This quiz works best with JavaScript enabled. Home > Cbse > Class 11 > Science > Mathematics > Class 11 Mathematics Chapter 8 Binomial Theorem – Quiz 7 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 11 Mathematics Chapter 8 Binomial Theorem Quiz 7 (60 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. If the fourth term of the binomial expansion of (px+(1/x))$^{n}$ is 5/2, then A) N=6, p=1/2. B) N=8, p=6. C) N=8, p= 1/2. D) N=6, p=6. Show Answer Correct Answer: A) N=6, p=1/2. 2. If 5th term in the expansion of $(y+\frac{2}{y^2})^n$ A) 13. B) 10. C) 12. D) 11. Show Answer Correct Answer: C) 12. 3. Expand(b-2)$^{3}$ A) B$^{3}$-6b$^{2}$ + 12b-8. B) 4b$^{3}$-12b$^{2}$ + 16b-8. C) B$^{3}$-2b$^{2}$ + 4b-8. D) 5b$^{3}$-20b$^{2}$ + 40b-40. Show Answer Correct Answer: A) B$^{3}$-6b$^{2}$ + 12b-8. 4. Find the next three terms:3, -18, 108, -648 A) -6480, -3880, -233280. B) 3888, -23328, 139968. C) 5184, -31104, 186624. D) 6480, -38880, 233280. Show Answer Correct Answer: B) 3888, -23328, 139968. 5. What is the 2nd term in the expansion of (3u + 2)$^{4}$ A) 24u$^{3}$. B) 216u$^{3}$. C) 72u$^{3}$. D) 4u$^{3}$. Show Answer Correct Answer: B) 216u$^{3}$. 6. Find the term containing $y^3$ $\left(y+2\right)^4$ A) $8y^3$. B) $32y^3$. C) $12y^3$. D) $24y^3$. Show Answer Correct Answer: A) $8y^3$. 7. Expand:$\left(x+2\right)^4$ A) $x^4+8x^3+16x^2+32x+16$. B) $x^4+8x^3+16x^2+24x+16$. C) $x^4+8x^3+24x^2+32x+16$. D) $x^4+8x^3+32x^2+16x+16$. Show Answer Correct Answer: C) $x^4+8x^3+24x^2+32x+16$. 8. When will you have imaginary components in your factors? A) Three terms with two-signs. B) Sum of squares (two terms with a + between them). C) Difference of squares (Two terms with a-between them.). D) Three terms with a + then-. Show Answer Correct Answer: C) Difference of squares (Two terms with a-between them.). 9. If n is odd, then middle termin the expansion (x +y)$^{n}$ is A) (n+1) th term. B) N/2 term. C) (n/2)+1 term. D) (n+1)/2 and (n+3)/2 terms. Show Answer Correct Answer: D) (n+1)/2 and (n+3)/2 terms. 10. Expand $\left(2x-y\right)^3$ A) $8x^3-2x^3y-2xy^3+y^3$. B) $\left(4x^2-y^2\right)\left(2x-y\right)$. C) $8x^3-y^3$. D) $8x^3-12x^2y+6xy^2-y^3$. Show Answer Correct Answer: D) $8x^3-12x^2y+6xy^2-y^3$. 11. If the co-efficient of $x^{30}$ $(ax^5+\frac{1}{x^3})^6$ A) 5. B) $\frac{1}{6}$. C) 6. D) 1. Show Answer Correct Answer: D) 1. 12. What is the second term in the expansion (2+3x)$^{7}$? A) 1344x. B) 1344. C) 128. D) 6048x. Show Answer Correct Answer: A) 1344x. 13. Find the z-score value corresponding if the location is below the mean by 2 standard deviations A) +1.25. B) +2.00. C) -2.00. D) -1.00. Show Answer Correct Answer: C) -2.00. 14. A collection of items in which order is not important because no matter the order once the combination is used it cannot be repeated. A) Pascal's Triangle. B) Permuation. C) Combination. D) Binomial Theorem. Show Answer Correct Answer: C) Combination. 15. Which of the following is the correct way to rewrite $\frac{3x^2 + 7x + 5}{x + 2}$ A) $3x + 1 + \frac{7}{x + 2}$. B) $3x + 1 + \frac{3}{x + 2}$. C) $3x + 7 + \frac{5}{x + 2}$. D) $3x + 1 + \frac{5}{x + 2}$. Show Answer Correct Answer: B) $3x + 1 + \frac{3}{x + 2}$. 