In a beaker, there is 200 ml of pure acetic acid. 25% of the acid is replaced by water. This process is repeated two more times. In a reaction with baking soda only 50 ml of acetic acid is required . Find the amount of acetic acid-water solution should be drawn off to perform the chemical process.

Gopal decided to give some money to Salman and Vivek. The amount given to both of them was such that if Salman gave 25 rupees to Vivek, they both will have the same amount. If Vivek gave 50 rupees to Salman, then Salman will have 4 times of what Vivek would have. How much money do they have in total?

What is the area enclosed by the curves (x + y) = 5 and (x – y) = 5?

If f(x) = 9 – 5x², then determine the value of f(3 – t).

Find the value of x if

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

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

Ganesh went to the market to buy sugar and ghee for making sweets. He calculated if he buys 8 kg of sugar and 9 kg of ghee, it will cost him Rs.1540. Ongoing to the market, he realized that he has some unused ghee at home and decided to buy 5 kg more sugar and 4 kg less ghee as it will cost him only Rs.1155. What is the cost of 2 kg of sugar?

What is the smallest possible value of $x + \frac{8}{x}$, if (x) can have real values only? 

F(1) = 0 

F(2) = 1 

F(3) = 4 

F(4) = 9 

Find sum of F(1) + F(2) + F(3) + ……..F(27) 

The equation log_xy + log_x(1 + y) = 0 can be written as:

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

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?

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

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?

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?