rt solutions-04!03!2012 xiii vxy paper ii final test code a

7/30/2019 Rt Solutions-04!03!2012 XIII VXY Paper II Final Test Code A

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Class: XIII (VXY) Date: 04/03/2012 Time: 3 Hours. Max. Marks: 240

VERY IMPORTANTA. The question paper consists of 3 section (Section-1containsMathematics , Section-2containsPhysics and

Section-3contains Chemistry). Please fill the OMR answer Sheet accordingly and carefully.B. Each Section contains (11 questions in Part-A, 1 question in Part-B and 6 questions in Part-C) and total

number of pages are 32.C. Please ensure that the Question Paper you have received contains ALL THE QUESTIONS in each

Section and PAGES. If you found some mistake like missing questions or pages then contact

immediately to the Invigilator.

INSTRUCTIONS

PART-A1. Q.1 to Q.5 are single correct type questions. Each question has four choices (A), (B), (C) and (D) out of

which ONLY ONE is correct. For each question, you will be awarded 4 marks, if you have darkened only thebubble corresponding to the correct answer and zero mark if no bubble are darkened. In all other cases,minus one (1) mark will be awarded.

2. Q.6 to Q.11 are Paragraph type. Based upon the paragraph3 single correct typequestions have to be answered.

Each of these questions has four choices (A), (B), (C) and (D) out of whichONLY ONE is correct. For each question,you will be awarded 3 marks if you have darkened only the bubble corresponding to the correct answer and zeromark if no bubble are darkened. In all other cases, minus one (1) mark will be awarded.

PART-B3. Q.1 is Matrix Match type question. The question has Four statements (A, B, C, D) given in Column-I and Five

statements (P, Q, R, S, T) given in Column-II. Any given statement in Column-Ican have correct matching with oneor more statement(s) given in Column-II. For example, if for a given question, statement B matches with thestatement given in Q and R, then for the particular question, against statement B darken the bubbles correspondingto Q and R in the OMR.For each row, you will be awarded 3 marks for each row in which you have darkened the bubble(s) corresponding

to the correct answer. Thus Q.1 carries a maximum of 12 marks.

PART-C

4. Q.1 to Q.6 are Integer Type questions. The answer to each question is upto 4 digit ranging from 0 to9999. The correct digit below the question number in the OMR is to be bubbled.For each question, you will be awarded 5 marks if you darken the bubble corresponding to the correct answerand zero mark if no bubble is darkened.For example, if for a given question, your answer is 25, then for the particular question, against question numberyou must fill as 0025 in the OMR. No negative marks will be awarded in this section.

5. Indicate the correct answer for each question by filling appropriate bubble in your answer sheet.

6. Use of Calculator, Log Table, Slide Rule and Mobile is not allowed.

7. The answers of the questions must be marked by shading the circle against the question by dark Black Ball pointPen only.

USEFUL DATA

Atomic weights: Al = 27, Mg = 24, Cu = 63.5, Mn = 55, Cl = 35.5, O = 16, H = 1, P = 31, Ag = 108, N = 14,Li = 7, I = 127, Cr = 52, K=39, S = 32, Na = 23, C = 12, Br = 80, Fe = 56, Ca = 40, Zn = 65.5, Ti = 48,Ba = 137, U = 238, Co= 59, B =11, F = 19, He = 4, Ne = 20, Ar = 40 , Mo = 96[Take : ln 2 = 0.69, ln 3 = 1.09, e = 1.6 1019, m

e= 9.1 1031 kg, hc = 1240 eVnm, h = 6.6 1034 Js,

c = 3 108 m/s] Take g = 10 m/s2 unless otherwise stated

CODEAINAL TESTPAPER- II


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MATHEMATICS

XIII (VXY) Final Test [Paper-II] Code-A Page # 2

Rough Work

PART-A

[SINGLE CORRECT CHOICE TYPE]

Q.1 to Q.5 has four choices (A), (B), (C), (D) out of which ONLY ONE is correct.

