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.
How many pairs of integer (a, b) are possible such that a^{2} – b^{2} = 288?
Solve the inequality x^{3} – 5x^{2} + 8x – 4 > 0.
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
What is the sum of 1^{2} + 3^{2} + 5^{2} …….31^{2}?
What is the remainder when x^{4} + 5x^{3} – 3x^{2} + 4x + 3 is divided by x + 2?
If x^{4} – 8x^{3} + ax^{2} – bx + 16 = 0 has positive real roots, find a – b.
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.
How many of the following are factors of 3^{200} – 5^{100}?
1. 7
2. 16
3. 53
4. 12
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.
What is the value of 27x^{3} + 18x^{2}y + 12xy^{2} + y^{3} when x = 4, y = – 8?
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?
6 + 24 + 60 + 120 + 210 + 336 + 504 + 720…. upto 10 terms is equal to?
1(1!) + 2(2!) + 3(3!) + 4(4!)………….50(50!) is a multiple of prime P. P lies in the range........?
What is the sum of{ \\frac{1}{1*4}\\) + \\frac{1}{2*5}\\) + \\frac{1}{3*6}\\) + \\frac{1}{4*7}\\) +...} ?
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
\\frac{(2^4 - 1)}{(2 - 1)}\\) + \\frac{(3^4 - 1)}{(3 - 1)}\\) + \\frac{(4^4 - 1)}{(4 - 1)}\\) + .. + \\frac{(10^4 - 1)}{(10 - 1)}\\) = ?
What is the sum of all numbers less than 200 that are either prime or have more than 3 factors?
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?
What is the sum of { \\frac{3}{4}\\) + \\frac{5}{36}\\) + \\frac{7}{144}\\) + \\frac{9}{400}\\) + }.... + \\frac{19}{8100}\\) = ?
x^{3} – 4x^{2} + mx – 2 = 0 has 3 positive roots, two of which are p and \\frac{1}{p}\\) Find m.
The Questions that follow, are from actual CAT papers. If you wish to take them separately or plan to solve actual CAT papers at a later point in time, It would be a good idea to stop here.
If \(x\) is a positive real number such that \(x^8+\left(\frac{1}{x}\right)^8=47\), then the value of \(x^9+\left(\frac{1}{x}\right)^9\) is
If \(p^2+q^2-29=2 p q-20=52-2 p q\), then the difference between the maximum and minimum possible value of \(\left(p^3-q^3\right)\) is
Let \(a_n\) and \(b_n\) be two sequences such that \(a_n=13+6(n-1)\) and \(b_n=15+7(n-1)\) for all natural numbers \(n\). Then, the largest three digit integer that is common to both these sequences, is
If \(x\) and \(y\) are real numbers such that \(x^2+(x-2 y-1)^2=-4 y(x+y)\), then the value \(x-2 y\) is
The number of integer solutions of equation \( 2|x|\left(x^2+1\right)=5 x^2 \) is
For natural numbers \(x, y\), and \(z\), if \(x y+y z=19\) and \(y z+x z=51\), then the minimum possible value of \(x y z\) is
Let \(A\) be the largest positive integer that divides all the numbers of the form \(3^k+4^k+5^k\), and \(B\) be the largest positive integer that divides all the numbers of the form \(4^k+3\left(4^k\right)+4^{k+2}\), where \(k\) is any positive integer. Then \((A+B)\) equals
If \(n\) is a positive integer such that \((\sqrt[7]{10})(\sqrt[7]{10})^{2} \ldots(\sqrt[7]{10})^{n}>999\), then the smallest value of \(n\) is
Consider the pair of equations: x^{2} - xy - x = 22 and y^{2} - xy + y = 34. If x > y, then x - y equals
For all real numbers x the condition |3x - 20| + |3x - 40| = 20 necessarily holds if
If r is a constant such that |x^{2} - 4 x - 13| = r has exactly three distinct real roots, then the value of r is
For real x, the maximum possible value of \\frac{x}{√(1 + x^{4})}) is
If a and b are integers of opposite signs such that (a + 3)^{2} : b^{2} = 9 : 1 and (a - 1)^{2} : (b - 1)^{2} = 4 : 1, then the ratio a^{2} : b^{2} is:
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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