Basic Mathematics and Logarithm questions
509 published questions with worked solutions.
- If _ 10 2 _210+ _ 10 (10^x)=2, then what is the value of x?
- For x R , the number of real roots of the equation 3x^2 - 4|x^2 - 1| + x - 1 = 0 is _____.
- The product of all positive real values of x satisfying the equation x^ (16( _5 x)^3 - 68 _5 x ) = 5^ -16 is _____.
- Let a = 3 2 and b = 1 5^ 1/6 6 . If x, y R are such that 3x + 2y = _a(18)^ 5 4 and 2x - y = _b ( 1080 ), then 4x + 5y is equal to...
- Let f(x) = 2 + |x| − |x − 1| + |x + 1|, x R. Consider (S1) : f'(-3/2) + f'(-1/2) + f'(1/2) + f'(3/2) = 2 (S2) : _ -2 ^ 2 f(x)dx =...
- The remainder when (2021)^ 2022 + (2022)^ 2021 is divided by 7 is
- If the sum of all the roots of the equation e^ 2x − 11e^ x - 45e^ -x + 81/2 = 0 is log_e p, the p is equal to _____.
- Let S = x [−6, 3] − −2, 2 : (|x + 3| − 1)/(|x| − 2) 0 and T = x Z : x^ 2 − 7|x| + 9 0 . Then the number of elements in S T is
- The remainder when 7^ 2022 + 3^ 2022 is divided by 5 is:
- What are the roots of the equation |x^2-x-6|=x+2?
- If f(x)= _ 10 (1+x), then what is 4f(4)+5f(1)- _ 10 2 equal to?
- The sum of all the roots of the equation |x^2-8x+15|-2x+7=0 is-
- 25^ 190 -19^ 190 -8^ 190 +2^ 190 is divisible by
- Let the number (22)^ 2022 +(2022)^ 22 leave the remainder when divided by 3 and when divided by 7. Then ( ^2+ ^2) is equal to -
- Let a, b, c be the three distinct positive real numbers such that (2a)^ _ea =(bc)^ _eb and b^ _e2 =a^ _ec . Then 6a + 5bc is...
- The number of integral solutions x of _ (x+ 7 2 ) ( x-7 2x-3 )^2 0 is :
- The remainder, when 7^ 103 is divided by 17, is ________
- Fractional part of the number 4^ 2022 15 is equal to
- The set of all a for which the equation x|x – 1| + |x + 2| + a = 0 has exactly one real root, is
- The number of real roots of the equation x|x|-5|x+2|+6=0, is-
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