A relation S in the set of real numbers is defined as xSy ⇒  x – y+ √3 is an irrational number, then relation S is
(a) reflexive
(b) reflexive and symmetric
(c) transitive
(d) symmetric and transitive

Set A has 3 elements and the set B has 4 elements. Then the number of injective functions that can be defined from set A to set B is
(a) 144
(b) 12
(c) 24
(d) 64

Given a function lf as f(x) = 5x + 4, x ∈ R. If g : R → R is inverse of function ‘f then
(a) g(x) = 4x + 5
(b) g(x) = 54𝑥−5
(c) g(x) = 𝑥−45
(d) g(x) = 5x – 4

If A = [a_ij] is a 2 × 3 matrix, such that  a_ij= (−𝑖+2𝑗)25.then a₂₃ is

Total number of possible matrices of order 2 × 3 with each entry 1 or 0 is
(a) 6
(b) 36
(c) 32
(d) 64

If |𝑎⃗| = 4 and -3 ≤ λ ≤ 2 then the range of |𝜆𝑎⃗| is
(a) [0, 8]
(b) [-12, 8]
(c) [0, 12]
(d) [8, 12]

Find the probability of throwing atmost 2 sixes in 6 throws of a single die.
(a) 3518(56)3
(b) 3518(56)4
(c) 1829(23)4
(d) 1829(23)3
 

A die is thrown again and again until three sixes are obtained. Find the probability of obtaining third six in the sixth throw of the die.
(a) 62523329
(b) 62125329
(c) 62523328
(d) 62023328
 

Ten eggs are drawn successively with replacement from a lot containing 10% defective eggs. Then, the probability that there is atleast one defective egg is
(a) 1−7101010
(b) 1+7101010
(c) 1+9101010
(d) 1−9101010
 

The probability of a man hitting a target is 14. How many times must he fire so that the probability of his hitting the target at least once is greater than 23?
(a) 4
(b) 3
(c) 2
(d) 1

A die is thrown and card is selected a random from a deck of 52 playing cards. The probability of gettingan even number on the die and a spade card is
(a) 1/2
(b) 1/4
(c) 1/8
(d) 3/4