Q.1 If the equation of plane passing through the intersection of the planes x + y1= 0 and 2yz = 0

and perpendicular to the plane x + y + 4z = 9, is x + 3yz = k, then k equals

(A) 0 (B)

1 (C) 1 (D) 2

Q.2 The equation of the curve passing through (1, 2), if the x-intercept of normal at any point P(x, y)

of the curve is three times the abscissa of point, is

(A) 3x2y2 + 1 = 0 (B) x22y2 + 7 = 0 (C) 2x2y2 + 2 = 0 (D) x2y2 +3 = 0

Q.3 Let f be a differentiable function on R (the set of all real numbers) and satisfies

x

5

22dt)t('f3t

5

28)x(fx . The value of f '(5) is equal to

(A) 1 (B) 5 (C) 10 (D) 15

Q.4 A tangent to the hyperbola1

y

4

x2

= 1 meets ellipse x2 + 4y2 = 4 at two distinct points. The locus of

mid point of this chord is

(A) (x2 + 4y2)2 = 4(x24y2) (B) (x24y2) = 4(x2 + 4y2)

(C) (x24y2)2 = 4(4x2 + y2) (D) (x2 + 4y2)2 = 4(4x2y2)

Q.5 Let there are 5 apples (3 alike and 2 different), 4 mangoes (2 alike and 2 different) and 3 guavas (all

different). The number of ways in which these fruits can be distributed between two children equally and

each having exactly two identical fruits, is

(A) 35 (B) 70 (C) 105 (D) 140


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[PARAGRAPH TYPE]


Paragraph for Question no. 6 to 8

Consider the parabola 0zz8zz 2 and an ellipse 41z1z

where z = x + iy 1iandRy,x .They intersect at P and Q in the first and the fourth quadrants, respectively. Tangents to the parabola at

P and Q intersect the x-axis at R and tangents to the ellipse at P and Q intersect the x-axis at S.

Q.6 The ratio of the area of the triangles PQS and PQR is

(A) 2 : 1 (B) 3 : 2 (C) 4 : 1 (D) 5 : 3

Q.7 If L (x1, y

1) where x

1> 0, y

1> 0 be an end point of the latus rectum of the ellipse then coordinates of

centroid of triangle LRS is

(A)

2

1,

6

19(B)

2

1,

9

19(C)

3

2,

9

19(D)

3

2,

3

19

Q.8 If normals are drawn at points A, B and C lying on the parabola which intersect at D(3, 0) then radiusof circumcircle of triangle ABC is

(A) 2 (B)3

2(C)

2

3(D)

2

5


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Paragraph for question nos. 9 to 11

Let g (x) be a polynomial of degree 3 passing through origin and have a local maximum at x =22

1.

Also g' (x) has a local minimum at x = 0, and g(1) = 5.

Q.9 The value of g(2) is equal to

(A) 48 (B) 54 (C) 58 (D) 68

Q.10 Let f(x) = sgn (x) where sgn (x) denotes signum function of x, then which one of the following statement

is incorrect for )x(gf ?

(A) Area enclosed by )x(gf with x-axis between ordinates x = to x = is 2.

(B)

1

1

dx)x(gf = 0

(C) )x(gf is a many-one function.

(D) )x(gf is periodic function.

Q.11 Consider a real-valued function y = h(x) satisfying the differential equation

dx

dy+ g'(x) y = 1)x(g g'(x) such that h(0) = 1, then h(1) equals

(A) 5 + e5 (B) 11 + e11 (C)5 + e5 (D) 11 + e11


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PART-B

[MATRIX TYPE]

Q.1 has four statements (A, B, C, D) given in Column-I and five statements (P, Q, R, S, T) given in Column-II.

Any given statement in Column-Ican have correct matching with one or more statement(s) given in Column-II.

