JEE Advanced 2010 Paper-1

JEE Advanced 2010 Paper-1 - Question 1

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The correct structure of ethylenedianlinetetraacetic acid (EDTA) is

A

B

C

D

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JEE Advanced 2010 Paper-1 - Question 2

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The ionization ísomer of $$[Cr(H_{2}O)_{4}Cl(NO_{2})]Cl$$ is

A

$$[Cr(H_{2}O)_{4}(O_{2}N)]Cl_{2}$$

B

$$[Cr(H_{2}O)_{4}Cl_{2}](NO_{2})$$

C

$$[Cr(H_{2}O)_{4}Cl(ONO)]Cl$$

D

$$[Cr(H_{2}O)_{4}Cl_{2}(NO_{2})]H_{2}O$$

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JEE Advanced 2010 Paper-1 - Question 3

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The synthesis of 3-octyne is achieved by adding a bromoalkane into a mixture of sodium amide and an alkyne. The bromoalkane and alkyne respectively are

A

$$BrCH_{2}CH_{2}CH_{2}CH_{2}CH_{3}$$ and $$CH_{3}CH_{2}C\equiv CH$$

B

$$BrCH_{2}CH_{2}CH_{3}$$ and $$CH_{3}CH_{2}CH_{2}C\equiv CH$$

C

$$BrCH_{2}CH_{2}CH_{2}CH_{2}CH_{3}$$ and $$CH_{3}C\equiv CH$$

D

$$BrCH_{2}CH_{2}CH_{2}CH_{3}$$ and $$CH_{3}CH_{2}C\equiv CH$$

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JEE Advanced 2010 Paper-1 - Question 4

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The correct statement about the following disaccharide is

A

Ring (a) is pyranose with a-glycosiclic link

B

Ring (a) is furanose with a-glycosiclic link

C

Ring (b) is furanose with cx -glycosidic link

D

Ring (b) is pyranose with $$\beta$$-glycosidic link

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JEE Advanced 2010 Paper-1 - Question 5

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A

B

C

D

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JEE Advanced 2010 Paper-1 - Question 6

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Plots showing the variation of the rate constant (k) with temperature (T) are given below. The plot that follows Arrhenius equation is

A

B

C

D

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JEE Advanced 2010 Paper-1 - Question 7

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The species which by definition has ZERO standard molar enthalpy of formation at 298 K is

A

$$Br_{2}(g)$$

B

$$Cl_{2}(g)$$

C

$$H_{2}O(g)$$

D

$$CH_{4}(g)$$

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JEE Advanced 2010 Paper-1 - Question 8

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The bond energy (in kcal $$mol^{-1}$$) of a C-C single bond is approximately

A

1

B

10

C

100

D

1000

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JEE Advanced 2010 Paper-1 - Question 9

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The reagent(s) used for softening the temporary hardness of water is(are)

A

$$Ca_{3}(PO_{4})_{2}$$

B

$$Ca(OH)_{2}$$

C

$$Na_{2}Co_{3}$$

D

$$NaOCl$$

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JEE Advanced 2010 Paper-1 - Question 10

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A

B

C

D

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JEE Advanced 2010 Paper-1 - Question 11

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In the Newman projection for 2-2 dimethylbutane

X and Y can respectively be

A

$$H$$ and $$H$$

B

$$H$$ and $$C_{2}H_{5}$$

C

$$C_{2}H_{5}$$ and $$H$$

D

$$CH_{3}$$ and $$CH_{3}$$

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JEE Advanced 2010 Paper-1 - Question 12

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Among the following, the intensive property is (properties are)

A

molar conductivity

B

electromotive force

C

resistance

D

heat capacity

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JEE Advanced 2010 Paper-1 - Question 13

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Aqueous solutions of $$HNO_{3}, KOH, CH_{3}COOH$$ and $$CH_{3}COONa$$ of identical concentrations are provided. The pair(s) of solutions which form a buffer upon mixing is(are)

