Pre scholarship Mock Test

In the given figure, PQRSTV is a regular hexagon with each side of length 5 cm.
A circle is drawn with its centre at V such that it passes through P. What is the area (in cm²) of the shaded region? (The diagram is representative)

Let a = 30!, b = 50!, and c =100! . Consider the following numbers:

log_ac      log_Ca,       log_ba,       log_ab

Which one of the following inequalities is CORRECT?

If x satisfies the equation = 256, then x is equal to ________ .

A and B alternatively cut a pack of cards and the pack is shuffled after each cut. If A starts the game and game is continued until one cuts diamond, then what is the chance that ‘A’ wins at his second cut

The Eigen value of 2 × 2 matrix A are 3 and 4. Determine The A^–1

If Z = log _e (x³ + y³ – x²y – xy²), then

The value of the integral  is

The function   at x = 4 attains_____.