IIT-JEE 2008 Paper 1 Offline | Definite Integration Question 48 | Mathematics

1

IIT-JEE 2008 Paper 1 Offline

MCQ (Single Correct Answer)

+3

-1

Consider the functions defined implicitly by the equation $$y^3-3y+x=0$$ on various intervals in the real line. If $$x\in(-\infty,-2)\cup(2,\infty)$$, the equation implicitly defines a unique real valued differentiable function $$y=f(x)$$. If $$x\in(-2,2)$$, the equation implicitly defines a unique real valued differentiable function $$y=g(x)$$ satisfying $$g(0)=0$$

$$\int\limits_{ - 1}^1 {g'\left( x \right)dx = } $$

A

$$2g(-1)$$

B

$$0$$

C

$$-2g(1)$$

D

$$2g(1)$$

2

IIT-JEE 2007 Paper 1 Offline

MCQ (Single Correct Answer)

+3

-1

$$\mathop {\lim }\limits_{x \to {\pi \over 4}} {{\int\limits_2^{{{\sec }^2}x} {f(t)\,dt} } \over {{x^2} - {{{\pi ^2}} \over {16}}}}$$ equal

A

$${8 \over \pi }f(2)$$

B

$${2 \over \pi }f(2)$$

C

$${2 \over \pi }f\left( {{1 \over 2}} \right)$$

D

$$4f(2)$$

3

IIT-JEE 2007 Paper 1 Offline

MCQ (Single Correct Answer)

+3

-1

Match the integrals in Column I with the values in Column II.

	Column I		Column II
(A)	$$\int\limits_{ - 1}^1 {{{dx} \over {1 + {x^2}}}} $$	(P)	$${1 \over 2}\log \left( {{2 \over 3}} \right)$$
(B)	$$\int\limits_0^1 {{{dx} \over {\sqrt {1 + {x^2}} }}} $$	(Q)	$$2\log \left( {{2 \over 3}} \right)$$
(C)	$$\int\limits_2^3 {{{dx} \over {1 + {x^2}}}} $$	(R)	$${\pi \over 3}$$
(D)	$$\int\limits_1^2 {{{dx} \over {x\sqrt {{x^2} - 1} }}} $$	(S)	$${\pi \over 2}$$

A

A - s, B - s, C - r, D - p

B

A - s, B - q, C - p, D - r

C

A - s, B - s, C - p, D - r

D

A - s, B - q, C - s, D - r

4

IIT-JEE 2005 Screening

MCQ (Single Correct Answer)

+3

-0.75

$$\int\limits_{ - 2}^0 {\left\{ {{x^3} + 3{x^2} + 3x + 3 + \left( {x + 1} \right)\cos \left( {x + 1} \right)} \right\}\,\,dx} $$ is equal to

A

$$-4$$

B

$$0$$

C

$$4$$

D

$$6$$

JEE Advanced Subjects