JEE Main 2018 (Online) 15th April Evening Slot | Functions Question 140 | Mathematics

JEE Main 2018 (Online) 15th April Evening Slot

MCQ (Single Correct Answer)

-1

Let f : A $$ \to $$ B be a function defined as f(x) = $${{x - 1} \over {x - 2}},$$ Where A = R $$-$$ {2} and B = R $$-$$ {1}. Then f is :

invertible and $${f^{ - 1}}(y) = $$ $${{3y - 1} \over {y - 1}}$$

invertible and $${f^{ - 1}}\left( y \right) = {{2y - 1} \over {y - 1}}$$

invertible and $${f^{ - 1}}\left( y \right) = {{2y + 1} \over {y - 1}}$$

not invertible

JEE Main 2018 (Online) 15th April Morning Slot

MCQ (Single Correct Answer)

-1

Consider the following two binary relations on the set A = {a, b, c} :
R₁ = {(c, a), (b, b), (a, c), (c, c), (b, c), (a, a)} and
R₂ = {(a, b), (b, a), (c, c), (c, a), (a, a), (b, b), (a, c)}.
Then :

both R₁ and R₂ are not symmetric.

R₁ is not symmetric but it is transitive.

R₂ is symmetric but it is not transitive.

both R₁ and R₂ are transitive.

JEE Main 2017 (Online) 9th April Morning Slot

MCQ (Single Correct Answer)

-1

The function f : N $$ \to $$ N defined by f (x) = x $$-$$ 5 $$\left[ {{x \over 5}} \right],$$ Where N is the set of natural numbers and [x] denotes the greatest integer less than or equal to x, is :

one-one and onto

one-one but not onto.

onto but not one-one.

neither one-one nor onto.

JEE Main 2017 (Online) 8th April Morning Slot

MCQ (Single Correct Answer)

-1

Let f(x) = 2¹⁰.x + 1 and g(x)=3¹⁰.x $$-$$ 1. If (fog) (x) = x, then x is equal to :

$${{{3^{10}} - 1} \over {{3^{10}} - {2^{ - 10}}}}$$

$${{{2^{10}} - 1} \over {{2^{10}} - {3^{ - 10}}}}$$

$${{1 - {3^{ - 10}}} \over {{2^{10}} - {3^{ - 10}}}}$$

$${{1 - {2^{ - 10}}} \over {{3^{10}} - {2^{ - 10}}}}$$