Question:
The alphabets a, b, c represent integers forming a two-digit number 'ab' and a three digit number 'ccb'. Both defined under the usual decimal number system. If $(ab)^2 = ccb$ and $ccb>300$, then the value of b is:
The alphabets a, b, c represent integers forming a two-digit number 'ab' and a three digit number 'ccb'. Both defined under the usual decimal number system. If $(ab)^2 = ccb$ and $ccb>300$, then the value of b is:
Show Hint
When dealing with quadratic equations, carefully solve for the unknowns and check the conditions for consistency.
Updated On: Aug 5, 2025
- 1
- 0
- 5
- 6
Hide Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
We solve the equation $(ab)^2 = ccb$ under the conditions given. By solving for b, we find that $b = 5$ satisfies the equation.
Was this answer helpful?
0
0
Top Questions on Algebra
- All the values of \(k\) such that the quadratic expression \(2kx^2 - (4k+1)x + 2\) is negative for exactly three integral values of \(x\), lie in the interval:
- If \(\alpha, \beta, \gamma\) are the roots of the equation \[ x^3 - 13x^2 + kx + 189 = 0 \] such that \(\beta - \gamma = 2\), then find the ratio \(\beta + \gamma : k + \alpha\).
The relationship between two variables \( x \) and \( y \) is given by \( x + py + q = 0 \) and is shown in the figure. Find the values of \( p \) and \( q \). Note: The figure shown is representative.
- If \(x^2 + y^2 = 25\) and \(xy = 12\), then what is the value of \(x^4 + y^4\)?
- In \( \triangle ABC \), if \( \sin^2 B = \sin A \) and \( 2\cos^2 A = 3\cos^2 B \), then the triangle is:
View More Questions
Questions Asked in CAT exam
- Five jumbled up sentences (labelled 1, 2, 3, 4 and 5), related to a topic, are given below. Four of them can be put together to form a coherent paragraph. Identify the odd sentence and key in the number of that sentence as your answer.
- CAT - 2024
- Para Jumbles
- \( 10^{68} \) is divided by 13, the remainder is is
- CAT - 2024
- Divisibility and Remainder
- ABCD is a rectangle with sides AB = 56 cm and BC = 45 cm, and E is the midpoint of side CD. Then, the length, in cm, of radius of incircle of \(\triangle ADE\) is
- CAT - 2024
- Mensuration
- Two places A and B are 45 kms apart and connected by a straight road. Anil goes from A to B while Sunil goes from B to A. Starting at the same time, they cross each other in exactly 1 hour 30 minutes. If Anil reaches B exactly 1 hour 15 minutes after Sunil reaches A, the speed of Anil, in km per hour, is
- CAT - 2024
- Time, Speed and Distance
- The selling price of a product is fixed to ensure 40% profit. If the product had cost 40% less and had been sold for 5 rupees less, then the resulting profit would have been 50%. The original selling price, in rupees, of the product is
- CAT - 2024
- Profit and Loss
View More Questions