IIT-JEE 2011 Paper 2 Offline | Functions Question 23 | Mathematics

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 10 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 :

IIT-JEE 2010 Paper 2 Offline

MCQ (Single Correct Answer)

-1

Consider the polynomial
$$f\left( x \right) = 1 + 2x + 3{x^2} + 4{x^3}.$$
Let $$s$$ be the sum of all distinct real roots of $$f(x)$$ and let $$t = \left| s \right|.$$

The real numbers lies in the interval

$$\left( { - {1 \over 4},0} \right)$$

$$\left( { - 11, - {3 \over 4}} \right)$$

$$\left( { - {3 \over 4}, - {1 \over 2}} \right)$$

$$\left( {0,{1 \over 4}} \right)$$

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