Pre scholarship Mock Test

Which one of the following is an eigen vector of the matrix:-

A =

Find the magnitude of the gradient for given scalar field at point (3, 5)

Given the following curve: ,The length of the arc of the curve from x = 0 to x = π/4________.

Consider the following equations:

3x – y – z = 2 
3x + y – z = –2
12x + 3y – 4z = –6


The above system of equations will be______.

In how many ways a cricketer can make a century(exactly 100 runs) with fours and sixes only?

Two pipes A and B can fill a cistern in 6.25 hours and 12.5 hours, respectively. The pipes are opened simultaneously and it is found that due to a leakage in the bottom, it took 1 hour 50 minutes more to fill the cistern. When the cistern is full, in how much time will the leak empty the cistern (in hours) ?

Aman and Mukund travel a distance of 60 km. The sum of their speeds is 75 km/h and the total time taken by both to travel the distance is 3 hours 36 minutes. The difference between their speeds is:

x, 17, 3x – y² – 2 and 3x + y² – 30, are four consecutive terms of an increasing arithmetic sequence.
The sum of the four numbers is divisible by :

A, B, C and D can finish a task in 10, 12, 15 and 18 days respectively. They can either choose to work or remain absent on a particular day. If 50 percent of the total work gets completed after 3 days, then, which of the following options is possible?

In a box of mangoes, 80% of them are high-quality while 20% are low-quality. If 10 low-quality mangoes are removed, then 96% of the rest will be high-quality. What is the total number of mangoes from the start?