IIT-JEE 2006 | Application of Integration Question 34 | Mathematics

IIT-JEE 2006

MCQ (Single Correct Answer)

-0

$$ \text { Match the following : } $$

(i)	$$ \int_0^{\pi / 2}(\sin x)^{\cos x}\left(\cos x \cot x-\log \left(\sin ^x\right)^{\sin } x\right) \mathrm{d} x $$	(A)	1
(ii)	$$ \text { Area bounded by }-4 y^2=x \text { and } x-1=-5 y^2 $$	(B)	0
(iii)	Cosine of the angle of intersection of $y=3^{x-1} \log x$ and $y=x^{x-1}$ is	(C)	6 In 2
(iv)	$$ \frac{d y}{d x}=\frac{2}{(x+y)} ; y\left(-\frac{2}{3}\right)=0 \text {, then value of constant }(\mathrm{k})= $$	(D)	4/3

$$ \begin{aligned} & \text { (i)-(A); (ii)-(D); (iii)-(B); }\text { (iv)-(D) } \end{aligned} $$

$$ \begin{aligned} & \text { (i)-(A); (ii)-(C); (iii)-(B); }\text { (iv)-(D) } \end{aligned} $$

$$ \begin{aligned} & \text { (i)-(A); (ii)-(D); (iii)-(A); }\text { (iv)-(D) } \end{aligned} $$

$$ \begin{aligned} & \text { (i)-(A); (ii)-(B); (iii)-(C); }\text { (iv)-(D) } \end{aligned} $$

IIT-JEE 2005 Screening

MCQ (Single Correct Answer)

-0.75

The area bounded by the parabola $$y = {\left( {x + 1} \right)^2}$$ and
$$y = {\left( {x - 1} \right)^2}$$ and the line $$y=1/4$$ is

$$4$$ sq. units

$$1/6$$ sq. units

$$4/3$$ sq. units

$$1/3$$ sq. units

IIT-JEE 2005 Mains

MCQ (Single Correct Answer)

-1

If length of tangent at any point on the curve $$y = f(x)$$ intercepted between the point and the X-axis is of length 1. Find the equation of the curve.

$$\sqrt{1-y^{2}}-\frac{1}{2} \log \left|\frac{1+\sqrt{1-y^{2}}}{1-\sqrt{1-y^{2}}}\right|= \pm x+c$$

$$\sqrt{1-y^{2}}- \log \left|\frac{1+\sqrt{1-y^{2}}}{1-\sqrt{1-y^{2}}}\right|= \pm x+c$$

$$\sqrt{1-y^{2}}+\frac{1}{2} \log \left|\frac{1+\sqrt{1-y^{2}}}{1-\sqrt{1-y^{2}}}\right|= \pm x+c$$

$$\sqrt{1-y^{2}}-\frac{1}{2} \log \left|\frac{1+\sqrt{1-y^{2}}}{1-\sqrt{1-y^{2}}}\right|= \pm 5x+c$$

IIT-JEE 2005 Mains

MCQ (Single Correct Answer)

-1

Find the area bounded by the curves $$x^{2}=y, x^{2}=-y$$ and $$y^{2}=4 x-3$$.

$$\frac{1}{3}$$

$$\frac{1}{5}$$

$$\frac{2}{3}$$

$$\frac{1}{7}$$

PREVIOUS NEXT

JEE Advanced Subjects

Browse all chapters by subject