Basic Mathematics and Logarithm questions
509 published questions with worked solutions.
- The number of real solutions of the equation x|x + 5| + 2|x + 7| − 2 = 0 is _____.
- Let S be the set of all real roots of the equation, 3^x(3^x-1)+2=|3^x-1|+|3^x-2|. Then S :
- The sum of all the solutions of the equation (8)²ˣ − 16·(8)ˣ + 48 = 0 is:
- The number of distinct real roots of the equation |x + 1||x + 3| − 4|x + 2| + 5 = 0, is ________ .
- If n is a positive integer, then n^3 + 2n is divisible by
- The product of three consecutive natural numbers is divisible by
- The number a^n - b^n (a, b are distinct rational numbers and n N) is always divisible by
- For each n N, 10^ 2n-1 + 1 is divisible by
- For all n N, 2 4^ 2n+1 + 3^ 3n+1 is divisible by
- If x^ 2n-1 + y^ 2n-1 is divisible by x + y, if n is
- x(x^ n-1 - n ^ n-1 ) + ^n(n-1) is divisible by (x - )^2 for
- The remainder when 5^ 99 is divided by 13, is
- If n N, then 3^ 2n + 7 is divisible by
- The sum of the cubes of three consecutive natural numbers is divisible by
- If n N, then n(n^2 - 1) is divisible by
- If n is an odd positive integer, then a^n + b^n is divisible by
- If x^n - 1 is divisible by x - k, then the least positive integral value of k is
- If 10^n + 3 4^ n+2 + is exactly divisible by 9 for all n N, then the least positive integral value of is
- The set of all real x satisfying the inequality
- If r is a real number such that |r| < 1 and if a = 5(1 - r), then
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