A

$$HNO_{3}$$ and $$CH_{3}COOH$$

B

$$KOH$$ and $$CH_{3}COONa$$

C

$$HNO_{3}$$ and $$CH_{3}COONa$$

D

$$CH_{3}COOH$$ and $$CH_{3}COONa$$

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JEE Advanced 2010 Paper-1 - Question 14

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Partial roasting of chalcopyrite produces

A

$$Cu{2}S$$ and $$FeO$$

B

$$Cu{2}O$$ and $$FeO$$

C

$$CuS$$ and $$Fe_{2}O_{3}$$

D

$$Cu_{2}O$$ and $$Fe_{2}O_{3}$$

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JEE Advanced 2010 Paper-1 - Question 15

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Iron is removed from chalcopyrite as

A

$$FeO$$

B

$$FeS$$

C

$$Fe_{2}O_{3}$$

D

$$FeSiO_{3}$$

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JEE Advanced 2010 Paper-1 - Question 16

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In self-reduction, the reducing species is

A

$$S$$

B

$$O^{2-} $$

C

$$S^{2-} $$

D

$$SO{2} $$

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JEE Advanced 2010 Paper-1 - Question 17

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For the above cell

A

$$E_{cell}<0;\ \triangle G>0$$

B

$$E_{cell}>0;\ \triangle G<0$$

C

$$E_{cell}<0;\ \triangle G^{0}>0$$

D

$$E_{cell}>0;\ \triangle G^{0}<0$$

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JEE Advanced 2010 Paper-1 - Question 18

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If the 0.05 molar solution of $$M^{+}$$ is replaced by a 0.0025 molar $$M^{+}$$ solution, then the magnitude of the cell potential would be

A

$$35 mV$$

B

$$70 mV$$

C

$$140 mV$$

D

$$700 mV$$

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JEE Advanced 2010 Paper-1 - Question 19

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The total number of basic groups in the following form of lysine is

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JEE Advanced 2010 Paper-1 - Question 20

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The total numberof cyclic isomers possible for a hydrocarbon with the molecular formula $$C_{4}H_{6}$$ is

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JEE Advanced 2010 Paper-1 - Question 21

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In the scheme given below, the total number of intramolecular aldol condensation products form 'Y' is

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JEE Advanced 2010 Paper-1 - Question 22

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Amongst the following, the total number of compounds soluble in aqueous $$NaOH$$ is

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JEE Advanced 2010 Paper-1 - Question 23

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Amongst the following, the total number of compounds whose aqueous solution turns red litmus paper blue is

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JEE Advanced 2010 Paper-1 - Question 24

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Based on VSEPR theory, the number of 90 degree F-Br-F angles in $$BrF_{5}$$ is

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JEE Advanced 2010 Paper-1 - Question 25

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The value of n in the molecular formula $$Be_{n}Al_{2}Si_{6}O_{18}$$ is

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JEE Advanced 2010 Paper-1 - Question 26

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A student performs a titration with different burettes and finds titre values of 25.2 mL, 25.25 mL, and 25.0 mL. The numberof significant figures in the average titre value is

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JEE Advanced 2010 Paper-1 - Question 27

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The concentration of R in the reaction $$R\rightarrow P$$ was measured as a function of time and the following data is obtained:

The order of the reaction is

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JEE Advanced 2010 Paper-1 - Question 28

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The number of neutrons emitted when $$_{92}^{235}U$$ undergoes controlled nuclear fission to $$_{54}^{142}Xe$$ and $$_{38}^{90}Sr$$ is

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JEE Advanced 2010 Paper-1 - Question 29

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If the angles A, B andC of a triangle are in an arithmetic progression andif a, b and c denote the lengths of the sides opposite to A, B andC respectively, then the value of the expression $$\frac{a}{c}\sin 2C+\frac{c}{a}\sin 2A$$ is

A

$$\frac{1}{2}$$

B

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

C

$$1$$

D

$$\sqrt{3}$$

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JEE Advanced 2010 Paper-1 - Question 30

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Equation of the plane containing the straight line $$\frac{X}{2}=\frac{Y}{3}=\frac{Z}{4}$$ and perpendicular to the plane containing the straight lines $$\frac{X}{3}=\frac{Y}{4}=\frac{Z}{2}$$ and $$\frac{X}{4}=\frac{Y}{2}=\frac{Z}{3}$$ is

