# CAT Questions | CAT Algebra Questions

###### CAT Quantitative Aptitude | CAT Algebra: Polynomials Questions

A CAT Algebra question from Polynomials that appears in the Quantitative Aptitude section of the CAT Exam consists of concepts from Number Theory and Algebra. Polynomial Remainder Theorem is an important concept in Polynomials. Sum of Squares, Sequences and Series, Finding roots of an equation all appear in Polynomials. In CAT Exam, one can generally expect to get 1~2 questions from Polynomials. Make use of 2IIMs Free CAT Questions, provided with detailed solutions and Video explanations to obtain a wonderful CAT score. If you would like to take these questions as a Quiz, head on here to take these questions in a test format, absolutely free.

1. #### CAT Polynomials - Possible pairs of solution

How many pairs of integer (a, b) are possible such that a2 – b2 = 288?

1. 6
2. 12
3. 24
4. 48

2. #### CAT Polynomials - Polynomial Remainder Theorem

Solve the inequality x3 – 5x2 + 8x – 4 > 0.

1. (2,$$infty \\$) 2.$1, 2) $$cup\\$$2, $$infty\\$) 3.$-$$infty \\$, 1) $\cup\\$$2, $$infty \\$) 4.$-$$infty \\$, 1) 3. #### CAT Polynomials - Remainder Theorem x4 – ax3 + bx2 – cx + 8 = 0 divided by x – 1 leaves a remainder of 4, divided by x + 1 leaves remainder 3, find b 1. 2.5 2. -5.5 3. 3.5 4. 6.5 4. #### CAT Polynomials - Sum of squares of nos. What is the sum of 12 + 32 + 52 …….312? 1. 9455 2. 5456 3. 3468 4. 4892 5. #### CAT Polynomials - Polynomial Remainder Theorem What is the remainder when x4 + 5x3 – 3x2 + 4x + 3 is divided by x + 2? 1. -41 2. -31 3. -18 4. 41 6. #### CAT Polynomials - Finding the Roots If x4 – 8x3 + ax2 – bx + 16 = 0 has positive real roots, find a – b. 1. -8 2. 6 3. -12 4. -14 7. #### CAT Polynomials - Remainders 4x3 + ax2 – bx + 3 divided by x – 2 leaves remainder 2, divided by x + 3 leaves remainder 3. Find remainder when it is divided by x + 2. 1. 26.8 2. 29.2 3. 32.2 4. 35.2 8. #### CAT Polynomials - Factors How many of the following are factors of 3200 – 5100? 1. 7 2. 16 3. 53 4. 12 1. 3 2. 2 3. 1 4. All of the above 9. #### CAT Polynomials - Roots x3 – 18x2 + bx – c = 0 has positive real roots, p, q and z. If geometric mean of the roots is 6, find b. 1. 36 2. -216 3. 108 4. -72 10. #### CAT Polynomials - Cubic Equation What is the value of 27x3 + 18x2y + 12xy2 + y3 when x = 4, y = – 8? 1. 64 2. 256 3. 512 4. 1984 11. #### CAT Polynomials - Sequence A sequence of numbers is defined as 2 = an – an-1. Sn is sum upto n terms in this sequence and a3 = 5. How many values m, n exist such than Sm – Sn = 65? 1. 4 2. 6 3. 2 4. More than 6 possibilities 12. #### CAT Polynomials - Summation 6 + 24 + 60 + 120 + 210 + 336 + 504 + 720…. upto 10 terms is equal to? 1. 3680 2. 4290 3. 5720 4. 6170 13. #### CAT Polynomials - Factorials 1$1!) + 2(2!) + 3(3!) + 4(4!)………….50(50!) is a multiple of prime P. P lies in the range........?

1. 30 < P < 40
2. 10 < P < 20
3. 30 < P < 40
4. P > 40

14. #### CAT Polynomials - Fractions

What is the sum of{ $$frac{1}{1*4}\\$ + $\frac{1}{2*5}\\$ + $\frac{1}{3*6}\\$ + $\frac{1}{4*7}\\$ +...} ? 1. $\frac{9}{17}\\$ 2. $\frac{7}{15}\\$ 3. $\frac{11}{18}\\$ 4. $\frac{92}{173}\\$ 15. #### CAT Polynomials - Sequences 2 + 6 + 10 + 14 ………..upto n term is given by Sn. How many of the following statements are true? 1. S2m – S2k could be a multiple of 16 2. 18Sn is a perfect square for all n 3. S2n > 2Sn for all n > 1 4. Sm+n > Sm + Sn for all m, n > 1 1. 1 2. 2 3. 3 4. 4 16. #### CAT Polynomials - Sequences $\frac{$2^4 - 1$}{(2 - 1)}$ + $\frac{$3^4 - 1$}{(3 - 1)}$ + $\frac{$4^4 - 1$}{(4 - 1)}$ + .. + $\frac{$10^4 - 1$}{(10 - 1)}$ = ? 1. 3462 2. 3581 3. 3471 4. 4022 17. #### CAT Polynomials - Factors What is the sum of all numbers less than 200 that are either prime or have more than 3 factors? 1. 19900 2. 19533 3. 19522 4. 19534 18. #### CAT Polynomials - Sum of a Series What is the sum of { $\frac{7}{1}\\$ + $\frac{26}{2}\\$ + $\frac{63}{3}\\$ + $\frac{124}{4}\\$ + $\frac{215}{5}\\$ }.... 19 terms or 7 + 13 + 21 + 31 + 43 + 57 + 73... 19 terms? 1. 3100 2. 3025 3. 3044 4. 3097 19. #### CAT Polynomials - Sum of fractions What is the sum of { $\frac{3}{4}\\$ + $\frac{5}{36}\\$ + $\frac{7}{144}\\$ + $\frac{9}{400}\\$ + }.... + $\frac{19}{8100}\\$ = ? 1. $\frac{9}{10}\\$ 2. $\frac{11}{18}\\$ 3. $\frac{99}{100}\\$ 4. $\frac{80}{81}\\$ 20. #### CAT Polynomials - Cubic Equation x3 – 4x2 + mx – 2 = 0 has 3 positive roots, two of which are p and $\frac{1}{p}\\$ Find m. 1. 5 2. -11 3. 8 4. -2 ###### Signup and sample 9 full classes for freein Online CAT CoachingBest CAT Online Coaching Signup Now! ###### Already have an Account? ###### CAT Coaching in ChennaiCAT 2020Enroll at 44,000/- Next Weekend Batch Starts Sun, Jan 26th, 2020 ###### Best CAT Coaching in ChennaiRegister Online, get Rs 4000/- off Attend a Demo Class ##### Where is 2IIM located? 2IIM Online CAT Coaching A Fermat Education Initiative, 58/16, Indira Gandhi Street, Kaveri Rangan Nagar, Saligramam, Chennai 600 093 ##### How to reach 2IIM? Phone:$91) 44 4505 8484
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