1
JEE Advanced 2014 Paper 2 Offline
+3
-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

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

A
P - 3, Q - 1, R - 4, S - 2
B
P - 1, Q - 3, R - 4, S - 2
C
P - 3, Q - 1, R - 2, S - 4
D
P - 1, Q - 3, R - 2, S - 4
2
IIT-JEE 2012 Paper 1 Offline
+3
-1

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

A
one-one and onto.
B
onto but not one-one.
C
one-one but not onto.
D
neither one-one nor onto.
3
IIT-JEE 2011 Paper 2 Offline
+3
-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

A
$$\pm \sqrt {n\pi } ,\,n \in \{ 0,1,2,....\}$$
B
$$\pm \sqrt {n\pi } ,\,n \in \{ 1,2,....\}$$
C
$${\pi \over 2} + 2n\pi ,\,n \in \{ ....., - 2, - 1,0,1,2,....\}$$
D
$$2n\pi ,n \in \{ ....., - 2, - 1,0,1,2,....\}$$
4
IIT-JEE 2011 Paper 2 Offline
+3
-1

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

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