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

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?

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

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

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

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