JEE Main 2015 (Offline) | Definite Integrals and Applications of Integrals Question 265 | Mathematics

JEE Main 2015 (Offline)

MCQ (Single Correct Answer)

-1

The integral
$$\int\limits_2^4 {{{\log \,{x^2}} \over {\log {x^2} + \log \left( {36 - 12x + {x^2}} \right)}}dx} $$ is equal to :

$$1$$

$$6$$

$$2$$

$$4$$

JEE Main 2015 (Offline)

MCQ (Single Correct Answer)

-1

The area (in sq. units) of the region described by
$$\left\{ {\left( {x,y} \right):{y^2} \le 2x} \right.$$ and $$\left. {y \ge 4x - 1} \right\}$$ is

$${{15} \over {64}}$$

$${{9} \over {32}}$$

$${{7} \over {32}}$$

$${{5} \over {64}}$$

JEE Main 2014 (Offline)

MCQ (Single Correct Answer)

-1

The area of the region described by
$$A = \left\{ {\left( {x,y} \right):{x^2} + {y^2} \le 1} \right.$$ and $$\left. {{y^2} \le 1 - x} \right\}$$ is :

$${\pi \over 2} - {2 \over 3}$$

$${\pi \over 2} + {2 \over 3}$$

$${\pi \over 2} + {4 \over 3}$$

$${\pi \over 2} - {4 \over 3}$$

JEE Main 2014 (Offline)

MCQ (Single Correct Answer)

-1

The integral $$\int\limits_0^\pi {\sqrt {1 + 4{{\sin }^2}{x \over 2} - 4\sin {x \over 2}{\mkern 1mu} } } dx$$ equals:

$$4\sqrt 3 - 4$$

$$4\sqrt 3 - 4 - {\pi \over 3}$$

$$\pi - 4$$

$${{2\pi } \over 3} - 4 - 4\sqrt 3 $$

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