Which entrance exam we have to clear for University Of Delhi?

Let be defined as Then, is equal to ____________.
Option: 1 0
Option: 2 1
Option: 3 2
Option: 4 3

Let be a continuous function such that for all If and then the value of is equal to __________.
Option: 1 4
Option: 2 8
Option: 3 12
Option: 4 16

Consider an arithmetic series and a geometric series having four initial terms from the set {11, 8, 21, 16, 26, 32, 4}. If the last terms of these series are the maximum possible four digit numbers, then the number of common terms in these two series is equal to _____________.
Option: 1 1
Option: 2 3
Option: 3 5
Option: 4 7

The total number of matrices A having entries from the set such that the sum of all the diagonal entries of is 9 , is equal to ___________.
Option: 1 0
Option: 2 8
Option: 3 88
Option: 4 766

Let ABCD be a square of side of unit length. Let a circle centered at A with unit radius is drawn. Another circle which touches   and the lines AD and AB are tangent to it, is also drawn. Let a tangent line from the point C to the circle   meet the side AB at E. If the length of EB is where are integers, then is equal to _______________.
Option: 1 0
Option: 2 1
Option: 3 2
Option: 4 3