This quiz works best with JavaScript enabled. Home > Cbse > Class 11 > Science > Mathematics > Class 11 Mathematics Chapter 8 Binomial Theorem – Quiz 1 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 11 Mathematics Chapter 8 Binomial Theorem Quiz 1 (60 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. Rewrite $\frac{x^3 + 2x^2-x + 4}{x^2 + 1}$ $q(x) + \frac{r(x)}{x^2 + 1}$ A) $x + 1 + \frac{x + 4}{x^2 + 1}$. B) $x + 2 + \frac{x + 2}{x^2 + 1}$. C) $x + 2 + \frac{-x + 2}{x^2 + 1}$. D) $x + 1 + \frac{-x + 4}{x^2 + 1}$. Show Answer Correct Answer: C) $x + 2 + \frac{-x + 2}{x^2 + 1}$. 2. Expand completely. A.APR.5(3x-2y)$^{3}$ A) 108x$^{3}$-108x$^{2}$y + 48xy$^{2}$-8y$^{3}$. B) 27x$^{3}$ + 36x$^{2}$y + 36xy$^{2}$-8y$^{3}$. C) 27x$^{3}$-54x$^{2}$y + 36xy$^{2}$-8y$^{3}$. D) 27x$^{3}$-18x$^{2}$y + 12xy$^{2}$-8y$^{3}$. Show Answer Correct Answer: C) 27x$^{3}$-54x$^{2}$y + 36xy$^{2}$-8y$^{3}$. 3. What factoring technique must be used to factor? $27a^3-729$ A) Difference of 2 cubes. B) Difference of 2 squares. C) FOIL. D) Factoring using the GCF. Show Answer Correct Answer: A) Difference of 2 cubes. 4. Using the Binomial Theorem expand:$\left(x^2+4y\right)^3$ A) $x^6+12x^4y+48x^2y^2+64y^3$. B) X6+12x4y+48x2y2+64y3 Mathematical EquivalenceON. C) All the above. D) None of the above. Show Answer Correct Answer: A) $x^6+12x^4y+48x^2y^2+64y^3$. 5. Multiply the binomial:(x-2)$^{4}$ A) X$^{5}$-4x$^{4}$ + 6x$^{3}$-4x$^{2}$ + 1. B) X$^{5}$ + 8x$^{4}$ + 24x$^{3}$ + 32x$^{2}$ + 32. C) -x$^{5}$ + 8x$^{4}$-24x$^{3}$ + 32x$^{2}$-32. D) X$^{4}$ +-8x$^{3}$ + 24x$^{2}$ + 32x + 16. Show Answer Correct Answer: D) X$^{4}$ +-8x$^{3}$ + 24x$^{2}$ + 32x + 16. 6. Find the constant term in the expansion $\left(2w^3-\frac{5}{w^2}\right)^5$ A) -400. B) -5000. C) 2000. D) 32. Show Answer Correct Answer: B) -5000. 7. Find the common ratio (multiplier):a$_{1}$ = 4 and a$_{4}$ = 256 A) 8. B) 4. C) 84. D) 64. Show Answer Correct Answer: B) 4. 8. Expand (x + 5)$^{2 }$ A) X$^{2}$ + 10. B) X$^{2}$ + 10 x + 10. C) X$^{2}$ + 25. D) X$^{2}$ + 10x + 25. Show Answer Correct Answer: D) X$^{2}$ + 10x + 25. 9. Using $\left(2y-5x\right)^6$ A) $6000x^3y^5$. B) $6000x^2y^4$. C) $6001x^2y^4$. D) $6000x^4y^2$. Show Answer Correct Answer: B) $6000x^2y^4$. 10. What row of Pascal's Triangle would you use for (x-2)$^{7}$? A) 1, 5, 10, 10, 5, 1. B) 1, 7, 21, 35, 35, 21, 7, 1. C) 1, 5, 10, 5, 1. D) 1, 7, 21, 35, 21, 7, 1. Show Answer Correct Answer: B) 1, 7, 21, 35, 35, 21, 7, 1. 11. What is the middle term in the expansion of (2y-3x)$^{4}$ A) -6x$^{2}$y$^{2}$. B) 144x$^{2}$y$^{2}$. C) 216x$^{2}$y$^{2}$. D) -36x$^{2}$y$^{2}$. Show Answer Correct Answer: C) 216x$^{2}$y$^{2}$. 12. The binomial coefficients from the beginning and end are ..... A) Greater than the other. B) Equal. C) 0. D) None. Show Answer Correct Answer: B) Equal. 13. A building is constructed using bricks that can be modeled as right rectangular prisms with a dimension of 7.5 in by 2.75 in by 2.5 in. If the bricks weight 0.04 ounces per cubic inch and cost cost $ 0.09 per ounce, find the cost of 950 bricks. Round your answer to the nearest cent. A) $ 0.19. B) $ 18.05. C) $ 110.21. D) $ 176.34. Show Answer Correct Answer: D) $ 176.34. 