Q.1 Column-I Column-II

(A) Let B =

R},0{Rx,

x

axsin2,0a:a

2

2. (P) 2

The largest integral value of a is

(B) The slope of the tangent to a curve y = f(x) at )x(f,xP is (Q) 312x and the curve passes through the point M(2,2). If the

area bounded by the curve and the line y = mx is3

32,

then the value of m can be

(C) Number of solutions satisfying the equation

cos2

xsin

2

x= sin x1, where | x |

2

3, is (R) 4

(D) Let f (x) and g(x) be differentiable functions on R. (S) 5

If h(x) = )x(fgf , where f (2) = 1, g(1) = 2 and

f '(2) = g'(1) = 4, then )2('h is equal to (T) 8


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PART-C

[INTEGER TYPE]

Q.1 to Q.6 are "Integer Type" questions. (The answer to each of the questions are upto 4 digits)

Q.1 Let A =

2x02

5x1

203

, B =

1b

2

and C = 153 then find the number of integral values of b

for which Tr(ABC) 18 x R.[Note : Tr(P) denotes trace of matrix P.]


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Q.2 If the value of the definite integral

3

1

2

2x1n

x

1l dx is equal to

21 kk3

2n)23(

l, then find the

value of1

2

k

k.


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Q.3 If p1, p

2are the roots of the quadratic equation, 9x2 + bx + c = 0 and q

1, q

2are the roots of the

quadratic equation cx2 + bx9 = 0 such that p1, q

1, p

2, q

2(in that order) is an A.P. of distinct terms,

then find the value of c. (where a, bR)


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Q.4 Let f : R+ R be a differentiable function satisfying f(x) = e + (1x)

x

1

dt)t(fe

xnl x R+.

If the area enclosed by the curve g(x) = x(f(x)ex) lying in the fourth quadrant is A, then find the value

of A2.


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Q.5 Bag I contains 4 white and 3 black balls and another bag II contains 5 white and 2 black balls.

Two balls are drawn randomly from the first bag and put in the second bag and then a balls drawn from

the bag II. The probability that the ball drawn from the second bag is white is expressed as

q

p

where p, qN. Find the minimum value of (p + q).


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Q.6 Let A1

and A2

are the vertices of the conic C1

: 4(x3)2 + 9(y2)236 = 0 and a point P is moving

in the plane such that 23PAPA 21 then locus of P is another conic C2.

If D1

denotes distance between foci of the conic C2.

D2denotes product of the perpendiculars from the points A

1, A

2upon any tangent drawn to conic C

2.

and D3

denotes length of the tangent drawn from any point on auxiliary circle of conic C1

to the

auxiliary circle of the conic C2

, then find the value of

2

3

21

D

DD.


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PART-A



Q.1 A stick of length L and mass M lies on a frictionless horizontal surface on which it is free to move in any

way. A ball of mass m moving with speed v collides elastically with the stick as shown in figure. If after the

collision ball comes to rest, then what should be the mass of the ball?

(A) m = 2M (B) m = M (C) m = M/2 (D) m = M/4

Q.2 A student is calculating the thickness of a single sheet of paper. She measures the thickness of a stack of 80

sheets with vernier calipers, and finds the thickness to be l = 1.27 cm. To calculate the thickness of a

single sheet she divides the total thickness of sheets with number of sheets. Which of the following

answer has the correct number of significant digits?

(A) 0.15875 mm (B) 0.159 mm (C) 0.16 mm (D) 0.2 mm

Q.3 Find the amount of work required to be done to increase the temperature of one mole of an ideal gas by

30C if it is expanding under the condition PV2/3

(A) 150 J (B) 100 J (C) 50 J (D) 200 J

Q.4 An infinite conducting plate of thickness 0.0200 m is surrounded

by a uniform field E = 400 V/m directed left to right. See the

figure. Let the potential V0= 0 at distance 0.0200 m to the right

of the plate. What is V3, the potential 0.0300 m to the left of

the plate?

