Polynomials

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Polynomials is a simple topic which involves a lot of basic ideas. Make sure that you a get of hold of them by solving these questions!!

  1. Polynomials - Possible pairs of Solutions

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

    1. 6
    2. 12
    3. 24
    4. 48
    • Correct AnswerChoice (C): 24 Correct answer
    • Explanatory Answer
    • Possible pairs of Solutions
    • Hard

  2. Polynomial Remainder Theorem

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

    1. (2, )
    2. (1, 2) (2, )
    3. (-, 1) (2, )
    4. (-, 1)
    • Correct AnswerChoice (B): Correct answer
    • Explanatory Answer
    • Polynomial Remainder Theorem
    • Hard

  3. 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
    • Correct AnswerChoice (B): Correct answer
    • Explanatory Answer
    • Polynomial Remainder Theorem
    • Easy

  4. Sum of squares of nos.

    What is the sum of 12 + 32 + 52 …….312?

    1. 9455
    2. 5456
    3. 3468
    4. 4892

  5. 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
    • Correct AnswerChoice (A): -41 Correct answer
    • Explanatory Answer
    • Polynomial Remainder Theorem
    • Medium

  6. 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
    • Correct AnswerChoice (A): -8 Correct answer
    • Explanatory Answer
    • Bi-Quadratic Equation
    • Medium

  7. 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. 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. 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. 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. 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
    • Correct AnswerChoice (C): 2 Correct answer
    • Explanatory Answer
    • Difference between Sums
    • Medium

  12. Summation

    6 + 24 + 60 + 120 + 210 + 336 + 504 + 720…. upto 10 terms is equal to?

    1. 3680
    2. 4290
    3. 5720
    4. 6170

  13. 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. Fractions

    What is the sum of ?

  15. 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. Sequences


    1. 3462
    2. 3581
    3. 3471
    4. 4022

  17. 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. Sum of a Series

    What is the sum of .... 19 terms or 7 + 13 + 21 + 31 + 43 + 57 + 73... 19 terms?

    1. 3100
    2. 3025
    3. 3044
    4. 3097

  19. Sum of fractions

    = ?

  20. Cubic Equation

    x3 – 4x2 + mx – 2 = 0 has 3 positive roots, two of which are p and . Find m.

    1. 5
    2. -11
    3. 8
    4. -2

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