List of top Questions asked in CAT

If 25^{(3a - 2b)} = 5^{(b - a)} = 5² and \(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=\frac{13}{35}\), then find the value of ab - c.

If (Ax + By - Cz)² + 4\(\sqrt3\)xy - 2\(\sqrt6\)yz - 4\(\sqrt2\)xz, then find the value of A² + B²C².

Find the number of zeros at the end of the product :
5 × 10 × 15 × 20 × 25 × ……………………..× 500

For how many values of ‘n < 50’ are possible, such that n! is divisible by n².

Find the value of: \( \frac{x^4-81}{ 2x2+13x+15 }\times\frac{2x+3}{x^3+27}\times\frac{[(x-3)^2+3x](x+5)}{(x+3)^2-6x}\)

Is\( (\sqrt{x}-\frac{1}{\sqrt{x}})=\sqrt{-5}\) and x≠ 0, then what is the value of \(\frac{3(x^2+3)-6-3x}{4x}\) ?

How many numbers between 90 and 600 have exactly three factors?

How many factors of N=2⁶ x 3⁸ x 5¹⁰ x 7¹² are perfect squares as well as perfect cubes?

In a trinary base system, how many numbers from 0 to 100 end with digit 1?

What is the number of factors of the number formed by the last three digits of 1005¹⁰⁰¹?

A fruit basket contains 80 apples, 70 oranges, and 60 bananas. Some fruits might be rotten and discarded. What is the difference between the maximum and minimum possible number of fruits that are both apples and oranges?

Find the remainder when (345672) in base 9 is divided by 8.

If 25x² + y² = 41 and xy = 4 where x, y > 0, then the value of (125x³ + y³) is :

If x²-4x+3=0, then what is the value of (x³+4x²+7x+24)(x²+2x+3)^-1?

If \(A=\frac{x^2-y^2}{x^2-y^2}\), \(B=\frac{x+y}{x^2+y^2+xy}\) and \(C=\frac{ 3xy^2-3x^2y}{x^2-y^2}\), then find the value of AB (A+C)

How many natural numbers, when converted to base 3, are four-digit numbers, but when converted to base 4, are three-digit numbers ?

If x² - 12x + 1 = 0, then find the value of {x⁶ + x + x⁵ + 1}/x³

If x² - 8x = 1, then find the value of {(x⁶ + 12x³ - 1)/(x⁶ - 24x³- 1)}

Let X=11×12×13×_____×75. Suppose ‘X’ is divisible by 10^2k (where ‘k’ is a natural no.). Find the maximum value of ‘k’.

If (x² - xy + y²) = 8 and (x⁴ + x²y² + y⁴) = 16, then find the value of (x² + xy + y²).

Find the greatest integral power of 2 in 41! + 42! + 43! + ……………+ 50!

For any natural number n, suppose the sum of the first n terms of an arithmetic progression is n(n+1). If the nth term of the progression is divisible by 7, then the smallest possible value of n is:

How many natural numbers, when converted to base 5 are four- digit numbers ?

How many four-digit numbers in base 4, when converted to base 5, will have unit digit zero ?

If \(\frac{5(4x^2+1)-3x}{4x}=8\) and x ≠ 0, then what is the value of \((√2x-\frac{1}{√2x}) \)?