Mathematics – Class 12 – Assertion & Reason Type Questions – by O P Gupta

, By O.P. GUPTA
Indira Award Winner
M.+919650350480

In the following questions, a statement of Assertion (A) is followed by a statement of Reason (R).
Choose the correct answer out of the following choices.
(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true and R is not the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true.



Unit 1 (Relations & Functions)
Relations & Functions, Inverse Trig. Functions

Q01. Assertion (A) : The relation R  {(a, b) : a  b 2} on the set R of real nos. is not reflexive.
Reason (R) : A relation on a set A is reflexive if (a, a)  R  a  A .
Q07. Assertion (A) : Let f : R  R defined as f (x)   x  , here  .  represents the greatest integer
function. Then f is not one-one.
Reason (R) : A function is one-one if f ()  f () implies    .
Q11. Assertion (A) : Number of all onto functions from the set {1, 2, 3, 4} to itself is 24.
Reason (R) : Onto functions from the set {1, 2, 3, …, n} to itself is simply a permutation on n
symbols namely 1, 2, 3, …, n.
Q27. Assertion (A) : Inverse of sin x does not exist in x  R .
Reason (R) : All trigonometric functions are many-one in their respective domain.
Q30. Assertion (A) : A function f shown below by the arrow diagram, is one-one.




Reason (R) : A function f : A  B is one-one if f (α)  f (β) implies α  β for all α, β  A .
Q38. X  {0, 2, 4, 6, 8}.
P is a relation on X defined by P  {(0, 2), (4, 2), (4, 6), (8, 6), (2, 4), (0, 4)}.
Assertion (A) : The relation P on set X is a transitive relation.
Reason (R) : The relation P has a subset of the form {(a , b), (b, c), (a , c)}, where a , b, c  X.


492 MATHEMATICIA By O.P. GUPTA : A New Approach in Mathematics