IIT-JEE 2006 | JEE Advanced Year Wise Previous Years Questions

IIT-JEE 2006

MCQ (Single Correct Answer)

-0

$$ \text { Normals are drawn at points } \mathrm{P}, \mathrm{Q} \text { and } \mathrm{R} \text { lying on the parabola } y^2=4 x \text { which intersect at }(3,0) \text {. Then } $$

(i)	Area of $\triangle \mathrm{PQR}$	(A)	2
(ii)	Radius of circumcircle of $\triangle \mathrm{PQR}$	(B)	5/2
(iii)	Centroid of $\triangle \mathrm{PQR}$	(C)	(5/2,0)
(iv)	Circumcentre of $\triangle \mathrm{PQR}$	(D)	(2/3,0)

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

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

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

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

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 2006

MCQ (Single Correct Answer)

-0

(i)	Two rays in the first quadrant $x+y=\|a\|$ and $a x-y=1$ Intersects each other in the interval $a \in\left(a_0, \infty\right)$, the value of $a_0$ is	(A)	2
(ii)	Point $(\alpha, \beta, \gamma)$ lies on the plane $x+y+z=2$. Let $\vec{a}=\alpha \hat{i}+\beta \hat{j}+\gamma \hat{k}, \hat{k} \times(\hat{k} \times \vec{a})=0$, then $\gamma=$	(B)	4/3
(iii)	$$ \left\|\int_0^1\left(1-y^2\right) d y\right\|+\left\|\int_1^0\left(y^2-1\right) d y\right\| $$	(C)	$$ \left\|\int_0^1 \sqrt{1-x} d x\right\|+\left\|\int_1^0 \sqrt{1+x} d x\right\| $$
(iv)	If $\sin A \sin B \sin C+\cos A \cos B=1$, then the value of $\sin C=$	(D)	1

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

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

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

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

IIT-JEE 2006

MCQ (Single Correct Answer)

-0.75

A student performs an experiment for determination of $g\left(=\frac{4 \pi^2 l}{\mathrm{~T}^2}\right), l=1 m$, and he commits an error of $\Delta l$. For T , he takes the time of $n$ oscillations with the stop watch of least count $\Delta \mathrm{T}$ and he commits a human error of 0.1 s . For which of the following data, the measurement of $g$ will be most accurate?

$$\begin{array}{l}\triangle\mathcal l\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\triangle\mathrm T\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\mathrm n\\5\;\mathrm{mm}\;\;\;\;\;\;\;\;\;\;\;\;0.2\;\sec\;\;\;\;\;\;\;\;\;\;\;\;10\end{array}$$

$$\begin{array}{l}\triangle\mathcal l\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\triangle\mathrm T\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\mathrm n\\1\;\mathrm{mm}\;\;\;\;\;\;\;\;\;\;\;\;0.1\;\sec\;\;\;\;\;\;\;\;\;\;\;\;50\end{array}$$

PREVIOUS NEXT

JEE Advanced Papers

All year-wise previous year question papers

2026