V3 V2 V1 V0

E E

(A)28 V (B)20 V (C) +20 V (D) +28 V

Q.5 A resistance of 2 is connected across one gap of a metre-bridge and unknown resistance, greater than

2, is connected across the other gap. When these resistances are interchanged, the balance point shifts

by 20 cm, neglecting any end correction, the unknown resistance is

(A) 3 (B) 4 (C) 5 (D) 6


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[PARAGRAPH TYPE]



A turning fork is mounted on a movable trolley. A microphone connected to an oscilloscope is mounted

on another movable trolley. The oscilloscope can be used to plot the graph of sine wave, and thus find

the equation of the sound wave detected by the microphone. In case-I, both the trolleys are stationary.

In case-II, the trolley with the tuning fork moves towards the microphone. The microphone is stationary.

In case-III, the trolley with the tuning fork is stationary, but the trolley with microphone moves towards

the tuning fork.The person who is making observation was a little careless. He writes 3 correct equations for the

detected wave, but forget which wave belongs to which case. The 3 detected waves are :

pA

= p0sin

t527x

20

31

pB

= p0sin

t512

5

x8

pC

= p0

sin

t496

20

x31

Q.6 Choose the correct matching

(A) I B, IIA, III C (B) I B, II C, IIIA

(C) IA, II C, III B (D) I C, II B, IIIA

Q.7 The velocity of the trolley in case-II is

(A) 10 m/s (B) 20 m/s (C) 15 m/s (D) 12 m/s

Q.8 The velocity of the trolley in case-III is

(A) 10 m/s (B) 20 m/s (C) 15 m/s (D) 12 m/s


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PHYSICS


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Consider the reaction

HHHH1

1

3

12

1

2

1

The Q value is 4.0 MeV, and so this nuclear reaction liberates about 1 MeV per nucleon, roughly the

same as the fission reaction. This reaction can be performed in the laboratory, by accelerating a beam of

deuterons on to a deuterium target. In order to observe the reaction, we must get the incident and target

deuterons closed enough that the nuclear force can produce the reaction ; that is, we must overcome the

mutual Coulomb repulsion of the two particles. We can estimate this Coulomb repulsion by calculatingthe electrostatic repulsion of two deuterons when they are just touching. The radius of a deuteron is

about 1.5 fm, and the electrostatic potential energy of the two charges separated by about 3 fm is about

0.5 MeV.

We can produce such a beam of deuterons in many of the accelerators available in nuclear physics

laboratories. The beam currents of such accelerators are typically of the order of microamperes. If every

particle in the beam produced a reaction (hardly a reasonable assumption!), the total power produced

would be 4W. an output of 4W (assuming we could extract every bit of the energy liberated in the

reaction, which appears as the kinetic energies of the products 1H and 3H) hardly makes this device a

useful power source!.

Q.9 According to the passage, the fusion reaction initiated by accelerators in laboratories is not useful source

of energy because.

(A) Q value per reaction is very low. (B) The energy losses are high.

(C) Radioactive daughter nuclei are produced. (D) The power output is low.

Q.10 For initiating the reaction, the energy of incident deuterons should be of the order of

(A) 0.5 MeV (B) 1.0 MeV (C) 4.0 MeV (D) 4.5 MeV

Q.11 What is the mass of tritium atom, if mass of hydrogen atom = 1.0078 amu. Mass of Deuterium

atom = 2.0141 amu, 1 amu = 931.5 MeV/c2.

(A) 3.0161 amu (B) 3.0204 amu (C) 3.0247 amu (D) 3.0118 amu


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PART-B

[MATRIX TYPE]

Q.1 has fourstatements (A, B, C, D) given in Column-I and fivestatements (P, Q, R, S, T) given in Column-II.

Any given statement in Column-Ican have correct matching with one or more statement(s) given inColumn-II.

Q.1 Column-I Column-II

(A) -decay (P) Charged particles are emitted having continous

energy till certain maximum value.

(B) -decay (Q) Charged particles are emitted having discrete energies.

