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Try yourself:How many factors of 2^{4} × 3^{5} × 10^{4} are perfect squares which are greater than 1?

[2019]

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Try yourself:How many pairs (m, n) of positive integers satisfy the equation m^{2} + 105 = n^{2}?

[2019]

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Try yourself:In a six-digit number, the sixth, that is, the rightmost, digit is the sum of the first three digits, the fifth digit is the sum of first two digits, the third digit is equal to the first digit, the second digit is twice the first digit and the fourth digit is the sum of fifth and sixth digits. Then, the largest possible value of the fourth digit is?

[2019]

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Try yourself:If m and n are integers such that (√2)^{19 }3^{4} 4^{2} 9^{m} 8^{n} = 3^{n} 16^{m} (∜64) then m is

[2019]

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Try yourself:The product of two positive numbers is 616. If the ratio of the difference of their cubes to the cube of their difference is 157 : 3, then the sum of the two numbers is

[2019]

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Try yourself:The number of integers x such that 0.25 < 2x < 200, and 2x + 2 is perfectly divisible by either 3 or 4, is

[2018]

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Try yourself:A sequence of 4 digits, when considered as a number in base 10 is four times the number it represents in base 6. What is the sum of the digits of the sequence?

[2016]

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Try yourself:Which of the following will completely divide (10690 – 4990)?

[2015]

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Try yourself:Let P be the set of all odd positive integers such that every element in P satisfies the following conditions.

I. 100 ≤ n < 1000

II. The digit at the hundred’s place is never greater than the digit at tens place and also never less than the digit at units place.

I. 100 ≤ n < 1000

II. The digit at the hundred’s place is never greater than the digit at tens place and also never less than the digit at units place.

How many elements are there in P?

[2015]

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Try yourself:A four-digit number is divisible by the sum of its digits. Also, the sum of these four digits equals the product of the digits. What could be the product of the digits of such a number?

[2015]

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Try yourself:P is the product of the first 100 multiples of 15 and Q is the product of the first 50 multiples of 2520. Find the number of consecutive zeroes at the end of P2/Q × 101767

[2015]

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Try yourself:The number of factors of the square of a natural number is 105. The number of factors of the cube of the same number is ‘F’. Find the maximum possible value of ‘F’.

[2013]

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Try yourself:‘ab’ is a two-digit prime number such that one of its digits is 3. If the absolute difference between the digits of the number is nota factor of 2, then how many values can ‘ab’ assume?

[2013]

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Try yourself:If E = 3 + 8 + 15 + 24 + … + 195, then what is the sum of the prime factors of E?

[2013]

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Try yourself:The number 44 is written as a product of 5 distinct integers. If ‘n’ is the sum of these five integers then what is the sum of all the possible values of n?

[2012]

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Try yourself:All the two-digit natural numbers whose unit digit is greater than their ten’s digit are selected. If all these numbers are written one after the other in a series, how many digits are there in the resulting number?

[2012]

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Try yourself:A positive integer is equal to the square of the number of factors it has. How many such integers are there?

[2011]

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Try yourself:If ‘a’ is one of the roots of x^{5} – 1 = 0 and a ≠ 1, then what is the value of a^{15} + a^{16 }+ a^{17} +.......a^{50}?

[2010]

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