List of top Mathematics Questions on Number Systems

The remainder when \(64^{{32}^{32}}\) is divided by 9 is.

25¹⁹⁰ - 19¹⁹⁰ - 8¹⁹⁰ + 2¹⁹⁰ is divisible by

Find the sum of following hexadecimal numbers (7CA)₁₆+ (4B2)₁₆ =?

Let  denote the (r + 2) digit number where the first and the last digits are 7 and the remaining r digits are 5. Consider the sum S = 77 + 757 + 7557 + …+ . If S = , where m and n are natural numbers less than 3000, then the value of m + n is ______.

If all the six digit numbers x₁ x₂ x₃ x₄ x₅ x₆ with \(0<x_1<x_2<x_3<x_4<x_5<x_6\) are arranged in the increasing order, then the sum of the digits in the 72^th number is _____________.

If \(m = 2\), \(n = 3\), then the value of \(12m^2n-3mn^2\) is:

The set of all positive integers less than 50 forming the equivalence class of 8 for modulo 11 is:

If x is the least positive integer satisfying 100 ≡ x(mod 6), then (2x+1) is equal to :

Process of indicating addition [3+2=5] at number system

Choose the correct answer from the options given below:

Two natural numbers are in the ratio 3:5 and their product is 2160. The smaller of the numbers is

Given below are two statements: One is labelled as Assertion (A) and the other is labelled as Reason (R):
Assertion (A): Sum of n terms of series 1²+3²+5²+... to n terms is \(\frac{n}{3}(4n^2-1)\).
Reasons (R): Sum of the squares of first a natural numbers 1², 2², 3²,....,n² is \(\frac{n(n+1)(2n+1)}6\).
In the light of the above Statements, choose the correct answer from the options given below:

Given below are two statements:
Statement I: For n ≥1, we have \(\frac{1}{1·2}+\frac{1}{2·3}+\frac{1}{3·4}+.....+\frac{1}{n(n+1)}=\frac{n^2}{n+1}\)
Statement II: (1+x)ⁿ ≥ (1+nx) for all natural number n, where x > -1.
In the light of the above Statements, choose the most appropriate answer from the options given below :

Given below are two statements:
Statement I: If (12P)₃ = (123)_p, then the value of p is 8.
Statement II: In 16-bit 2's complement representation, the decimal number -28 is 11111 111111100100.
In the light of the above Statements, choose the most appropriate answer from the options given below :

The lines 2x + y -1=0, ax+3y-3=0 and 3x+2y-2=0 are concurrent for

Find the sum of two consecutive numbers in which four times are first number is 12 more than the thrice of the second number

The sum of two digits no. is 10, on reversing the digits of a number the number is decrease by 36. Find the number.

The number of vectors of unit length perpendicular to vectors \(\vec{a}\) = (1,1,0) and \(\vec{b}\) = (0,1,1) is

For x = 3, find the value of \(x^5+x^4-x^3-x^2+x-1.\)

If a=130, b=133 and c=137, There the value of a³+b³+c³-3 abc is

A. If (12 P)₃ = (123)_p, then value of P is infeasible.
B. The simplified sum of product form of the Boolean expression is \((P+\vec{Q}+\vec{R}).(P+\vec{Q}+R). (P+Q+\vec{R}) \;is\; (P+\vec{Q}.\vec{R})\).
C. The minimum number of D flip-flops needed to design a mod(258) counter is 8.
Choose the correct answer from the options given below :

Given below are two statements :
Statement I: The number of different number each of 6 digits that can be formed by using all the digits 1, 2, 1, 0, 2, 2 is 50.
Statement II: These are 4536 possibilities of writing the four digit numbers which have all distinct digits.
In the light of the above statements, choose the correct answer from the options given below:

Let a, b, c be three distinct positive real numbers such that (2a)^log_ea = (bc)^log_eb and b^log_e2 = a^log_ec. Then 6a + 5bc is equal to _____.

Five digit numbers are formed using the digits 1, 2, 3, 5, 7 with repetitions and are written in descending order with serial number. For example, the number 77777 has serial number 1. Then the serial number of 35337 is _________

The number of distinct real roots of \(x^4 – 4x + 1 = 0\) is :