This quiz works best with JavaScript enabled. Home > Class 11 > 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 (25 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. Explain the concept of combinations with an example. A) Combinations involve arranging items in a specific order. B) Combinations are the selection of items without considering the order. For example, choosing 2 colors out of 5 different colors. C) Combinations are used to calculate the perimeter of a shape. D) Combinations only involve selecting one item at a time. 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. 2. What is the Binomial expansion of (a-b)$^{7}$? A) A$^{7}$-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$^{7}$ + 7a$^{6}$b-21a$^{5}$b$^{2}$ + 35a$^{4}$b$^{3}$-35a$^{3}$b$^{4}$ + 21a$^{2}$b$^{5}$-7ab$^{6}$ + 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$^{7}$. 3. The 3rd term in row 6 of Pascal's Triangle is A) 15. B) 20. C) 24. D) 50. Show Answer Correct Answer: A) 15. 4. $\left(3r-5\right)^3$ A) $27r^3-125$. B) $27r^3-135r^2+225r-125$. C) $27r^3+135r^2+225r+125$. D) $27r^3-45r^2+75r-125$. Show Answer Correct Answer: B) $27r^3-135r^2+225r-125$. 5. What is the Pascal triangle used for in binomial theorems? A) To determine coefficients of terms in binomial expansions. B) To find the area of a circle. C) To calculate square roots of numbers. D) To determine prime numbers in a sequence. Show Answer Correct Answer: A) To determine coefficients of terms in binomial expansions. 6. Write the general term rule for this arithmetic sequence:25, 21, 17, 13, ..... A) A$_{n}$ = 4n + 29. B) A$_{n}$ =-4n + 25. C) A$_{n }$=-4n + 29. D) A$_{n}$ = 4n + 25. Show Answer Correct Answer: C) A$_{n }$=-4n + 29. 7. (x-y) $^{3}$ A) X$^{3}$-3x$^{2}$ y + 3xy$^{2}$-y$^{3}$. B) 16m$^{ 4}$-32m $^{3}$ + 24m $^{2}$-8m + 1. C) All the above. D) None of the above. Show Answer Correct Answer: A) X$^{3}$-3x$^{2}$ y + 3xy$^{2}$-y$^{3}$. 8. $\left(4-3x\right)^7$ A) -193563. B) -86016. C) -20412. D) -240920. Show Answer Correct Answer: B) -86016. 9. 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. 10. 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) 0.04. B) 0.10. C) 10. D) 50. Show Answer Correct Answer: B) 0.10. 11. Find the 12th term in the expansion of (x-5)$^{13}$. A) -48828125x$^{9}$. B) -3808593750x$^{2}$. C) -3808593750. D) -48828125. Show Answer Correct Answer: B) -3808593750x$^{2}$. 12. According to the empirical rule, approximately what percentage of data falls within three standard deviations of the mean? A) 68%. B) 95%. C) 99.7%. D) 100%. Show Answer Correct Answer: C) 99.7%. 13. 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. 14. Which of the following is the correct expansion of $(x-3)^2$ A) $x^2-6x + 9$. B) $x^2 + 6x + 9$. C) $x^2-9x + 9$. D) $x^2-3x + 9$. Show Answer Correct Answer: A) $x^2-6x + 9$. 15. What is the 4th row of Pascal's Triangle? A) 1 3 3 1. B) 1 4 8 4 1. C) 1 2 1. D) 1 4 6 4 1. Show Answer Correct Answer: D) 1 4 6 4 1. 16. 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) $16n^4+32n^3m+24n^2m^2+8nm^3+m^4$. 17. Find the product:(5x + 2) (x$^{2 }$-3x +6) A) 5x$^{3 }$-17x$^{2 }$+24x +12. B) 5x$^{3 }$+ 17x$^{2}$-24x +12. C) 5x$^{3}$-13x$^{2}$ + 24x +12. D) 5x$^{3}$ +13x$^{2}$-24x-12. Show Answer Correct Answer: C) 5x$^{3}$-13x$^{2}$ + 24x +12. 18. 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) $455x^{15}y^{36}$. 19. Using the Binomial Theorem, what is the constant term in the expansion of $(2x-1)^4$ A) 1. B) -8. C) 16. D) 24TagsAZ.MA.9-12.P.A-APR.C.5. Show Answer Correct Answer: C) 16. 20. If the top row of Pascal's Triangle is row 0, then what is the sum of the numbers in the eighth row? A) 255. B) 256. C) 257. D) 260. E) 264. Show Answer Correct Answer: B) 256. 21. Determine the number of 5 card combinations out of a deck of 52 cards if there is exactly one ace in each combination. A) $_{52}$C$_{5}$. B) $_{4}$C$_{1}$ x $_{48}$C$_{4}$. C) 10246. D) $4\times52_{C_3}$. Show Answer Correct Answer: B) $_{4}$C$_{1}$ x $_{48}$C$_{4}$. 22. Expand the binomial (2x+3)$^{4}$ A) 16x$^{4}$+81. B) X$^{4}$+4x$^{3}$+6x$^{2}$+4x+1. C) 16x$^{4}$+96x$^{3}$+216x$^{2}$+216x+81. D) 16x$^{4}$+186x$^{3}$+398x$^{2}$+312x+81. Show Answer Correct Answer: C) 16x$^{4}$+96x$^{3}$+216x$^{2}$+216x+81. 23. Row 0 on pascal triangle A) 1. B) 11. C) 121. D) 1331. E) 14641. Show Answer Correct Answer: A) 1. 24. 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: D) X$^{4 }$-4x$^{3 }$+ 6x$^{2 }$-4x + 1. 25. How many terms are in this expansion? $\left(x+52\right)^5$ A) 5. B) 6. C) 25. D) 50. E) 3. Show Answer Correct Answer: B) 6. ← PreviousNext →Related 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 9Class 11 Mathematics Chapter 8 Binomial Theorem Quiz 10Class 11 Mathematics Chapter 8 Binomial Theorem Quiz 11 🏠 Back to Homepage 📘 Download PDF Books 📕 Premium PDF Books