A

$$x+2y-2z=0$$

B

$$3x+2y-2z=0$$

C

$$x-2y+z=0$$

D

$$5x+2y-4z=0$$

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JEE Advanced 2010 Paper-1 - Question 31

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Let $$\omega$$ be a complex cube root of unity with $$\omega\neq1$$. A fair die is thrownthree times. If $$r_{1},r_{2}$$ and $$r_{3}$$ are the numbers obtained on the die, then the probability that is $$\omega^{r_{1}}+\omega^{r_{2}}+\omega^{r_{3}}=0$$

A

$$\frac{1}{18}$$

B

$$\frac{1}{9}$$

C

$$\frac{2}{9}$$

D

$$\frac{1}{36}$$

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JEE Advanced 2010 Paper-1 - Question 32

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Let P, Q, R and S be the points on the plane with position vectors $$-2\hat{i}-\hat{j},4\hat{i},3\hat{i}+3\hat{j}$$ and $$-3\hat{i}+2\hat{j}$$ respectively. The quadrilateral PQRS must be a

A

parallelogram, which is neither a rhombus nor a rectangle

B

square

C

rectangle, but not a square

D

rhombus, but not a square

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JEE Advanced 2010 Paper-1 - Question 33

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The number of $$3\times3$$ matrices A whose entries are either O or 1 and for which the system $$A\begin{bmatrix}x\\y\\z\end{bmatrix}=\begin{bmatrix}1\\0\\0\end{bmatrix}$$ has exactly two distinct solutions, is

A

$$0$$

B

$$2^{9}-1$$

C

$$168$$

D

$$2$$

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JEE Advanced 2010 Paper-1 - Question 34

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The value of $$\lim_{x \rightarrow 0}\frac{1}{x^{3}}\int_{0}^{x} \frac{t \ln(1+t)}{t^{4}+4}dt$$ is

A

$$0$$

B

$$\frac{1}{12}$$

C

$$\frac{1}{24}$$

D

$$\frac{1}{64}$$

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JEE Advanced 2010 Paper-1 - Question 35

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Let p and q be real numbers such that $$p\neq 0,p^{3}\neq q$$ and $$p^{3}\neq -q$$. If $$\alpha$$ and $$\beta$$ are nonzero complex numbers satisfying $$\alpha+\beta=-p$$ and $$\alpha^{3}+\beta^{3}=q$$, then a quadratic equation having $$\frac{\alpha}{\beta}$$ and $$\frac{\beta}{\alpha}$$ as its roots is

A

$$(p^{3}+q)x^{2}-(p^{3}+2q)x+(p^{3}+q)=0$$

B

$$(p^{3}+q)x^{2}-(p^{3}-2q)x+(p^{3}+q)=0$$

C

$$(p^{3}-q)x^{2}-(5p^{3}-2q)x+(p^{3}-q)=0$$

D

$$(p^{3}-q)x^{2}-(5p^{3}+2q)x+(p^{3}-q)=0$$

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JEE Advanced 2010 Paper-1 - Question 36

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Let f, g and h be real-valued functions defined on the interval [0,1] by $$f(x) = e^{x^2} + e^{-x^2}, g(x) = xe^{x^2} + e^{-x^2}$$ and $$h(x) = x^2 e^{x^2} + e^{-x^2}$$. If a, b and c denote, respectively, the absolute maximum of f, g and h on [0, 1], Then

A

$$a = b$$ and $$c \neq b$$

B

$$a = c$$ and $$a \neq b$$

C

$$a \neq b$$ and $$c \neq b$$

D

$$a = b = c$$

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JEE Advanced 2010 Paper-1 - Question 37

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Let A and B be two distinct points on the parabola $$y^2 = 4x$$. If the axis of the parabola touches a circle of radius r having AB as its diameter, then the slope of the line joining A and B can be

