List of practice Questions

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).

If 4^{4b - 3a} = 2^{2b + c} = 8^{c - a} and a + b + c = 11 , then find the value of \(4(\frac{1}{ab}+\frac{1}{bc}+\frac{1}{ca})\)

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

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

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

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

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

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

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

Find the number of zeros at the end of
P = 35! + 36! + 37! + 38! + 39! + 40!

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

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

What is the minimum value of (a + b) such that 4a x 5b will be a multiple of 5000?

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?

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

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

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

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

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.

Find the minimum numbers starting from 74 that are multiplied to get 50 zeros at the end ?

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

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