List of top Quantitative Aptitude Questions on Linear & Quadratic Equations asked in CAT

If x and y are real numbers such that x² + (x-2y-1)² = 4y(x+y), here the value x-2y is?

Let \(\alpha\) and \(\beta\) be the two distinct roots of the equation of 2x²-6x+k=0, such that (\(\alpha+\beta\)) and \(\alpha\beta\) are the distinct roots of the equation x²+px+p=0, then, the value of 8(k-p) ?

The price of a precious stone is directly proportional to the square of its weight. Sita has a precious stone weighing 18 units. If she breaks it into four pieces with each piece having distinct integer weight, then the difference between the highest and lowest possible values of the total price of the four pieces will be 288000. Then, the price of the original precious stone is

A lab experiment measures the number of organisms at 8 am every day. Starting with 2 organisms on the first day, the number of organisms on any day is equal to 3 more than twice the number on the previous day. If the number of organisms on the nth day exceeds one million, then the lowest possible value of n is

A lab experiment measures the number of organisms at 8 am every day. Starting with 2 organisms on the first day, the number of organisms on any day is equal to 3 more than twice the number on the previous day. If the number of organisms on the nth day exceeds one million, then the lowest possible value of n is

The equation \(x^3+(2r+1)x^2+(4r-1)x+2=0\) has -2 as one of the roots. If the other two roots are real, then the minimum possible non-negative integer value of \(r\) is

Let \(\alpha\) and \(\beta\) be the two distinct roots of the equation of 2x²-6x+k=0, such that (\(\alpha+\beta\)) and \(\alpha\beta\) are the distinct roots of the equation x²+px+p=0, then, the value of 8(k-p) ?

Let \(k\) be the largest integer such that the equation \((x-1)^2+2kx+11=0\) has no real roots. If \(y\) is a positive real number, then the least possible value of \(\frac{k}{4y}+9y\) is

How many numbers of integral solutions of the equation \(2|x|(x^2+1)=5x^2 ?\)

Two boats met at a point and one of them moves towards West while one towards South. After 2 hours, distance between them is 60 km. Find the speed of the slower boat if the difference in two speeds is 6 kmph.

Let \(k\) be the largest integer such that the equation \((x-1)^2+2kx+11=0\) has no real roots. If \(y\) is a positive real number, then the least possible value of \(\frac{k}{4y}+9y\) is

The equation \(x^3+(2r+1)x^2+(4r-1)x+2=0\) has -2 as one of the roots. If the other two roots are real, then the minimum possible non-negative integer value of \(r\) is

Let \(f(x)\) be a quadratic polynomial in x such that \(f(x)≥0\) for all real numbers x.If \(f(2)=0\) and \(f(4)=6\),then \(f(−2)\) is equal to

In an examination,there were 75 questions.3 marks were awarded for each correct answer,1 mark was deducted for each wrong answer and 1 mark was awarded for each unattempted question.Rayan scored a total of 97 marks in the examination.If the number of unattempted questions was higher than the number of attempted questions,then the maximum number of correct answers that Rayan could have given in the examination is

A donation box can receive only cheques of ₹100,₹250 and ₹500. On one good day,the donation box was found to contain exactly 100 cheques amounting to a total sum of ₹15250. Then, the maximum possible number of cheques of ₹500 that the donation box may have contained,is

In an examination,there were 75 questions.3 marks were awarded for each correct answer,1 mark was deducted for each wrong answer and 1 mark was awarded for each unattempted question.Rayan scored a total of 97 marks in the examination.If the number of unattempted questions was higher than the number of attempted questions,then the maximum number of correct answers that Rayan could have given in the examination is

Consider the pair of equations: \(x^2 - xy - x = 22\) and \(y^2 - xy + y = 34\). If x > y, then x- y equals

Three positive integers x, y and z are in arithmetic progression. If \(y − x > 2 \) and \(xyz = 5(x + y + z),\) then \(z − x\) equals

For all real values of x, the range of the function \(f(x) =\frac{ x^2+2x+4}{2x^2+4x+9}\) is

If 3x+2|y|+y=7 and x+|x|+3y=1, then x+2y is

\(f(x) = \) \(\frac{x^2+2x−15}{x^2−7x−18}\) is negative if and only if

If \(f(x)=x^2−7x\) and \(g(x)=x+3\), then the minimum value of \(f(g(x))−3x\) is

If n is a positive integer such that (10−−√7)(10−−√7)2…(10−−√7)n > 999, then the smallest value of n is

For all possible integers n satisfying 2.25 ≤ 2 + 2n + 2 ≤ 202, the number of integer values of 3 + 3n + 1 is