A flower shop was selling artificial and natural flowers. The shop has 4 varieties of each. All the 4 varieties of natural flower cost 250 collectively while the 4 types of artificial cost 70 collectively. The cheapest artificial flower costs 10 rupees. The combined price of 3 of the natural flowers is twice the cost of the rest of the artificial flower. What is the cost of the costliest natural flower? 

Find the value of x if

${\left(\frac{21}{10}\right)}^x=3$

Marvel is celebrating the success of Endgame and decided to throw a party. All the persons involved in the making were invited. People came in car and bikes. In total, there were 100 vehicles in the parking. A guard counted that there were 280 wheels in total. How many bikes were there?

If HCF of $x^3-27$ and $x^3+4x^2+12x+k$ is quadratic polynomial then, the value of k, is

In a university, $\frac{4}{5}$of the students are studying engineering and $\frac{1}{8}$th of them are mechanical engineers. If 350 students in the university are non-mechanical engineers, how many students are studying in the university?

If, f(y) = y² + 12(y) + 36, then how many real values of y exists for f(y) $\le$0?

A barrel contains a mixture of wine and water in the ratio 3:1. How much fraction of the mixture must be drawn off and substituted by water so that the ratio of wine and water in the resultant mixture in the barrel becomes 1:1?

$\alpha$ and $\beta$ are roots of equation x2 – 5x + 6. Which of the following equation will have roots as $\frac{1}{\alpha}$ and $\frac{1}{\beta}$. 

If roots of equation k2 – 5K + 1 = 0 are (a) and (b) then find the equation whose roots are (2a + 1) and (2b + 1). 

Find the value of y if ${\left(\frac{144}{100}\right)}^y=4$.

Find a and b if product of and sum of roots of equation 2x2 + ax + b = 0 are 5 and 6 respectively. 

A two-digit number, N was taken. Atul was asked to multiply the number with $\frac{3}{4}$and subtract 9 from it. He mistakenly reversed the original number, multiplied it by $\frac{4}{3}$ and added 9 to it and got the same result. What was the original number if the sum of the digits is 9?

S1 is a series of six consecutive numbers divisible by 3. Average of S1 is 16.5. S2 is a series of six consecutive odd numbers starting with second highest term in S1. Find the difference between fourth term of S2 and the highest term of S1.

Find the value of log₁₀(100000K) if log₁₀(10K) = 2.7532.

If $\left(\left(\right. \frac{a}{b} \left.\right)\right)^{2 x - 3} = \left(\left(\right. \frac{b}{a} \left.\right)\right)^{x - 9}$, then x is equal to