14. In the expansion of $(x-2y)^5$ $x^3y^2$ A) -80. B) 40. C) 80. D) -40. Show Answer Correct Answer: D) -40. 15. Rewrite the rational expression $\frac{x^2 + 3x + 2}{x + 1}$ $q(x) + \frac{r(x)}{x + 1}$ $q(x)$ $r(x)$ $r(x)$ $x + 1$ A) $x + 1 + \frac{2}{x + 1}$. B) $x + 2 + \frac{1}{x + 1}$. C) $x + 1 + \frac{1}{x + 1}$. D) $x + 2 + \frac{0}{x + 1}$. Show Answer Correct Answer: D) $x + 2 + \frac{0}{x + 1}$. 16. How many terms are the in the expansion of (a+b)$^{7}$ A) 9. B) 8. C) 7. D) 14. Show Answer Correct Answer: B) 8. 17. You want to save $ 5, 000 for future family vacation. If the bank pays 4.3% compounded monthly for 3 years, then how much will you need to invest to reach your vacation goal? A) $ 4, 395.89. B) $ 3, 250. C) $ 307, 042, 791. D) $ 5, 000. Show Answer Correct Answer: A) $ 4, 395.89. 18. How many 7 card hands are possible if all the jacks must be in the hand? A) 17, 296. B) 17, 298. C) 17, 299. D) 17, 297. Show Answer Correct Answer: A) 17, 296. 19. Using the Binomial Theorem expand:$\left(x+2\right)^4$ A) $x^4+8x^3+24x^2+32x+16$. B) X4+8x3+24x2+32x+16 Mathematical EquivalenceON. C) All the above. D) None of the above. Show Answer Correct Answer: A) $x^4+8x^3+24x^2+32x+16$. 20. $Evaluate:\\sum_{k=-3}^3\left(k^2-k\right)$ A) 16. B) 20. C) 28. D) None of the above. Show Answer Correct Answer: C) 28. 21. What is the constant term in the expansion of $(x + \frac{1}{x})^6$ A) 30TagsCCSS.HSA.APR.C.5. B) 15. C) 20. D) 10. Show Answer Correct Answer: C) 20. 22. What is the constant term in the expansion of (x + 4)$^{5}$? A) 160. B) 1024. C) 64. D) 640. Show Answer Correct Answer: B) 1024. 23. Multiply (x + y)$^{5}$ A) X$^{5}$ + x$^{4}$y + x$^{3}$y$^{2}$ + x$^{2}$y$^{3}$ + xy$^{4}$ + y$^{5}$. B) X$^{5}$ + 5x$^{4}$y + 10x$^{3}$y$^{2}$ + 10x$^{2}$y$^{3}$ + 5xy$^{4}$ + y$^{5}$. C) X$^{5 }$+ 5x$^{4}$ + 10x$^{3}$ + 10x$^{2}$ + 5x + 1. D) None of the above. Show Answer Correct Answer: B) X$^{5}$ + 5x$^{4}$y + 10x$^{3}$y$^{2}$ + 10x$^{2}$y$^{3}$ + 5xy$^{4}$ + y$^{5}$. 24. Express $\frac{1}{\left(1-i\sqrt[]{3}\right)^3}$ $\frac{a}{b}$ $a, \b\\in Z$ A) $-\frac{1}{8}$. B) $\frac{1}{6}$. C) $-\frac{1}{6}$. D) $\frac{1}{8}$. Show Answer Correct Answer: A) $-\frac{1}{8}$. 25. A bag contains 4 yellow balls and 6 green balls. A ball is taken from the bag and not replaced. A second ball is then taken. Draw a tree diagram and find the probability that the two balls are different colours. A) $\frac{4}{9}$. B) $\frac{24}{90}$. C) $\frac{8}{15}$. D) None of the above. Show Answer Correct Answer: C) $\frac{8}{15}$. 26. The American Red Cross says that about 11% of the U.S. population has Type B blood. A blood drive is being held at your school.What is the probability that exactly 2 of the first 20 blood donors have Type B blood? A) 0.001. B) 0.316. C) 0.282. D) Not here. Show Answer Correct Answer: C) 0.282. 27. Factor 216x$^{3}$ + 125 A) (6x-5)(36x$^{2}$ + 30x + 25). B) (6x + 5)(6x$^{2}$-30x + 25). C) 6(x + 5)$^{3}$. D) (6x + 5)(36x$^{2 }$-30x + 25). Show Answer Correct Answer: D) (6x + 5)(36x$^{2 }$-30x + 25). 