List of top Questions asked in CAT

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?

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 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).

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 \((√2x-\frac{1}{√2x}) \)?

Let A be the largest positive integer that divides all the numbers of the form\( (2^{k}+3^{k}+5^{k})\) and B be the largest positive integer that divides all the numbers of the form \((3^{k}+4^{k}+5^{k}) \), where k is any positive integer. Then (A + B) equals

How many odd factors of the number 45⁶ x 56⁵ x 77⁶ are multiples of 63?

If \(N = 2^5 \times 3^4 \times 5^5 \times 11^2\), then how many factors of N are multiples of 66 but not of 72?

If (3x-\(\frac{1}{3x}\))=4, , then what is the value of (27x³-\(\frac{1}{27x^3}\)) ?

If=\(\frac{2x^2+x-6}{(x+2)^2-(x-2)^2}\), Q=\(\frac{x^2+3x+9}{(2x-3)(x^2-4)}\) and \(R=\frac{x^2-27}{x^4-4}\), then find the value of PXQ÷R

Which of the following words is a synonym for "magnificent" ?

Which of the following can be determined from the given information? I. The number of boys who are interested in attending a 1-day event and are neither dancers nor singers. II. The number of female dancers who are interested in attending a 1-day event.

What fraction of the class are interested in attending a 2-day event?

What BEST can be concluded about the number of male dancers who are interested in attending a 1-day event?

What is the sum of all roots of the equation \(|x+4|^2–10|x+4|=24\)?

The average weight of a group of people increases by 2 kg when a person weighing 65 kg joins them. If the initial average weight of the group was 55 kg, find the ratio of the number of people initially in the group to the total number of people in the new group.

In the questions two columns are given. You are required to solve the equations given in the "equations" column and match them with the correct statement given about the desired equation in the "conditions" column.

	Equations		Conditions
(a)	2x2 – 11x + 12 = 0	(d)	Product of roots is negative
(b)	5x2 21x – 20 = 0	(e)	Product of roots is completely divisible by 6
( c)	x2 – 17x + 72 = 0	(f)	Sum of both roots is positive

Find the HCF of (81²⁵-1) and (2⁷⁴-1).