A

$$-\frac{1}{r}$$

B

$$\frac{1}{r}$$

C

$$\frac{2}{r}$$

D

$$-\frac{2}{r}$$

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JEE Advanced 2010 Paper-1 - Question 38

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Let ABC be a triangle such that $$\angle ACB = \frac{\pi}{6}$$ and let a, b and c denote the lengths of the sides opposite to A, B and C respectively. The value(s) of x for which $$a = x^2 + x + 1, b = x^2 - 1$$ and $$c = 2x + 1$$ is (are)

A

$$-(2 + \sqrt{3})$$

B

$$(1 + \sqrt{3})$$

C

$$(2 + \sqrt{3})$$

D

$$4\sqrt{3}$$

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JEE Advanced 2010 Paper-1 - Question 39

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Let $$z_1$$ and $$z_2$$ be two district complex numbers and let $$z = (1 - t)z_1 + tz_2$$ for some real number t with 0 < t 1. If Arg(w) denotes the principal argument of a nonzero complex number w, then

A

$$\mid z - z_1\mid + \mid z - z_2\mid = \mid z_1 - z_2\mid$$

B

$$Arg(z - z_1) = Arg(z - z_2)$$

C

D

$$Arg(z - z_1) = Arg(z_2 - z_1)$$

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JEE Advanced 2010 Paper-1 - Question 40

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Let f be a real-valued function defined on the interval $$(0, \infty)$$ by $$f(x) = \ln x + \int_{0}^{x}\sqrt{1 + \sin t}$$ dt. Then which of the following statement(s) is (are) true ?

A

$$f''(x)$$ exists for all $$x \in (0, \infty)$$

B

$$f'(x)$$ exists for all $$x \in (0, \infty)$$ $$f'$$ is continuous on $$(0, \infty)$$, but not differentiable on $$(0, \infty)$$

C

there exists $$\alpha > 1$$ such that $$\mid f'(x) \mid < \mid f(x) \mid$$ for all $$x \in (\alpha, \infty)$$

D

there exists $$\beta > 0$$ such that $$\mid f(x) \mid + \mid f'(x) \mid \leq \beta$$ for all $$x \in (0, \infty)$$

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JEE Advanced 2010 Paper-1 - Question 41

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The value(s) of $$\int_{0}^{1}\frac{x^4(1-x)^4}{1+x^2}dx $$ is(are)

A

$$\frac{22}{7} - \pi$$

B

$$\frac{2}{105}$$

C

0

D

$$\frac{71}{15} - \frac{3 \pi}{2}$$

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JEE Advanced 2010 Paper-1 - Question 42

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The number of A in $$T_p$$, such that A is either symmetric or skew-symmetric or both, and det (A) divisible by p is

A

$$(p-1)^2$$

B

$$2(p-1)$$

C

$$(p-1)^2 + 1$$

D

$$2p-1$$

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JEE Advanced 2010 Paper-1 - Question 43

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The number of A in $$T_p$$, suchthat the trace of A is not divisible by p but det (A) is divisible by p is
[Note : The trace of a matrix is the sumofits diagonal entries.]

A

$$(p-1)(p^2 - p + 1)$$

B

$$p^3 - (p - 1)^2$$

C

$$(p-1)^2$$

D

$$(p-1)(p^2 - 2)$$

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JEE Advanced 2010 Paper-1 - Question 44

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The number of A in $$T_p$$, such that det (A) is not divisible byp is

A

$$2p^2$$

B

$$p^3 - 5p$$

C

$$p^3 - 3p$$

D

$$p^3 - p^2$$

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JEE Advanced 2010 Paper-1 - Question 45

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Equation of a common tangent with positive slope to the circle as well as to the hyperbola is

A

$$2x - \sqrt{5}y - 20 = 0$$

B

$$2x - \sqrt{5}y + 4 = 0$$

C

$$3x - 4y + 8 = 0$$

D

$$4x - 3y + 4 = 0$$

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JEE Advanced 2010 Paper-1 - Question 46

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Equation of the circle with AB as its diameter is

