IIT-JEE 2011 Paper 1 Offline | JEE Advanced Year Wise Previous Years Questions

IIT-JEE 2011 Paper 1 Offline

Numerical

-0

Let $$f\left( \theta \right) = \sin \left( {{{\tan }^{ - 1}}\left( {{{\sin \theta } \over {\sqrt {\cos 2\theta } }}} \right)} \right),$$ where $$ - {\pi \over 4} < \theta < {\pi \over 4}.$$

Then the value of $${d \over {d\left( {\tan \theta } \right)}}\left( {f\left( \theta \right)} \right)$$ is

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IIT-JEE 2011 Paper 1 Offline

MCQ (Single Correct Answer)

-1

The value of $$\,\int\limits_{\sqrt {\ell n2} }^{\sqrt {\ell n3} } {{{x\sin {x^2}} \over {\sin {x^2} + \sin \left( {\ell n6 - {x^2}} \right)}}\,dx} $$ is

$${1 \over 4}\,\ell n{3 \over 2}$$

$$\,{1 \over 2}\,\ell n{3 \over 2}$$

$$\ell n{3 \over 2}$$

$$\,\,{1 \over 6}\,\ell n{3 \over 2}$$

IIT-JEE 2011 Paper 1 Offline

MCQ (Single Correct Answer)

-1

Let the straight line $$x=b$$ divide the area enclosed by
$$y = {\left( {1 - x} \right)^2},y = 0,$$ and $$x=0$$ into two parts $${R_1}\left( {0 \le x \le b} \right)$$ and
$${R_2}\left( {b \le x \le 1} \right)$$ such that $${R_1} - {R_2} = {1 \over 4}.$$ Then $$b$$ equals

$${3 \over 4}$$

$${ 1\over 2}$$

$${1 \over 3}$$

$${1 \over 4}$$

IIT-JEE 2011 Paper 1 Offline

MCQ (Single Correct Answer)

-1

Let $${U_1}$$ and $${U_2}$$ be two urns such that $${U_1}$$ contains $$3$$ white and $$2$$ red balls, and $${U_2}$$ contains only $$1$$ white ball. A fair coin is tossed. If head appears then $$1$$ ball is drawn at random from $${U_1}$$ and put into $${U_2}$$. However, if tail appears then $$2$$ balls are drawn at random from $${U_1}$$ and put into $${U_2}$$. Now $$1$$ ball is drawn at random from $${U_2}$$ being white is

The probability of the drawn ball from $${U_2}$$ being white is

$${{13} \over {30}}$$

$${{23} \over {30}}$$

$${{19} \over {30}}$$

$${{11} \over {30}}$$

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