# 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

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) 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 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 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 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 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 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 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 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 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 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 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

1. 1
2. $$frac{1}{2}$ 3. $\frac{1}{√2}$ 4. $\frac{1}{√3}$ 5. #### CAT 2017 Question Paper Slot 1 - Algebra If a and b are integers of opposite signs such that$a + 3)2 : b2 = 9 : 1 and (a - 1)2 : (b - 1)2 = 4 : 1, then the ratio a2 : b2 is:

1. 9 : 4
2. 81 : 4
3. 1 : 4
4. 25 : 4

6. #### CAT 2017 Question Paper Slot 1 - Algebra

If a, b, c, and d are integers such that a + b + c + d = 30, then the minimum possible value of (a - b)2 + (a - c)2 + (a - d)2 is (TITA)

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