A

$$x^2 + y^2 - 12x + 24 = 0$$

B

$$x^2 + y^2 + 12x + 24 = 0$$

C

$$x^2 + y^2 + 24x - 12 = 0$$

D

$$x^2 + y^2 - 24x - 12 = 0$$

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JEE Advanced 2010 Paper-1 - Question 47

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The numberof values of $$\theta$$ in the interval $$\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$$ such that $$\theta \neq \frac{n \pi}{5}$$ for $$n = 0, \pm 1, \pm 2$$ and $$\tan \theta = \cot 5 \theta$$ as well as $$\sin 2 \theta = \cos 4 \theta$$ is

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JEE Advanced 2010 Paper-1 - Question 48

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The maximum value of the expression $$\frac{1}{\sin^2 \theta + 3 \sin \theta \cos \theta + 5 \cos^2 \theta}$$ is

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JEE Advanced 2010 Paper-1 - Question 49

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If $$\overrightarrow{a}$$ and $$\overrightarrow{b}$$ are vectors in space given by $$\overrightarrow{a} = \frac{\hat{i} - 2 \hat{j}}{\sqrt{5}}$$ and $$\overrightarrow{b} = \frac{2\hat{i} + \hat{j} + 3\hat{k}}{\sqrt{14}}$$, then the value of $$\left(2\overrightarrow{a} + \overrightarrow{b}\right).\left[\left(\overrightarrow{a} \times \overrightarrow{b}\right) \times \left(\overrightarrow{a} - 2\overrightarrow{b}\right)\right]$$ is

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JEE Advanced 2010 Paper-1 - Question 50

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The line 2x + y = 1 is tangent to the hyperbola $$\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$$. If this line passes through the point of intersection of the nearest directrix and the x-axis, then the eccentricity of the hyperbola is

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JEE Advanced 2010 Paper-1 - Question 51

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If the distance between the plane $$Ax - 2y + z = d$$ and the plane containing the lines $$\frac{x-1}{2} = \frac{y-2}{3} = \frac{z-3}{4}$$ and $$\frac{x-2}{3} = \frac{y-3}{4} = \frac{z-4}{5}$$ is $$\sqrt{6}$$, then $$\mid d \mid$$ is

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JEE Advanced 2010 Paper-1 - Question 52

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For any real numberx, let [x] denote the largest integer less than or equal to x. Let f be a real valued function defined on the interval [-10, 10] by
$$f(x) = \begin{cases}x-[x] & if & [x] & is & odd,\\1+[x]-x & if & [x] & is & even\end{cases}$$
Then the value of $$\frac{\pi^2}{10}\int_{-10}^{10}f(x) \cos \pi x dx$$ is

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JEE Advanced 2010 Paper-1 - Question 53

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Let $$\omega$$ be the complex number $$\cos \frac{2 \pi}{3} + i \sin \frac{2 \pi}{3}$$. Then the number of distinct complex numbers z satisfying

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JEE Advanced 2010 Paper-1 - Question 54

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Let $$S_k = 1, 2, .... 100$$, denote the sumof the infinite geometric series whose first term is $$\frac{k-1}{k!}$$ and the common ratio is $$\frac{1}{k}$$. Then the value of $$\frac{100^2}{100!}+\sum_{k=1}^{100}\mid (k^2 - 3k + 1)S_k \mid$$ is

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JEE Advanced 2010 Paper-1 - Question 55

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The number of all possible values of $$\theta$$ , where $$0 < \theta < \pi$$. for which the system of equations
$$(y + z) \cos 3 \theta = (xyz) \sin 3\theta$$
$$x \sin 3 \theta = \frac{2 \cos 3\theta}{y} + \frac{2 \sin 3\theta}{z}$$
$$(xyz) \sin 3\theta = (y + 2z) \cos 3 \theta + y \sin 3 \theta$$
have a solution $$(x_0, y_0, z_0)$$ with $$y_0z_0 \leq 0$$, is

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JEE Advanced 2010 Paper-1 - Question 56

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Let f be a real-valued differentiable function on R (the set of all real numbers) such that f(1) = 1. If the y-intercept of the tangent at any point P(x, y) on the curve y= f(x) is equal to the cube of the abscissa of P, then the value off(-3) is equal to