28. Identify the second term of $\left(2x-8\right)^5$ A) $-80x^4$. B) $-32x^3$. C) A. $-640x^4$. D) $640x$. E) $-256x^5$. Show Answer Correct Answer: C) A. $-640x^4$. 29. Simplify:(10+ 15i)-(48-30i) A) -38-15i. B) 58-45i. C) -38 + 45i. D) 58-15i. Show Answer Correct Answer: C) -38 + 45i. 30. Factor $8x^3-27$ A) (2x+3)(4x$^{2}$-6x+9). B) (2x-3)(2x$^{2}$+6x+9). C) (2x-3)(4x$^{2}$+6x+9). D) (2x-3)(4x$^{2}$+6x-9). Show Answer Correct Answer: C) (2x-3)(4x$^{2}$+6x+9). 31. What is the coefficient of $x^2y^3$ $(x + y)^5$ A) 30TagsAZ.MA.9-12.P.A-APR.C.5. B) 20. C) 10. D) 5. Show Answer Correct Answer: C) 10. 32. Find the first 4 terms of the expansion of $\left(2r-s\right)^{10}$ A) $1024r^{10}-512r^{9s}+11520r^8s^2-15360r^7s^3$. B) $1024r^{10}+5120r^{9s}+11520r^8s^2+15360r^7s^3$. C) $1024r^{10}+5120r^{9s}+11520r^8s^2-15360r^7s^3$. D) $1024r^{10}-5120r^{9s}+11520r^8s^2-15360r^7s^3$. Show Answer Correct Answer: D) $1024r^{10}-5120r^{9s}+11520r^8s^2-15360r^7s^3$. 33. What factoring technique must be used to factor? 27a$^{3 }$+ 343? A) Difference of 2 cubes. B) FOIL. C) Factoring using the GCF. D) Sum of 2 cubes. Show Answer Correct Answer: D) Sum of 2 cubes. 34. A dataset has a mean of 20 and a standard deviation of 4. What is the z-score of a data point that is 28? A) 3. B) 1. C) 2. D) 4. Show Answer Correct Answer: C) 2. 35. If the third term in the expansion of $(x + y)^n$ $120x^{n-2}y^2$ $n$ A) 5. B) 7. C) 6. D) 8. Show Answer Correct Answer: B) 7. 36. I want to arrange 5 boys and 5 girls together such that the same gender are together. The number of ways = A) 10!-(5!*5!). B) 2!*5!*5!. C) 2!. D) 10!. Show Answer Correct Answer: B) 2!*5!*5!. 37. How many terms are the in the expansion of (1+b)$^{5}$ A) 50. B) 25. C) 3. D) 5. E) 6. Show Answer Correct Answer: E) 6. 38. If $^{n}$C4=210, then the values of 'n' is A) 210. B) 10. C) 6. D) 4. Show Answer Correct Answer: B) 10. 39. Expand $\left(2x+4y\right)^3$ A) $8x^3+48x^2y+96xy^2+64y^3$. B) $32x^3+48x^2y+96xy^2+64y^3$. C) $8x^3+16x^2y+32xy^2+64y^3$. D) $40x^3+160x^2y+320xy^2+320y^3$. Show Answer Correct Answer: A) $8x^3+48x^2y+96xy^2+64y^3$. 40. Find the 3rd term in the expansion of $\left(3b+a\right)^4$ A) $54ba$. B) $50b^2a$. C) $54ba^2$. D) $54b^2a^2$. Show Answer Correct Answer: D) $54b^2a^2$. 41. What is the first term in the expansion of (2x-3)$^{5}$ A) -32x$^{5}$. B) -243. C) 270x$^{2}$. D) 32x$^{5}$. Show Answer Correct Answer: D) 32x$^{5}$. 42. The first three terms of (x + 1)$^{8}$ are ..... A) 1 + 8 + 28. B) 1 + 8x + 28x$^{2}$. C) X$^{8}$ + 8x$^{7 }$+ 28x$^{6}$. D) X$^{8}$ + x$^{7 }$+ x$^{6}$. Show Answer Correct Answer: C) X$^{8}$ + 8x$^{7 }$+ 28x$^{6}$. 43. What year was nickelodeon founded? A) 1985. B) 1923. C) 1930. D) 1977. E) 1990. Show Answer Correct Answer: D) 1977. 44. From a deck of 52 cards, how many 5 card hands have at least two red cards? A) 2, 144, 490. B) 2, 144, 470. C) 2, 144, 500. D) 2, 144, 480. Show Answer Correct Answer: D) 2, 144, 480. 45. Expand (4x+2y)$^{3}$ A) 64x$^{3 }$+ 96x$^{2}$y + 48xy$^{2 }$+ 8y$^{3}$. B) 64x$^{3 }$-96x$^{2}$y + 48xy$^{2 }$-8y$^{3}$. C) 64x$^{3 }$+ 96xy$^{2 }$+ 48x$^{2}$y + 8y$^{3}$. D) 64x$^{3 }$+ 96x$^{2}$y-48xy$^{2 }$+ 8y$^{3}$. Show Answer Correct Answer: A) 64x$^{3 }$+ 96x$^{2}$y + 48xy$^{2 }$+ 8y$^{3}$. 