IIT-JEE 2012 Paper 1 Offline | Functions Question 19 | Mathematics

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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

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

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

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

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

IIT-JEE 2011 Paper 2 Offline

MCQ (Single Correct Answer)

-1

Match the statements given in Column I with the intervals/union of intervals given in Column II :

IIT-JEE 2011 Paper 2 Offline Mathematics - Functions Question 6 English

(A) $$\to$$ (S), (B) $$\to$$ (T), (C) $$\to$$ (P), (D) $$\to$$ (Q)

(A) $$\to$$ (S), (B) $$\to$$ (T), (C) $$\to$$ (R), (D) $$\to$$ (P)

(A) $$\to$$ (S), (B) $$\to$$ (T), (C) $$\to$$ (R), (D) $$\to$$ (R)

(A) $$\to$$ (P), (B) $$\to$$ (Q), (C) $$\to$$ (R), (D) $$\to$$ (R)

IIT-JEE 2010 Paper 2 Offline

MCQ (Single Correct Answer)

-1

Let $S=\{1,2,3,4\}$. The total number of unordered pairs of disjoint subsets of $S$ is equal to :

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