Question:medium

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

Updated On: Nov 25, 2025

Top Questions on Linear & Quadratic Equations

If \(x\) and \(y\) are real numbers such that \(4x^2 + 4y^2 - 4xy - 6y + 3 = 0\), then the value of \((4x + 5y)\) is
- CAT - 2024
- Quantitative Aptitude
- Linear & Quadratic Equations
View Solution
If the equations $x^2 + mx + 9 = 0$, $x^2 + nx + 17 = 0$, and $x^2 + (m+n)x + 35 = 0$ have a common negative root, then the value of $(2m + 3n)$ is ?
- CAT - 2024
- Quantitative Aptitude
- Linear & Quadratic Equations
View Solution
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) ?
- CAT - 2023
- Quantitative Aptitude
- Linear & Quadratic Equations
View Solution
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
- CAT - 2023
- Quantitative Aptitude
- Linear & Quadratic Equations
View Solution
Want to practice more? Try solving extra ecology questions todayView All Questions

Questions Asked in CAT exam

Sam can complete a job in 20 days when working alone. Mohit is twice as fast as Sam and thrice as fast as Ayana in the same job. They undertake a job with an arrangement where Sam and Mohit work together on the first day, Sam and Ayana on the second day, Mohit and Ayana on the third day, and this three-day pattern is repeated till the work gets completed. Then, the fraction of total work done by Sam is

CAT - 2024
Time and Work

The number of all positive integers up to 500 with non-repeating digits is

CAT - 2024
Number Systems

The midpoints of sides AB, BC, and AC in ∆ABC are M, N, and P, respectively. The medians drawn from A, B, and C intersect the line segments MP, MN and NP at X, Y, and Z, respectively. If the area of ∆ABC is 1440 sq cm, then the area, in sq cm, of ∆XYZ is

CAT - 2024
Mensuration

Gopi marks a price on a product in order to make 20% profit. Ravi gets 10% discount on this marked price, and thus saves Rs 15. Then, the profit, in rupees, made by Gopi by selling the product to Ravi, is

CAT - 2024
Profit and Loss