16. The value of k, for which the coefficient of $x^2$ $x^3$ $\left(3+kx\right)^9$ A) $\frac{7}{9}$. B) $\frac{7}{3}$. C) $\frac{9}{7}$. D) $\frac{3}{7}$. Show Answer Correct Answer: C) $\frac{9}{7}$. 17. Is the sequence geometric or arithmetic?3, 6, 9, 12 ..... A) Arithmetic. B) Geometric. C) Neither. D) None of the above. Show Answer Correct Answer: A) Arithmetic. 18. Around 1665 Sir who came up with a "general" version of the formula that is not limited to exponents of 0, 1, 2, ..... I hope to write about that one day. A) Isaac Newton. B) Lewis Latimer. C) Thomas Eddison. D) None of the above. Show Answer Correct Answer: A) Isaac Newton. 19. Factor using sum/difference of cubes. $a^3+b^3$ A) $\left(a-b\right)\left(a^2-ab+b^2\right)$. B) $\left(a-b\right)\left(a^2+ab+b^2\right)$. C) $\left(a+b\right)\left(a^2+ab+b^2\right)$. D) $\left(a+b\right)\left(a^2-ab+b^2\right)$. Show Answer Correct Answer: D) $\left(a+b\right)\left(a^2-ab+b^2\right)$. 20. Which row of Pascal's Triangle would you use to expand (x+2)$^{3}$? A) 1 1. B) 1 3 3 1. C) 1. D) 1 2 1. Show Answer Correct Answer: B) 1 3 3 1. 21. Factor x$^{3}$-343 A) (x$^{2}$-343) (x + 1). B) (x + 7) (x$^{2}$-7x + 49). C) (x-7) (x$^{2}$ + 7x + 49). D) (x$^{2}$ + 1) (x-343). Show Answer Correct Answer: C) (x-7) (x$^{2}$ + 7x + 49). 22. Which row in Pascal's Triangle would you use to expand this binomial? $\left(x-2\right)^3$ A) Row 6. B) Row 3. C) Row 2. D) Row 5. Show Answer Correct Answer: B) Row 3. 23. Consider the expansion of $\left(3x^2-\frac{1}{x}\right)^9.$ A) 756. B) 759. C) 2265. D) 2268. Show Answer Correct Answer: D) 2268. 24. Expand $\left(x+y^3\right)^4$ A) $x^4+4x^3y^3+4x^2y^6+4xy^9+y^{12}$. B) $x^4+4x^3y^3+6x^2y^6+4xy^9+y^{12}$. C) $x^4+x^3y^3+x^2y^6+xy^9+y^{12}$. D) $6x^4+15x^3y^3+20x^2y^6+15xy^9+6y^{12}$. Show Answer Correct Answer: B) $x^4+4x^3y^3+6x^2y^6+4xy^9+y^{12}$. 25. $\frac{14}{8!-7!}=$ A) $\frac{2}{8!}$. B) $14$. C) $\frac{2}{7!}$. D) $1$. Show Answer Correct Answer: C) $\frac{2}{7!}$. 26. Find the sixth term of $\left(x-y\right)^9$ A) $84x^5y^4$. B) $-126x^5y^4$. C) $-126x^4y^5$. D) $126x^4y^5$. Show Answer Correct Answer: C) $-126x^4y^5$. 27. $83\times82\times81\times80\times79$ A) $\frac{78!}{83}$. B) $\frac{83!}{78!}$. C) $\frac{83!}{79!}$. D) $8378$. Show Answer Correct Answer: B) $\frac{83!}{78!}$. 28. Find the 5th term of the expansion:(x-2)$^{10}$ A) 3360x$^{6}$. B) -960x$^{6}$. C) -8064x$^{6}$. D) -8064x$^{5}$. Show Answer Correct Answer: A) 3360x$^{6}$. 29. What is the Binomial expansion of (x + 1)$^{5}$? A) X$^{5}$ + 6x$^{4}$ + 15x$^{3}$ + 15x$^{2}$ + 6x + 1. B) X$^{5}$ + 1. C) X$^{5}$ + 5x$^{4}$ + 15x$^{3}$ + 15x$^{2}$ + 5x + 1. D) X$^{5}$ + 5x$^{4}$ + 10x$^{3}$ + 10x$^{2}$ + 5x + 1. Show Answer Correct Answer: D) X$^{5}$ + 5x$^{4}$ + 10x$^{3}$ + 10x$^{2}$ + 5x + 1. 30. Find the 7th term of the expansion:(x-2)$^{10}$ A) -15360x$^{3}$. B) -15360x$^{4}$. C) 13440x$^{4}$. D) -8064x$^{4}$. Show Answer Correct Answer: C) 13440x$^{4}$. 31. Find the middle term in the expansion of $(2x-3)^4$ A) $-108x^2$. B) $-24x^2$. C) $54x^2$. D) $216x^2$. Show Answer Correct Answer: D) $216x^2$. 