# 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, ${\infty}$)
2. (1, 2) ${\cup}$ (2, ${\infty}$)
3. (-${\infty}$, 1) ${\cup}$ (2, ${\infty}$)
4. (-${\infty}$, 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 ${\frac{1}{1*4} + \frac{1}{2*5} + \frac{1}{3*6} + \frac{1}{4*7} +...}$ ?

1. ${\frac{9}{17}}$
2. ${\frac{7}{15}}$
3. ${\frac{11}{18}}$
4. ${\frac{92}{173}}$
15. ### 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

${\frac{(2^4 - 1)}{(2 - 1)} + \frac{(3^4 - 1)}{(3 - 1)} + \frac{(4^4 - 1)}{(4 - 1)}} + .. + \frac{(10^4 - 1)}{(10 - 1)} = ?$

1. 3462
2. 3581
3. 3471
4. 4022
17. ### 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 ${\frac{7}{1} + \frac{26}{2} + \frac{63}{3} + \frac{124}{4} + \frac{215}{5}}$.... 19 terms or 7 + 13 + 21 + 31 + 43 + 57 + 73... 19 terms?

1. 3100
2. 3025
3. 3044
4. 3097
19. ### Sum of fractions

${\frac{3}{4} + \frac{5}{36} + \frac{7}{144} + \frac{9}{400} +.... + \frac{19}{8100}}$ = ?

1. ${\frac{9}{10}}$
2. ${\frac{11}{18}}$
3. ${\frac{99}{100}}$
4. ${\frac{80}{81}}$
20. ### 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

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