### Polynomials - Possible pairs of Solutions

How many pairs of integer (a, b) are possible such that a

^{2}– b^{2}= 288?- 6
- 12
- 24
- 48

**Correct Answer**Choice (C): 24 Correct answer- Explanatory Answer
- Possible pairs of Solutions
- Hard

### Polynomial Remainder Theorem

Solve the inequality x

^{3}– 5x^{2}+ 8x – 4 > 0.- (2, )
- (1, 2) (2, )
- (-, 1) (2, )
- (-, 1)

**Correct Answer**Choice (B): Correct answer- Explanatory Answer
- Polynomial Remainder Theorem
- Hard

### Remainder Theorem

x

^{4}– ax^{3}+ bx^{2}– cx + 8 = 0 divided by x – 1 leaves a remainder of 4, divided by x + 1 leaves remainder 3, find b.- 2.5
- -5.5
- 3.5
- 6.5

**Correct Answer**Choice (B): Correct answer- Explanatory Answer
- Polynomial Remainder Theorem
- Easy

### Sum of squares of nos.

What is the sum of 1

^{2}+ 3^{2}+ 5^{2}…….31^{2}?- 9455
- 5456
- 3468
- 4892

**Correct Answer**Choice (B): Correct answer- Explanatory Answer
- Sum of squares of nos.
- Medium

### Polynomial Remainder Theorem

What is the remainder when x

^{4}+ 5x^{3}– 3x^{2}+ 4x + 3 is divided by x + 2?- -41
- -31
- -18
- 41

**Correct Answer**Choice (A): -41 Correct answer- Explanatory Answer
- Polynomial Remainder Theorem
- Medium

### Finding the Roots

If x

^{4}– 8x^{3}+ ax^{2}– bx + 16 = 0 has positive real roots, find a – b.- -8
- 6
- -12
- -14

**Correct Answer**Choice (A): -8 Correct answer- Explanatory Answer
- Bi-Quadratic Equation
- Medium

### Remainders

4x

^{3}+ ax^{2}– 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.- 26.8
- 29.2
- 32.2
- 35.2

**Correct Answer**Choice (D): 35.2 Correct answer- Explanatory Answer
- Cubic Equation
- Medium

### Factors

How many of the following are factors of 3

^{200}– 5^{100}?

1. 7

2. 16

3. 53

4. 12

- 3
- 2
- 1
- All of the above

**Correct Answer**Choice (A): 3 Correct answer- Explanatory Answer
- Remainders
- Medium

### Roots

x

^{3}– 18x^{2}+ bx – c = 0 has positive real roots, p, q and z. If geometric mean of the roots is 6, find b.- 36
- -216
- 108
- -72

**Correct Answer**Choice (C): 108 Correct answer- Explanatory Answer
- Geometric Mean
- Medium

### Cubic Equation

What is the value of 27x

^{3}+ 18x^{2}y + 12xy^{2}+ y^{3}when x = 4, y = – 8?- 64
- 256
- 512
- 1984

**Correct Answer**Choice (D): 1984 Correct answer- Explanatory Answer
- Value of Equation
- Medium

### 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 a_{3}= 5. How many values m, n exist such than S_{m}– S_{n}= 65?- 4
- 6
- 2
- More than 6 possibilities

**Correct Answer**Choice (C): 2 Correct answer- Explanatory Answer
- Difference between Sums
- Medium

### Summation

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

- 3680
- 4290
- 5720
- 6170

**Correct Answer**Choice (B): 4290 Correct answer- Explanatory Answer
- Series
- Medium

### Factorials

1(1!) + 2(2!) + 3(3!) + 4(4!)………….50(50!) is a multiple of prime P. P lies in the range........?

- 30 < P < 40
- 10 < P < 20
- 30 < P < 40
- P > 40

**Correct Answer**Choice (D): P > 40 Correct answer- Explanatory Answer
- Series
- Medium

### Fractions

What is the sum of ?

**Correct Answer**Choice (C) Correct answer- Explanatory Answer
- Sequences
- Medium

### 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

- 1
- 2
- 3
- 4

**Correct Answer**Choice (D). 4 Correct answer- Explanatory Answer
- Summation
- Medium

### Sequences

- 3462
- 3581
- 3471
- 4022

**Correct Answer**Choice (C). 3471 Correct answer- Explanatory Answer
- Summation
- Medium

### Factors

What is the sum of all numbers less than 200 that are either prime or have more than 3 factors?

- 19900
- 19533
- 19522
- 19534

**Correct Answer**Choice (C). 19522 Correct answer- Explanatory Answer
- Number Systems
- Medium

### Sum of a Series

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

- 3100
- 3025
- 3044
- 3097

**Correct Answer**Choice (D). 3097 Correct answer- Explanatory Answer
- Series
- Medium

### Sum of fractions

= ?

**Correct Answer**Choice (C) Correct answer- Explanatory Answer
- Series
- Medium

### Cubic Equation

x

^{3}– 4x^{2}+ mx – 2 = 0 has 3 positive roots, two of which are p and . Find m.

- 5
- -11
- 8
- -2

**Correct Answer**Choice (A). 5 Correct answer- Explanatory Answer
- Roots
- Medium

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