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JEE Advanced 2010 Paper-1 - Question 57

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Consider a thin square sheet of side L and thickness t, made of a material of resistivity $$\rho$$. The resistance between two opposite faces, shown by the shaded areas in the figure is

A

directly proportional to L

B

directly proportional to t

C

independent of L

D

independent of t

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JEE Advanced 2010 Paper-1 - Question 58

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A real gas behaves like an ideal gas if its

A

pressure and temperature are both high

B

pressure and temperature are both low

C

pressure is high and temperature is low

D

pressure is low and temperature is high

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JEE Advanced 2010 Paper-1 - Question 59

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Incandescent bulbs are designed by keeping in mind that the resistance of their filament increases with the increase in temperature. If at room temperature. 100 W, 60 Wand 40 Wbulbs have filament resistances $$R_{100}, R_{60}$$ and $$R_{40}$$, respectively, the relation between these resistances is

A

$$\frac{1}{R_{100}} = \frac{1}{R_{40}} + \frac{1}{R_{60}}$$

B

$$R_{100} = R_{40} + R_{60}$$

C

$$R_{100} > R_{60} > R_{40}$$

D

$$\frac{1}{R_{100}} > \frac{1}{R_{60}} > \frac{1}{R_{40}}$$

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JEE Advanced 2010 Paper-1 - Question 60

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To verify Ohm's law, a student is provided with a test resistor $$R_{T}$$, a high resistance $$R_1$$, a small resistance $$R_2$$, two identical galvanometers $$G_1$$ and $$G_2$$, and a variable voltage source V. The correct circuit to carry out the experiment is

A

B

C

D

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JEE Advanced 2010 Paper-1 - Question 61

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An AC voltage source of variable angular frequency $$\omega$$ and fixed amplitude $$V_0$$ is connected in series with a capacitance C and anelectric bulb of resistance R (inductance zero). When $$\omega$$ is increased

A

the bulb glows dimmer

B

the bulb glows brighter

C

total impedance of the circuit is unchanged

D

total impedance of the circuit increases

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JEE Advanced 2010 Paper-1 - Question 62

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A thin flexible wire of length L is connected to two adjacent fixed points and carries a current I in the clockwise direction, as shown in the figure. When the system is put in a uniform magnetic field of strength B going into the plane of the paper, the wire takes the shape of a circle. The tension in the wire is

A

$$IBL$$

B

$$\frac{IBL}{\pi}$$

C

$$\frac{IBL}{2 \pi}$$

D

$$\frac{IBL}{4 \pi}$$

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JEE Advanced 2010 Paper-1 - Question 63

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A block of mass m is on an inclined plane of angle $$\theta$$. The coefficient of friction between the block and the plane is $$\mu$$ and $$\tan \theta > \mu$$. The block is held stationary by applying a force P parallel to the plane. The direction of force pointing up the plane is taken to be positive. As P is varied from $$P_1 = mg(\sin \theta - \mu \cos \theta)$$ to $$P_2 = mg(\sin \theta + \mu \cos \theta)$$, the frictional force f versus P graph will look like

A

B

C

D

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JEE Advanced 2010 Paper-1 - Question 64

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A thin uniform annular disc (see figure) of mass M has outer radius 4R and inner radius 3R. The work required to take a unit mass from point P on its axis to infinity is

A

$$\frac{2GM}{7R}(4\sqrt{2} - 5)$$

B

$$-\frac{2GM}{7R}(4\sqrt{2} - 5)$$

C

$$\frac{GM}{4R}$$

D

$$\frac{2GM}{5R}(\sqrt{2} - 1)$$

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JEE Advanced 2010 Paper-1 - Question 65

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A few electric field lines for a system of two charges $$Q_1$$ and $$Q_2$$ fixed at two different points on the x-axis are shown in the figure. These lines suggest that

A

$$\mid Q_1 \mid > \mid Q_2 \mid$$

B

$$\mid Q_1 \mid < \mid Q_2 \mid$$

C

at a finite distance to the left of $$Q_1$$ the electric field is zero

D

at a finite distance to the right of $$Q_2$$ the electric field is zero

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JEE Advanced 2010 Paper-1 - Question 66

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A student uses a simple pendulumof exactly 1m length to determine g, the acceleration due to gravity. He uses a stop watch with the least count of 1 sec for this and records 40 secondsfor 20 oscillations. For this observation, which of the following statement(s) is (are) true ?

