1.

Average of 5 integers is 38 and all the numbers are between 0 and 50 (both inclusive). In these 5 numbers, a is the minimum. If exactly 3 of them are more than 32, find the difference between the minimum and the maximum value of a.

2.

Let \(a, b, m\) and \(n\) be natural numbers such that \(a >1\) and \(b >1\) . If \(a^m+b^n = 144^{145}\) , then the largest possible value of \(n − m\) is

• 579
• 289
• 580
• 290

3.

Suppose \(f(x,y)\) is a real-valued function such that \(f(3x+2y,2x-5y)=19x\), for all real numbers \(x\) and \(y\) . The value of x for which \(f(x,2x) = 27\) , is

• 3
• 4
• 42
• None of Above

4.

A container has 40 liters of milk. Then, 4 liters are removed from the container and replaced with 4 liters of water. This process of replacing 4 liters of the liquid in the container with an equal volume of water is continued repeatedly. The smallest number of times of doing this process, after which the volume of milk in the container becomes less than that of water, is

• 5
• 7
• 4
• None of Above

5.

For some positive real number \(x\) , if  \(log_{\sqrt 3}(x)+\frac{log_x(25)}{log_x(0.008)}=\frac{16}{3}\), then the value of \(log_3(3x^2)\) is 

• 4
• 6
• 7
• 9

6.

If \(x\) and \(y\) are positive real numbers such that \(log_x(x^2+12)=4\) and \(3\;log_yx=1\),then \(x+y\) equals

• 11
• 20
• 10
• 68