CAT Questions | CAT Algebra Questions | Polynomials

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?
   
   A. 6
   
   B. 12
   
   C. 24
   
   D. 48
   
   

   Correct Answer

   Choice C
   24

   Explanation
   

   ---

2. CAT Polynomials - Polynomial Remainder Theorem

   Solve the inequality x³ – 5x² + 8x – 4 > 0.
   
   A. (2, ∞)
   
   B. (1, 2) ∪ (2, ∞)
   
   C. (-∞, 1) ∪ (2, ∞)
   
   D. (-∞, 1)
   
   

   Correct Answer

   Choice B
   (1, 2) \\cup\\) (2, \\infty\\))

   Explanation
   

   ---

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
   
   A. 2.5
   
   B. -5.5
   
   C. 3.5
   
   D. 6.5
   
   

   Correct Answer

   Choice B
   -5.5

   Explanation
   

   ---

4. CAT Polynomials - Sum of squares of nos.

   What is the sum of 1² + 3² + 5² ......... + 31²?
   
   A. 9455
   
   B. 5456
   
   C. 3468
   
   D. 4892
   
   

   Correct Answer

   Choice B
   5456

   Explanation
   

   ---

5. CAT Polynomials - Polynomial Remainder Theorem

   What is the remainder when x⁴ + 5x³ – 3x² + 4x + 3 is divided by x + 2?
   
   A. -41
   
   B. -31
   
   C. -18
   
   D. 41
   
   

   Correct Answer

   Choice A
   -41

   Explanation

   ---

6. CAT Polynomials - Finding the Roots

   If x⁴ – 8x³ + ax² – bx + 16 = 0 has positive real roots, find a – b.
   
   A. -8
   
   B. 6
   
   C. -12
   
   D. -14
   
   

   Correct Answer

   Choice A
   -8

   Explanation

   ---

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.
   
   A. 26.8
   
   B. 29.2
   
   C. 32.2
   
   D. 35.2
   
   

   Correct Answer

   Choice D
   35.2

   Explanation

   ---

8. CAT Polynomials - Factors

   How many of the following are factors of 3²⁰⁰ – 5¹⁰⁰?
   1. 7
   2. 16
   3. 53
   4. 12
   
   A. 3
   
   B. 2
   
   C. 1
   
   D. All of the above
   
   

   Correct Answer

   Choice A
   3

   Explanation

   ---

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.
   
   A. 36
   
   B. -216
   
   C. 108
   
   D. -72
   
   

   Correct Answer

   Choice C
   108

   Explanation
   

   ---

10. CAT Polynomials - Cubic Equation

    What is the value of 27x³ + 18x²y + 12xy² + y³ when x = 4, y = – 8?
    A. 64
    
    B. 256
    
    C. 512
    
    D. 1984
    
    

    Correct Answer

    Choice D
    1984

    Explanation
    

    ---

11. CAT Polynomials - Sequence

    A sequence of numbers is defined as 2 = a_n – a_n-1. S_n is sum upto n terms in this sequence and a₃ = 5. How many values m, n exist such than S_m – S_n = 65?
    
    A. 4
    
    B. 6
    
    C. 2
    
    D. More than 6 possibilities
    
    

    Correct Answer

    Choice C
    2

    Explanation
    

    ---

12. CAT Polynomials - Summation

    6 + 24 + 60 + 120 + 210 + 336 + 504 + 720…. upto 10 terms is equal to?
    
    A. 3680
    
    B. 4290
    
    C. 5720
    
    D. 6170
    
    

    Correct Answer

    Choice B
    4290

    Explanation
    

    ---

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........?
    
    A. 30 < P < 40
    
    B. 10 < P < 20
    
    C. 30 < P < 40
    
    D. P > 40
    
    

    Correct Answer

    Choice D
    P > 40

    Explanation
    

    ---

14. CAT Polynomials - Fractions

    What is the sum of{ + + + +.....} ?
    
    A.
    
    B.
    
    C.
    
    D.
    
    

    Correct Answer

    Choice C
    ¹¹⁄₁₈.

    Explanation
    

    ---

15. CAT Polynomials - Sequences

    2 + 6 + 10 + 14.......upto n term is given by S_n. How many of the following statements are true?
    1. S_2m – S_2k could be a multiple of 16
    2. 18S_n is a perfect square for all n
    3. S_2n > 2S_n for all n > 1
    4. S_m+n > S_m + S_n for all m, n > 1
    
    A. 1
    
    B. 2
    
    C. 3
    
    D. 4
    
    

    Correct Answer

    Choice D
    4

    Explanation
    

    ---

16. CAT Polynomials - Sequences

    + + + ........+ = ?
    
    A. 3462
    
    B. 3581
    
    C. 3471
    
    D. 4022
    
    

    Correct Answer

    Choice C
    3471

    Explanation
    

    ---

17. CAT Polynomials - Factors

    What is the sum of all numbers less than 200 that are either prime or have more than 3 factors?
    
    A. 19900
    
    B. 19533
    
    C. 19522
    
    D. 19534
    
    

    Correct Answer

    Choice C
    19522

    Explanation
    

    ---

18. CAT Polynomials - Sum of a Series

    What is the sum of { + + + + }.... 19 terms or 7 + 13 + 21 + 31 + 43 + 57 + 73... 19 terms?
    
    A. 3100
    
    B. 3025
    
    C. 3044
    
    D. 3097
    
    

    Correct Answer

    Choice D
    3097

    Explanation
    

    ---

19. CAT Polynomials - Sum of fractions

    What is the sum of + + + + .... + = ?
    
    A.
    
    B.
    
    C.
    
    D.
    
    

    Correct Answer

    Choice C
    ⁹⁹⁄₁₀₀

    Explanation
    

    ---

20. CAT Polynomials - Cubic Equation

    x³ – 4x² + mx – 2 = 0 has 3 positive roots, two of which are p and Find m.
    
    A. 5
    
    B. -11
    
    C. 8
    
    D. -2
    
    

    Correct Answer

    Choice A
    5

    Explanation
    

    ---