32. Complete the formula $a^3-b^3$ A) $\left(a+b\right)\left(a^2+ab+b^2\right)$. B) $\left(a-b\right)\left(a^2-ab+b^2\right)$. C) $\left(a-b\right)\left(a^2+ab+b^2\right)$. D) $\left(a+b\right)\left(a^2-ab+b^2\right)$. Show Answer Correct Answer: C) $\left(a-b\right)\left(a^2+ab+b^2\right)$. 33. Find the fourth term of the expansion (5+3y)$^{5}$. A) 75y$^{4}$. B) 750y$^{3}$. C) 6750y$^{3}$. D) 2025y$^{4}$. Show Answer Correct Answer: C) 6750y$^{3}$. 34. Find the element in Pascal's Triangle. 12th row and 5 element. A) 495. B) 1. C) 330. D) 792. Show Answer Correct Answer: D) 792. 35. Given $\left(3x-\frac{2}{3}y^2\right)^5$ A) $-\frac{80}{3}x^2y^2$. B) $-\frac{80}{3}x^2y^4$. C) $-\frac{88}{3}x^2y^6$. D) $-\frac{80}{3}x^2y^6$. Show Answer Correct Answer: D) $-\frac{80}{3}x^2y^6$. 36. What is the formula for combinations in mathematics? A) NCr = n! / r. B) NCr = n! / r(n-r). C) NCr = n! / r. D) NCr = n! / r!(n-r)!. Show Answer Correct Answer: D) NCr = n! / r!(n-r)!. 37. Find the 2nd term in the expansion of $\left(b+a\right)^4$ A) $4b^3a$. B) $4ab$. C) $4a^3b^3$. D) $4ba$. Show Answer Correct Answer: A) $4b^3a$. 38. Find the coefficient of the term $x^8y^3$ $\left(3x^2-2y^3\right)^5$ A) -810. B) -811. C) -910. D) -800. Show Answer Correct Answer: A) -810. 39. Expand (x-7)$^{2}$ A) 49x$^{2}$. B) -x$^{2}$-14x-49. C) X$^{2}$ + 14x-49. D) X$^{2}$-14x + 49. Show Answer Correct Answer: D) X$^{2}$-14x + 49. 40. Which of the following is the induction step in mathematical induction? A) Show that if the statement is true for the first k elements, then it is true for the (k+1)st element in the set. B) Show that the statement is true for the first few elements in the set. C) Show that your math problem is different from all other math problems. D) None of these are correct. Show Answer Correct Answer: A) Show that if the statement is true for the first k elements, then it is true for the (k+1)st element in the set. 41. $\left(4m-4m^3+m^2\right)-\left(m^3-5-2m\right)$ A) $-5m^3-2m^2+m+9$. B) $-5m^3-2m^2+6m+9$. C) $-5m^3+m^2+6m+9$. D) $-5m^3+m^2+6m+5$. Show Answer Correct Answer: D) $-5m^3+m^2+6m+5$. 42. How many terms are the in the expansion of (a+b)$^{5}$ A) 5. B) 25. C) 6. D) 3. E) 50. Show Answer Correct Answer: C) 6. 43. State the coefficient for the a$^{4}$b$^{2}$ term of (2a-3b)$^{6}$. A) 2160. B) -90. C) 15. D) -3240. Show Answer Correct Answer: A) 2160. 44. Find the 13th term of the geometric sequence:2, 6, 18, 54, ..... A) 5 bazillion. B) 1, 062, 882. C) 1, 000, 000. D) 123, 587. Show Answer Correct Answer: B) 1, 062, 882. 45. $Evaluate:\\sum_{j=-2}^2\left(n^{n+1}\right)$ A) $\frac{25}{4}$. B) $\frac{19}{4}$. C) $\frac{17}{2}$. D) $\frac{19}{2}$. Show Answer Correct Answer: D) $\frac{19}{2}$. 46. Expand Correctly (Using Pascal's Triangle) $\left(x-3y\right)^4$ A) $x^4-12x^3y+54x^2y^2-108xy^3+81y^4$. B) $x^4+12x^3y-54xy+108x^3y-81y^4$. C) $x^4+12x^3+54x^2y-108xy-81$. D) None of the above. Show Answer Correct Answer: A) $x^4-12x^3y+54x^2y^2-108xy^3+81y^4$. 47. Which row of Pascal's Triangle would you use to expand (x+y)$^{4}$? A) 1 2 1. B) 1 1. C) 1 3 3 1. D) 1 4 6 4 1. Show Answer Correct Answer: D) 1 4 6 4 1. 