $x^2$ A) 17200. B) 16800. C) 2240. D) 70000. Show Answer Correct Answer: B) 16800. 24. Find the coefficient in terms of the given term in the binomial expansion x$^{4 }$in (x-3)$^{11}$ A) -721710. B) -990. C) 330. D) 721710. Show Answer Correct Answer: A) -721710. 25. If $(1+x)^n=1+\frac{2}{3}.\\frac{1}{2}+\frac{2.5}{3.6}.\\frac{1}{2^2}+\frac{2.5.8}{3.6.9}.\\frac{1}{2^3}+ ..... $ A) $\frac{2}{3}$. B) $\frac{\left(-1\right)}{2}$. C) $\frac{1}{2}$. D) $\frac{\left(-2\right)}{3}$. Show Answer Correct Answer: B) $\frac{\left(-1\right)}{2}$. 26. Coefficient of (1-x)$^{2}$ is A) -1. B) 1. C) 0. D) None. Show Answer Correct Answer: B) 1. 27. The arrangement of the binomial coefficients is called A) Permutation. B) Pascal's triangle. C) Combination. D) Binomial theorem. Show Answer Correct Answer: B) Pascal's triangle. 28. What is row 6 of Pascal's Triangle? A) 1, 6, 15, 15, 6, 1. B) 1, 7, 21, 35, 35, 21, 7, 1. C) 1, 6, 15, 20, 15, 6, 1. D) 1, 7, 21, 35, 21, 7, 1. Show Answer Correct Answer: C) 1, 6, 15, 20, 15, 6, 1. 29. Select the correct expansion of(1 + 4x)$^{3}$ A) 1 + 12x + 12x$^{2}$ + 4x$^{3}$. B) 1 + 3x + 3x$^{2}$ + x$^{3}$. C) 1 + 12x + 48x$^{2}$ + 64x$^{3}$. D) 1 + 4x + 16x$^{2}$ + 64x$^{3}$. Show Answer Correct Answer: C) 1 + 12x + 48x$^{2}$ + 64x$^{3}$. 30. Riley invested $ 1, 000 in savings bonds. If the bonds earn 6.75% interest compounded semi-annually, how much total will Riley earn in 15 years? A) $ 2, 651.39. B) $ 2, 706.86. C) $ 1, 584.62. D) $ 1, 825.10. Show Answer Correct Answer: B) $ 2, 706.86. 31. The coefficient of a$^{3}$b in the expansion of (4b+3a)$^{4}$ A) 108. B) 768. C) 81. D) 432. Show Answer Correct Answer: D) 432. 32. The word "selection" usually refers to A) Probability. B) Counting. C) Combination. D) Permutation. Show Answer Correct Answer: C) Combination. 33. If $^{n}$P3= 1320, then the values of 'n' is A) 4. B) 12. C) 6. D) 10. Show Answer Correct Answer: B) 12. 34. What does the n stand for in the binomial probability formula? A) Probability of Successes. B) Probability of Failures. C) Number of Successes. D) Number of trials. Show Answer Correct Answer: D) Number of trials. 35. Expand Completely. (Using Pascal's Triangle) $\left(3v-u\right)^4$ A) $81v^4-108v^3u-54v^2u^2-12vu^3-u^4$. B) $81v^4-108v^3u+54v^2u^2-12vu^3+u^4$. C) $82v^4-110v^3u+56v^2u^2-14vu^3+u^4$. D) None of the above. Show Answer Correct Answer: B) $81v^4-108v^3u+54v^2u^2-12vu^3+u^4$. 36. What is the value of 7C4 in Pascal's triangle? A) 35. B) 21. C) 42. D) 28. Show Answer Correct Answer: A) 35. 37. How many rows in The Pascal's triangle? A) 8. B) 100. C) Infinite. D) 7. Show Answer Correct Answer: C) Infinite. 38. What would be the 4th term of the expansion of (a+3)$^{4}$? A) 27a. B) 108a. C) 81. D) 12a$^{3}$. Show Answer Correct Answer: B) 108a. 39. Consider the binomial expansion of $\left(3x^2-2y^3\right)^5$ A) $1088x^6y^4$. B) $1180x^4y^5$. C) $1080x^6y^6$. D) $1011x^6y^6$. Show Answer Correct Answer: C) $1080x^6y^6$. 40. Given the binomial $\left(5+2x^5\right)^{10}$ A) $288000x^{40}$. B) $115200x^{40}$. C) $2250x^{40}$. D) $288000x^{13}$. Show Answer Correct Answer: A) $288000x^{40}$. 41. Row 3 on pascal triangle A) 1331. B) 14641. C) 121. D) 11. E) 1. Show Answer Correct Answer: A) 1331. 42. What is the LAST term in the expansion of (x + 4)$^{5}$? A) 1024. B) 640. C) 160. D) 64. Show Answer Correct Answer: A) 1024. 43. Which of the following is the correct expansion for $(a + b)^3$ A) $a^3 + 3a^2b + ab^2 + b^3$. B) $a^3 + a^2b + ab^2 + b^3$. C) $a^3 + 2a^2b + 2ab^2 + b^3$. D) $a^3 + 3a^2b + 3ab^2 + b^3$. Show Answer Correct Answer: D) $a^3 + 3a^2b + 3ab^2 + b^3$. 