A

Error $$\triangle T$$ in measuring T, the time period, is 0.05 seconds

B

Error $$\triangle T$$ in measuring T, the time period, is 1 second

C

Percentage error in the determination of g is 5%

D

Percentage error in the determination of g is 2.5%

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JEE Advanced 2010 Paper-1 - Question 67

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A point mass of 1 kg collides elastically with a stationary point mass of 5 kg. After their collision, the 1 kg mass reverses its direction and moves with a speed of 2 $$ms^{-1}$$.
Which of the following statement(s) is (are) correct for the system of these two masses ?

A

Total momentumof the system is 3 kg $$ms^{-1}$$

B

Momentum of 5 kg massaftercollision is 4 kg $$ms^{-1}$$

C

Kinetic energy of the centre of mass is 0.75 J

D

Total kinetic energy of the system is 4 J

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JEE Advanced 2010 Paper-1 - Question 68

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A ray OP of monochromatic light is incident on the face AB of prism ABCD near vertex B at an incident angle of $$60^\circ$$ (see figure). If the refractive index of the material of the prism is $$\sqrt{3}$$, which of the following is (are) correct ?

A

The raygets totally internally reflected at face CD

B

The ray comes out through face AD

C

The angle between the incident ray and the emergent ray is $$90^\circ$$

D

The angle between the incident ray and the emergent ray is $$120^\circ$$

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JEE Advanced 2010 Paper-1 - Question 69

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One mole of an ideal gas in initial state A undergoes a cyclic process ABCA, as shown in the figure. Its pressure at A is $$P_0$$. Choose the correct option(s) from the following

A

Internal energies at A and B are the same

B

Work donebythe gas in process AB is $$P_0V_0 \ln 4$$

C

Pressure at C is $$\frac{P_0}{4}$$

D

Temperature at C is $$\frac{T_0}{4}$$

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JEE Advanced 2010 Paper-1 - Question 70

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If the total energy of the particle is E, it will perform periodic motion only if

A

E < 0

B

E > 0

C

$$V_0 > E > 0$$

D

$$E > V_0$$

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JEE Advanced 2010 Paper-1 - Question 71

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For periodic motion of small amplitude A, the time period T of this particle is proportional to

A

$$A\sqrt{\frac{m}{\alpha}}$$

B

$$\frac{1}{A}\sqrt{\frac{m}{\alpha}}$$

C

$$A\sqrt{\frac{\alpha}{m}}$$

D

$$\frac{1}{A}\sqrt{\frac{\alpha}{m}}$$

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JEE Advanced 2010 Paper-1 - Question 72

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The acceleration of this particle for $$\mid x \mid > X_0$$ is

A

proportional to $$V_0$$

B

proportional to $$\frac{V_0}{mX_0}$$

C

proportional to $$\sqrt{\frac{V_0}{mX_0}}$$

D

zero

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JEE Advanced 2010 Paper-1 - Question 73

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In the graphs below, the resistance R of a super conductor is shown as a function of its temperature T for two different magnetic fields $$B_1$$ (solid line) and $$B_2$$ (dashed line). If $$B_2$$ is larger than $$B_1$$, which of the following graphs shows the correct variation of R with T in these fields ?