48. What is the coefficient of the $x^6y^3$ $\left(x+2y\right)^9$ A) 336. B) 672. C) 84. D) 168. Show Answer Correct Answer: B) 672. 49. Add or Subtract to Simplify:(5x + 2) + (4x + 5) A) X+7. B) 9x+7. C) 9x-7. D) -9x-11. Show Answer Correct Answer: B) 9x+7. 50. What is row 7 of Pascal's Triangle? A) 1, 6, 15, 20, 15, 6, 1. B) 1, 8, 28, 56, 70, 56, 28, 8, 1. C) 1, 7, 21, 35, 35, 21, 7, 1. D) 1, 7, 28, 56, 70, 56, 28, 7, 1. Show Answer Correct Answer: C) 1, 7, 21, 35, 35, 21, 7, 1. 51. $\left(3x+5\right)^4$ A) $12x^4+3x^3+15x^2+5x+15$. B) $81x^4+135x^3+225x^2+375x+625$. C) $81x^4+540x^3+1350x^2+1500x+625$. D) None of the above. Show Answer Correct Answer: C) $81x^4+540x^3+1350x^2+1500x+625$. 52. Find the 3rd term of the expansion:(2x-3)$^{13}$ A) 135104112x$^{3}$. B) -159744x$^{11}$. C) 1437696x$^{11}$. D) -7907328x$^{10}$. Show Answer Correct Answer: C) 1437696x$^{11}$. 53. How does the Binomial Theorem apply to negative exponents? A) The Binomial Theorem can be applied to negative exponents by using an infinite series expansion. B) The Binomial Theorem is irrelevant for any exponent type. C) The Binomial Theorem only applies to positive integers. D) Negative exponents cannot be represented in the Binomial Theorem. Show Answer Correct Answer: A) The Binomial Theorem can be applied to negative exponents by using an infinite series expansion. 54. Insert 3 arithmetic means in the sequence 10, ..... , ..... , ..... , 130. A) 50, 80, 110. B) 40, 70, 100. C) 30, 60, 90. D) 20, 60, 120. Show Answer Correct Answer: B) 40, 70, 100. 55. Using the Binomial Theorem expand:$\left(2x+1\right)^4$ A) $16x^4+32x^3+24x^2+8x+1$. B) 16x4+32x3+24x2+8x+1 Mathematical EquivalenceON. C) All the above. D) None of the above. Show Answer Correct Answer: A) $16x^4+32x^3+24x^2+8x+1$. 56. Multiply.-3x$^{2}$(7x$^{2 }$-x + 4) A) -21x$^{4}$ + 3x$^{3}$-12x$^{2}$. B) 21x$^{}$$^{4 }$+ 3x$^{3 }$+ 12x$^{2}$. C) 7x$^{2}$-x + 4 (-3x$^{2}$). D) -12x$^{2 }$+ 3x$^{3 }$-21x$^{4}$. Show Answer Correct Answer: A) -21x$^{4}$ + 3x$^{3}$-12x$^{2}$. 57. Expand (x-7)(x + 7) A) X$^{2}$ + 7x-49. B) X$^{2}$-7x + 49. C) X$^{2}$ + 49. D) X$^{2}$-49. Show Answer Correct Answer: D) X$^{2}$-49. 58. Row 1 on pascal triangle A) 121. B) 1. C) 14641. D) 1331. E) 11. Show Answer Correct Answer: E) 11. 59. If three fair coins are tossed, what is the probability of getting at least two heads? A) 3/8. B) 2/3. C) 1/8. D) 1/2. Show Answer Correct Answer: A) 3/8. 60. Expand (a+b)$^{6}$ using the Binomial Theorem. A) A$^{6}$ + 6a$^{5}$b + 15a$^{4}$b$^{2}$ + 20a$^{3}$b$^{3}$ + 15a$^{2}$b$^{4}$ + 6ab$^{5}$ + b$^{6}$. B) A$^{6}$ + 6a$^{5}$b + 20a$^{4}$b$^{2}$ + 15a$^{3}$b$^{3}$ + 20a$^{2}$b$^{4}$ + 6ab$^{5}$ + b$^{6}$. C) A$^{6}$ + 3a$^{5}$b + 12a$^{4}$b$^{2}$ + 20a$^{3}$b$^{3}$ + 12a$^{2}$b$^{4}$ + 3ab$^{5}$ + b$^{6}$. D) A$^{6}$ + 3a$^{5}$b + 15a$^{4}$b$^{2}$ + 21a$^{3}$b$^{3}$ + 15a$^{2}$b$^{4}$ + 3ab$^{5}$ + b$^{6}$. Show Answer Correct Answer: A) A$^{6}$ + 6a$^{5}$b + 15a$^{4}$b$^{2}$ + 20a$^{3}$b$^{3}$ + 15a$^{2}$b$^{4}$ + 6ab$^{5}$ + b$^{6}$. ← 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 8Class 11 Mathematics Chapter 8 Binomial Theorem Quiz 9 🏠 Back to Homepage 📘 Download PDF Books 📕 Premium PDF Books