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

33% OFF

ExamGOAL

MOST RELEVANT

JEE Main Ultimate Online Test Series - 2027

458 Tests

10,140 Questions

English & Hindi (हिन्दी) Languages

331 Topic Tests87 Chapter Tests30 Full Tests10 Part Tests

Most Relevant Questions for JEE Main 2027
JEE Main Predictive Percentile and Rank
Best Solution to Every Question
Very Detailed Analysis

₹999 ₹1,499

Save ₹500

Access valid till 31 May 2027

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

In a screw gauge, the zero of main scale coincides with the fifth division of circular scale in figure (i).The circular division of screw gauge is 50. It moves 0.5 mm on main scale in one rotation.The diameter of the ball in figure (ii) is

IIT-JEE 2006 Physics - Units & Measurements Question 54 English

2.25 mm

2.20 mm

1.20 mm

1.25 mm

PREVIOUS NEXT

JEE Advanced Papers

All year-wise previous year question papers

2026