JEE Advanced 2017 Paper 2 Offline | Functions Question 11 | Mathematics

JEE Advanced 2017 Paper 2 Offline

MCQ (Single Correct Answer)

-1

Let S = {1, 2, 3, .........., 9}. For k = 1, 2, .........., 5, let N_k be the number of subsets of S, each containing five elements out of which exactly k are odd. Then N₁ + N₂ + N₃ + N₄ + N₅ =

210

252

126

125

JEE Advanced 2014 Paper 2 Offline

MCQ (Single Correct Answer)

-1

Let f₁ : R $$ \to $$ R, f₂ : [0, $$\infty $$) $$ \to $$ R, f₃ : R $$ \to $$ R, and f₄ : R $$ \to $$ [0, $$\infty $$) be defined by

$${f_1}\left( x \right) = \left\{ {\matrix{ {\left| x \right|} & {if\,x < 0,} \cr {{e^x}} & {if\,x \ge 0;} \cr } } \right.$$

f₂(x) = x² ;

$${f_3}\left( x \right) = \left\{ {\matrix{ {\sin x} & {if\,x < 0,} \cr x & {if\,x \ge 0;} \cr } } \right.$$

and

$${f_4}\left( x \right) = \left\{ {\matrix{ {{f_2}\left( {{f_1}\left( x \right)} \right)} & {if\,x < 0,} \cr {{f_2}\left( {{f_1}\left( x \right)} \right) - 1} & {if\,x \ge 0;} \cr } } \right.$$

JEE Advanced 2014 Paper 2 Offline Mathematics - Functions Question 9 English

P - 3, Q - 1, R - 4, S - 2

P - 1, Q - 3, R - 4, S - 2

P - 3, Q - 1, R - 2, S - 4

P - 1, Q - 3, R - 2, S - 4

IIT-JEE 2012 Paper 1 Offline

MCQ (Single Correct Answer)

-1

The function $$f:[0,3] \to [1,29]$$, defined by $$f(x) = 2{x^3} - 15{x^2} + 36x + 1$$, is

one-one and onto.

onto but not one-one.

one-one but not onto.

neither one-one nor onto.

IIT-JEE 2011 Paper 2 Offline

MCQ (Single Correct Answer)

-1

Let f(x) = x² and g(x) = sin x for all x $$\in$$ R. Then the set of all x satisfying $$(f \circ g \circ g \circ f)(x) = (g \circ g \circ f)(x)$$, where $$(f \circ g)(x) = f(g(x))$$, is

$$ \pm \sqrt {n\pi } ,\,n \in \{ 0,1,2,....\} $$

$$ \pm \sqrt {n\pi } ,\,n \in \{ 1,2,....\} $$

$${\pi \over 2} + 2n\pi ,\,n \in \{ ....., - 2, - 1,0,1,2,....\} $$

$$2n\pi ,n \in \{ ....., - 2, - 1,0,1,2,....\} $$

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