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

If, $\frac{-8p^2+36p-20}{p^2+16}-1>0$, then how many natural numbers for p are there that satisfies the above inequality.

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?

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 ${\log }_{10}(4x-8)=2$, find the value of x.

Sum of square of three consecutive positive odd numbers is 155. Find the sum of the numbers. 

4 Friends, Sansa, Arya, Jon and Tyrion have 700 rupees collectively. Sansa have 70 rupees more than Arya. Jon has 50 rupees less than Arya. Tyrion has 80 rupees more than the money Arya and Jon have combined. They all have only 10- and 20-rupees notes. If the amount in 20-rupee notes is less than the amount in 10 rupees notes by 220, how many 20-rupee notes are there in total?

In the first alloy, zinc and copper are in the ratio 1:2. In the second alloy the same element are in the ratio 2:3. If these two alloys be mixed to form a new alloy in which two elements are in the ratio 5:8, the ratio of these two alloys in the new alloy is.

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?

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

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

F(1) = 0 

F(2) = 1 

F(3) = 4 

F(4) = 9 

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

A mixture contains wine and water in the ratio 3: 2 and another mixture contains them in the ratio 4: 5. How many liters of the latter must be mixed with 3L of the former, so that the resulting mixture may contain equal quantities of the wine and water?

Find the value of m for which the sum of the square of the roots of the equation y² – (m – 3)y + (m – 4) = 0 is minimum?