46. Which of the following expresses 1+3+5+ ..... +39 A) $\sum_{k=2}^{40}k-1$. B) $\sum_{k=1}^{39}2k-1$. C) $\sum_{k=1}^{20}2k-1$. D) $\sum_{k=-1}^{37}k+2$. Show Answer Correct Answer: C) $\sum_{k=1}^{20}2k-1$. 47. Which number is a coefficient found in the eighth row? A) 1452. B) 284. C) 5. D) 70. E) 36. Show Answer Correct Answer: D) 70. 48. Kamali has 7 unique bracelets and is trying to decide which 3 to wear for a party. Find the number of different combinations of 3 bracelets that Kamali could choose from the 7 she owns? A) 35. B) 21. C) 1. D) 7. Show Answer Correct Answer: A) 35. 49. Find the term that does not contain x in the expansion of $\left(8x^2+\frac{1}{2x}\right)^9$ A) 16777216. B) 32768. C) 1024. D) 1080. Show Answer Correct Answer: B) 32768. 50. If p (n) is a proposition about a positive integer n such that p (n) is true for n = 1 and p (n) is true for n = k whenever P (n) is true for any positive integer n = K + 1, p (n ) is true for every positive integer n, this principle is called principle of A) Mathematical induction. B) Mathematical deduction. C) Logic used. D) None of these. Show Answer Correct Answer: A) Mathematical induction. 51. If $^{n+1}$P5:$^{n}$C6= 2:7 then the values of 'n' is A) 17. B) 15. C) 11. D) 13. Show Answer Correct Answer: C) 11. 52. Find the Z-score.Mean = 22Standard Deviation:3.1x = 29 A) 2.26. B) 1.26. C) -2.26. D) 16.45. Show Answer Correct Answer: A) 2.26. 53. $\left(n^3-3n-5n^2\right)+\left(n^2+3+2n^3\right)$ A) $2n^3-4n^2+n+3$. B) $-n^3-4n^2+n+3$. C) $3n^3-4n^2-3n+3$. D) $3n^3-4n^2+n+3$. Show Answer Correct Answer: C) $3n^3-4n^2-3n+3$. 54. Find the constant term in $\left(x+\frac{1}{x}\right)^{10}$ A) $120$. B) $45$. C) $210$. D) $252$. Show Answer Correct Answer: D) $252$. 55. Coefficient of $x^{-3}$ $\left(x+\frac{1}{x^2}\right)^9$ A) 126x. B) 126. C) $125x^2$. D) 125. Show Answer Correct Answer: B) 126. 56. Simplify:3x$^{3}$(2x$^{2}$ + 9x + 6) A) 6x$^{5}$ + 45x$^{3}$. B) 6x$^{5}$ + 18x$^{2}$ + 9. C) 6x$^{5}$ + 27x$^{4}$ + 18x$^{3}$. D) 6x$^{5}$ + 27x$^{4}$ + 18x. Show Answer Correct Answer: C) 6x$^{5}$ + 27x$^{4}$ + 18x$^{3}$. 57. Use the Binomial Theorem to expand $(x + 2)^3$ A) $x^3 + 3x^2 + 6x + 8$. B) $x^3 + 3x^2 + 3x + 8$. C) $x^3 + 6x^2 + 12x + 8$. D) $x^3 + 6x^2 + 6x + 8$. Show Answer Correct Answer: C) $x^3 + 6x^2 + 12x + 8$. 58. Determine the first three terms in the expansion of $\left(1-2x\right)^5\cdot\left(1+x\right)^7$ A) $1+3x+9x^2+ $. B) $1+3x-9x^2+ $. C) $1-3x-9x^2+ $. D) $1-3x+9x^2+ $. Show Answer Correct Answer: C) $1-3x-9x^2+ $. 59. What is the degree of the following polynomial?x$^{3 }$+ y$^{2}$x$^{2 }$+ x$^{7}$y$^{7 }$+ x$^{8}$ A) 3. B) 8. C) 14. D) 4. Show Answer Correct Answer: C) 14. 60. $\frac{4x}{x-5}-\frac{3}{x-6}$ A) $\frac{4x^2+21x+15}{\left(x-5\right)\left(x+6\right)}$. B) $\frac{4x^2-27x+15}{\left(x-6\right)\left(x-5\right)}$. C) $\frac{4x-3}{2x+1}$. D) $\frac{4x^2-27x+21}{\left(x-6\right)\left(x-5\right)}$. Show Answer Correct Answer: B) $\frac{4x^2-27x+15}{\left(x-6\right)\left(x-5\right)}$. 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