This quiz works best with JavaScript enabled. Home > Class 11 > Class 11 Mathematics Chapter 8 Binomial Theorem – Quiz 9 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 11 Mathematics Chapter 8 Binomial Theorem Quiz 9 (25 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. Find the 32nd term of the arithmetic sequence:9, 4, -1, -6, -11, ..... A) 81. B) -34. C) -146. D) -225. Show Answer Correct Answer: C) -146. 2. 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 +. 3. 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) 0.132. C) 0.831. D) 0.250. Show Answer Correct Answer: B) 0.132. 4. A method of expanding a binomial. A) Combination. B) Pascal's Triangle. C) Binomial Theorem. D) Permutation. Show Answer Correct Answer: C) Binomial Theorem. 5. Expand (x+4)$^{8}$ A) X$^{7}$ + 28 x$^{6}$ + 336 x$^{5}$ + 2240 x$^{4}$ + 8960 x$^{3}$ + 21504 x$^{2}$ + 28672 x + 16384. 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$^{8}$ + 8 x$^{7}$ + 28 x$^{6}$ + 56x$^{5}$ + 70x$^{4}$ + 56x$^{3}$ + 28x$^{2}$ + 8x +1. 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. 6. When using mathematical induction to prove:$\sum_{i=1}^ni^2=\frac{n\left(n+1\right)\left(2n+1\right)}{6}$ A) $\sum_{i=1}^{k+1}i^2=\frac{\left(k\right)\left(k+1\right)\left(2k+1\right)}{6}+\left(k+1\right)^2$. B) $S_{k+1}=\frac{k\left(k+1\right)\left(2k+1\right)}{6}$. C) $\sum_{k=1}^n\left(k+1\right)^2=\frac{\left(k+1\right)\left(k+2\right)\left(2k+3\right)}{6}$. D) $S_{k+1}=\left(k+1\right)^2$. Show Answer Correct Answer: C) $\sum_{k=1}^n\left(k+1\right)^2=\frac{\left(k+1\right)\left(k+2\right)\left(2k+3\right)}{6}$. 7. C0+C1+C2+C3+ ..... Cn= A) 2$^{n}$. B) 0. C) 1. D) None. Show Answer Correct Answer: A) 2$^{n}$. 8. Find the coefficient of x$^{4}$ in the expansion of (1-x)$^{14}$ A) 1001. B) -1001. C) 364. D) -364. Show Answer Correct Answer: A) 1001. 9. What is the sum of the coefficients in the expansion of $(2x-3)^5$ A) $-1$. B) $-32$. C) $-243$. D) $-25$. Show Answer Correct Answer: C) $-243$. 10. 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. 11. In the expansion of $(x^4-\frac{1}{x^3})^6$ $x^{-4}$ A) 5. B) 4. C) 3. D) 2. Show Answer Correct Answer: B) 4. 12. Find the sum.(2x$^{2}$ + 5x-7) + ( 3-4x$^{2}$ + 6x) A) 2x$^{2 }$+ 3x +1. B) -2x$^{2 }$-11x-4. C) 2x$^{2}$ $_{}$+ 5x-7. D) -2x$^{2}$ + 11x-4. Show Answer Correct Answer: D) -2x$^{2}$ + 11x-4. 13. The number of permutations using the letters of the word LOOPHOLE is: A) 3520. B) 3360. C) 4000. D) 4630. Show Answer Correct Answer: B) 3360. 14. 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) 92, 178 people. B) 95, 029 people. C) 167, 990 people. D) 163, 096 people. Show Answer Correct Answer: B) 95, 029 people. 15. The coefficient $x^{12}$ $(x^2+2x)^{10}$ A) 11520. B) 13410. C) 16520. D) 23040. Show Answer Correct Answer: A) 11520. 16. Given the binomial $\left(5x^4+3y^5\right)^8$ A) $3y^{13}$. B) $6561y^{13}$. C) $3y^{40}$. D) $6561y^{40}$. Show Answer Correct Answer: D) $6561y^{40}$. 17. 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) 7 + 24i. B) -3 + 79i. C) -12 + 316i. D) 28 + 96i. Show Answer Correct Answer: C) -12 + 316i. 18. What does the p stand for in the binomial probability formula? A) Number of trials. B) Number of Successes. C) Probability of Successes. D) Probability of Failures. Show Answer Correct Answer: C) Probability of Successes. 19. $\left(p+q\right)^6$ A) 1, 8, 28, 56, 70, 56, 28, 8, 1. B) 1, 6, 15, 20, 15, 6, 1. C) 1, 5, 10, 5, 1. D) 1, 4, 6, 4, 1. Show Answer Correct Answer: B) 1, 6, 15, 20, 15, 6, 1. 20. Find the third term of $\left(3x+y\right)^4$ A) $54x^3y$. B) $549xy^3$. C) $54x^2y^2$. D) $6x^2y^2$. Show Answer Correct Answer: C) $54x^2y^2$. 21. 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) $a^5-5a^4b+10a^2b^3-10a^3b^2+5ab^4-b^5$. D) $a^5-5a^4b-10a^3b^2-10a^2b^3-5ab^4-b^5$. Show Answer Correct Answer: B) $a^5-5a^4b+10a^3b^2-10a^2b^3+5ab^4-b^5$. 22. What is the relationship between the binomial coefficients and combinations? A) Combinations are a type of binomial coefficient. B) Binomial coefficients are unrelated to combinations. C) Binomial coefficients are the mathematical representation of combinations. D) Binomial coefficients are used only in probability calculations. Show Answer Correct Answer: C) Binomial coefficients are the mathematical representation of combinations. 23. Find term 3 in row 8 A) 56. B) 28. C) 8. D) 3. Show Answer Correct Answer: A) 56. 24. 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 at least 2 of the first 10 blood donors has Type B blood? A) 0.088. B) 0.697. C) 0.214. D) 0.303. Show Answer Correct Answer: D) 0.303. 25. What is the fourth row of Pascal's Triangle? A) 1 2 1. B) 1 3 3 1. C) 1 4 6 4 1. D) 1 5 10 10 5 1. Show Answer Correct Answer: C) 1 4 6 4 1. ← 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 4Class 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 10Class 11 Mathematics Chapter 8 Binomial Theorem Quiz 11 🏠 Back to Homepage 📘 Download PDF Books 📕 Premium PDF Books