Pre Scholarship Mock Test

For the three equations:

–2x + y + z = a

x – 2y + z = b

x + y – 2z = c

1. Unless a + b + c = 0, no solution exists.

2. If a + b + c ≠ 0, unique solution exists

3. If a + b + c ≠ 0, solution exists

4. If a + b + c = 0, infinite solutions exists.

Which of the given statements aren’t correct?

if

And f(x) is differentiable at x = c then the value of _________

Evaluate

Suppose there are two biased coins. The first coin when tossed, gives head with probability 4/9 while the second coin gives head with probability 2/7. One of the two coins is picked up at random with equal probability and tossed. What is the probability of obtaining heads on the tossed coin?

Consider Pankaj can read a page in 2 mins, Shivangi in 3 min and Aditya in 4 min. If they divide an article of 78 pages into 3 parts, such that all three of them spend an equal amount of time on the article, then the pages Shivangi should read is _________.

In a 100-meter race, Ravi beats Sahil by 6 seconds whereas in the same race Sahil beats Tony by 3 seconds. If Ravi beats Tony by 25 meters, then the time taken by Ravi to complete the race is ________ seconds.

If , where a₁, a₂, … a_n are in AP and all the values are non-negative. Then the value of M is ________.

If , then

Nitu is three time older than Pankaj, Niraj is half the age of Vidya, Pankaj is older than Niraj. Then choose the correct option:

The sum of the digits of the least number which when divided by 36, 72, 80 and 88 leaves the remainders 16, 52, 60 and 68, respectively, is: