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
    Choice C
    24

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

  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
    Choice B
    -5.5

  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
    Choice B
    5456

  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
    Choice A
    -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
    Choice A
    -8

  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
    Choice D
    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
    Choice A
    3

  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
    Choice C
    108

  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
    Choice D
    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
    Choice C
    2

  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
    Choice B
    4290

  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
    Choice D
    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}\\)
    Choice C
    \\frac{11}{18}\\)

  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
    Choice D
    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
    Choice C
    3471

  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
    Choice C
    19522

  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
    Choice D
    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}\\)
    Choice C
    \\frac{99}{100}\\)

  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
    Choice A
    5


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