A

B

C

D

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JEE Advanced 2010 Paper-1 - Question 74

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A superconductor has $$T_c (0) = 100 K$$. When a magnetic field of 7.5 Tesla is applied, its $$T_c$$ decreases to 75 K. For this material one candefinitely say that when

A

B = Tesla, $$T_c(B) = 80 K$$

B

B = 5 Tesla, 75 K < $$T_c(B)$$ < 100 K

C

B = 10 Tesla, 75 K < $$T_c(B) < 100 K$$

D

B = 10 Tesla, $$T_c(B)$$ = 70 K

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JEE Advanced 2010 Paper-1 - Question 75

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The focal length of a thin biconvex lens is 20cm. When anobject is moved from a distance of 25cmin front of it to 50cm, the magnification of its image changes from $$m_{25}$$ to $$m_{50}$$. The ratio $$\frac{m_{25}}{m_{50}}$$ is

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JEE Advanced 2010 Paper-1 - Question 76

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An $$\alpha$$-particle and a proton are accelerated from rest by a potential difference of 100V. After this, their de Broglie wavelengths are $$\lambda_{\alpha}$$ and $$\lambda_{p}$$ respectively. The ratio $$\frac{\lambda_p}{\lambda_{\alpha}$$, to the nearest integer, is

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JEE Advanced 2010 Paper-1 - Question 77

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When two identical batteries of internal resistance 1 Ω each are connected in series across a resistor R, the rate of heat produced in R is $$J_1$$. When the samebatteries are connected in parallel across R, the rate is $$J_2$$. If $$J_1 = 2.25 J_2$$ then the value of R in Ω is

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JEE Advanced 2010 Paper-1 - Question 78

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Two spherical bodies A (radius 6 cm) and B (radius 18 cm) are at temperatures $$T_1$$ and $$T_2$$, respectively. The maximum intensity in the emission spectrum of A is at 500 nm and in that of B is at 1500 nm. Considering themto be black bodies, what will be the ratio of the rate of total energy radiated by A to that of B ?

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JEE Advanced 2010 Paper-1 - Question 79

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When two progressive waves $$y_1 = 4 \sin(2x - 6t)$$ and $$y_2 = 3 \sin\left(2x - 6t - \frac{\pi}{2}\right)$$ are superimposed, the amplitude of the resultant wave is

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JEE Advanced 2010 Paper-1 - Question 80

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A 0.1 kg mass is suspended from a wire of negligible mass. The length of the wire is 1m and its cross-sectional area is $$4.9 \times 10^{-7} m^2$$. If the mass is pulled a little in
the vertically downward direction and released, it performs simple harmonic motion of angular frequency 140 rad $$s^{-1}$$. If the Young’s modulus of the material of the wire is $$n \times 10^9 Nm^{-2}$$, the value of n is

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JEE Advanced 2010 Paper-1 - Question 81

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A binarystar consists of two stars A (mass 2.2 $$M_s$$) and B (mass 11 $$M_s$$). where $$M_s$$ is the mass of the sun. They are separated by distance d and are rotating about their centre of mass, which is stationary. The ratio of the total angular momentum of the binarystar to the angular momentumof star B about the centre of mass is

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JEE Advanced 2010 Paper-1 - Question 82

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Gravitational acceleration on the surface of a planet is $$\frac{\sqrt{6}}{11} g$$, where g is the gravitational acceleration on the surface of the earth. The average mass density of the planet is $$\frac{2}{3}$$ times that of the earth. If the escape speed on the surface of the earth is taken to be 11 $$kms^{-1}$$, the escape speed on the surface of the planet in $$kms^{-1}$$ will be

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JEE Advanced 2010 Paper-1 - Question 83

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A piece of ice (heat capacity = 2100 J $$kg^{-1} {^\circ}C^{-1}$$ andlatent heat = $$3.36 \times 10^5 J kg^{-1}$$) of mass m grams is at $$-5 ^\circ C$$ at atmospheric pressure. It is given 420 J of heat so that the ice starts melting. Finally when the ice-water mixture is in equilibrium, it is found that 1 gmof ice has melted. Assuming there is no other heat exchange in the process, the value of m is

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JEE Advanced 2010 Paper-1 - Question 84

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A stationary source is emitting sound ata fixed frequency $$f_0$$, which is reflected by two cars approaching the source. The difference between the frequencies of sound reflected from the cars is 1.2% of $$f_0$$. What is the difference in the speeds of the cars (in km per hour) to the nearest integer ? The cars are moving at constant speeds much smaller than the speed of sound which is 330 $$ms^{-1}$$.

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