44. Expand $\left(b-2\right)^3$ A) 4b$^{3}$-12b$^{2}$ + 16b-8. B) 5b$^{3}$-20b$^{2}$ + 40b-40. C) B$^{3}$-6b$^{2}$ + 12b-8. D) B$^{3}$-2b$^{2}$ + 4b-8. Show Answer Correct Answer: C) B$^{3}$-6b$^{2}$ + 12b-8. 45. Expand $\left(d-5\right)^5$ A) D$^{4 }$+ 20d$^{3 }$+ 150d$^{2 }$+ 750d + 3125. B) D$^{5}$-25 d$^{4}$ + 250 d$^{3}$-1250 d$^{2}$ + 3125 d-3125. C) D$^{5}$ + 25 d$^{4}$ + 250 d$^{3}$ + 1250 d$^{2}$ + 3125 d + 3125. D) D$^{4 }$-20d$^{3 }$+ 150d$^{2 }$-750d + 3125. Show Answer Correct Answer: B) D$^{5}$-25 d$^{4}$ + 250 d$^{3}$-1250 d$^{2}$ + 3125 d-3125. 46. 4a(5a$^{2 }$-a + 4) A) 20a$^{2 }$+ $^{}$4a$^{2 }$+ 16a. B) 20a$^{3 }$-4a$^{2 }$+ 16a. C) 20a$^{3 }$+3a$^{2}$ + 16a. D) 20a$^{2 }$-5a + 8a. Show Answer Correct Answer: B) 20a$^{3 }$-4a$^{2 }$+ 16a. 47. Using the Binomial Theorem expand:$\left(2x+3y\right)^4$ A) $16x^4+96x^3y+216x^2y^2+216xy^3+81y^4$. B) 16x4+96x3y+216x2y2+216xy3+81y4 Mathematical EquivalenceON. C) All the above. D) None of the above. Show Answer Correct Answer: A) $16x^4+96x^3y+216x^2y^2+216xy^3+81y^4$. 48. Find the 4th term in the expansion of (4x-3)$^{5}$. A) -4320x$^{2}$. B) 5760. C) 5760x$^{3}$. D) -4320. Show Answer Correct Answer: A) -4320x$^{2}$. 49. What is the 4th term in the expansion of (m-2n)$^{5}$ A) -120m$^{2}$n$^{3}$. B) 20m$^{3}$n$^{2}$. C) -160m$^{2}$n$^{3}$. D) -80m$^{2}$n$^{3}$. Show Answer Correct Answer: D) -80m$^{2}$n$^{3}$. 50. Kamryn tosses a fair die six times. What is the probability that Kamryn will toss exactly two 5's? A) $_{6}$C$_{2}$(1/6)$^{2}$(5/6)$^{4}$. B) $_{6}$C$_{2}$(5/6)$^{2}$(1/6)$^{4}$. C) $_{6}$C$_{5}$(5/6)$^{2}$(1/6)$^{4}$. D) $_{6}$C$_{5}$(1/6)$^{2}$(5/6)$^{4}$. Show Answer Correct Answer: A) $_{6}$C$_{2}$(1/6)$^{2}$(5/6)$^{4}$. 51. $\left(x+10\right)^3$ A) $x^3+30x^2+30x+1000$. B) $x^3+1000$. C) $x^3+30x^2+300x+1000$. D) $x^2+20x+100$. Show Answer Correct Answer: C) $x^3+30x^2+300x+1000$. 52. Find the 3rd term of the expansion:(5x + 2)$^{7}$ A) 175000x$^{5}$. B) 175000x$^{4}$. C) 218750x$^{6}$. D) 262500x$^{5}$. Show Answer Correct Answer: D) 262500x$^{5}$. 53. An object is moving at a speed of 1300 inches every 9 seconds. Express this speed in kilometers per minute. Round your answer to the nearest hundredth. Hint:1 foot (ft) = 0.305 meters (m) A) 1.98 km/min. B) 0.22 km/min. C) 0.01 km/min. D) 2.20 km/min. Show Answer Correct Answer: B) 0.22 km/min. 54. Find the 2nd term in the expansion of (2b + 1)$^{3}$ A) 6b. B) 4b$^{2}$. C) 12b$^{2}$. D) 8b$^{3}$. Show Answer Correct Answer: C) 12b$^{2}$. 55. Expand:$\left(a+b\right)^3$ A) $a^3+3a^2b+3ab^2+b^3$. B) $a^3+3a^2b+3ab^{ }+b^3$. C) $a^3+3a^2+3ab^2+b^3$. D) $a^3-3a^2b+3ab^2+b^3$. Show Answer Correct Answer: A) $a^3+3a^2b+3ab^2+b^3$. 56. What is the value of the binomial coefficient $C(5, 2)$ A) 15. B) 20. C) 10. D) 5. Show Answer Correct Answer: C) 10. 57. What is the correct expansion of $\left(x+y\right)^5$ A) $x^5+5x^4y+10x^3y^2+10x^2y^3+5xy^4+y^5$. B) $x^5+4x^4y+6x^3y^2+4x^2y^4+y^5$. C) $x^5+5x^4y+10x^3y^2+5x^2y^4+y^5$. D) $x^5+4x^4y+6x^3y^2+6x^2y^3+4xy^4+y^5$. Show Answer Correct Answer: A) $x^5+5x^4y+10x^3y^2+10x^2y^3+5xy^4+y^5$. 58. Is the sequence geometric or arithmetic?6, 18, 54 ..... A) Arithmetic. B) Geometric. C) Neither. D) None of the above. Show Answer Correct Answer: B) Geometric. 59. What is the GCF of 18k and 15k$^{3}$ A) 3k$^{2}$. B) 3k. C) 3k$^{3}$. D) 5k. Show Answer Correct Answer: B) 3k. 60. If you are missing an exponent in your polynomial you must put a zero as a coefficient place holder for that exponent 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 4Class 11 Mathematics Chapter 8 Binomial Theorem Quiz 5Class 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