(C) Photoelectric emission from (R) Angular momentum of emitting body is changed in

a standard photoelectric process of emission

effect experiment apparatus.

(D) Photons of wavelength 90 nm (S) If external factors change, the process of emission

pass through a sample of may stop.

hydrogen gas in groundstate.

(T) Electronic configuration of the atom is changed

in process of emission.


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PART-C

[INTEGER TYPE]


Q.1 Two concentric coplanar circular loops made of wire, with resistance per unit length 104m1, have

diameters 0.2 m & 2 m . A time varying potential difference (4+ 2.5t) volts is applied across the larger

loop. Calculate the current (in mA) in the smaller loop.


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Q.2 Two spherical shaped equal sized glass fishbowls filled with water are standing on the table. In the

middle of each fishbowl a small fish is swimming. In what distance (in cm) can they see each other? The

refractive index of water is3

4, the radius of each bowl is 30 cm and they are kept such that their centres

are 90 cm from each other.


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Q.3 At the endpoints of a line segment of a length of m84

337d there are two identical positive electric

charges q. What is the ratio of the electric field strength and the electric potential (in m1) in a point

characterized by an angle= 37 on the circle drawn around the line segment. Round off to nearest

integer.

+ +d


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Q.4 In figure, a resistance coil, wired to an external battery, is placed inside a thermally insulated cylinder

fitted with a frictionless piston and containing an ideal diatomic gas. A current i = 200 mA exists in the

coil, which has a resistance R = 350. If the pressure of the gas remains constant, what should be the

speed v (in cm/s) of the piston, of mass m = 10kg ? (Take patm

= 105Pa, A = 10 cm2)

v

m

Coil

i

+


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Q.5 We start two pendulum-clocks at the same time. Of the two only one is accurate, and only at its100

swing the two clocks swing together again. By what percentage do we have to change the length of the

inaccurate pendulum to make it accurate?


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Q.6 Two blocks of mass 1 kg and 0.5 kg moving in opposite direction with velocity of 0.5 m/s and 1 m/s

respectively collide. Coefficient of restitution is e =2

1. After collision, the loss in energy is distributed

equally between both the blocks. The specific heat capacity of 1 kg block is 1000 J/kgC and the

change in its temperature (in 103C) is T. Find 64T.


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PART-A



Q.1 In an unielectronic species of unknown atomic number a transition of electron from a higher energy level

to ground state resulted in emission of a photon having energy approximately 108.9 eV . If the change in

wavelength of the electron in the two levels is two times the circumference of its first Bohr orbit then what

would be the atomic number Z and orbit number of the higher energy shell involved?

(A) Z = 3, n = 3 (B) Z = 2, n = 10 (C) Z = 6, n = 6 (D) Z = 4, n = 3

Q.2 The effective atomic number of Co(CO)4

is 35. It does not attain stability by

(A) Oxidation of [Co(CO)4] (B) Reduction of [Co(CO)

4]

(C) Dimerisation of [Co(CO)4] (D) By both (B) and (C)

Q.3 Which of the following compound(s) will give blue colour when it is converted into Lassaigne's extract

and FeSO4

is added followed by FeCl3.

(I) (II) (III) CH3NMe

2(IV) NH

2NH

2

(A) III only (B) II & III (C) II, III & IV (D) I, II, III & IV

Q.4 What is correct name of linkage isomer of [Cr(H2O)

5(NO

2)] Br

2.

(A) Pentaaquanitrito-'O' chromium (III) bromide. (B) Pentaaquanitro chromium (III) bromide.

(C) Pentaaquonitro chromium (III) bromide. (D) Pentaaquanitrito-'O' chromium (II) bromide.

Q.5 What is the hybridisation of Fe in sodium thionitroprusside?

(A) sp3d2 (B) d2sp3 (C) sp3d (D) no hybridisation.


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[PARAGRAPH TYPE]



In quantitative estimation of any element using an oxidizing agent it is essential to predict which substance(s)

gets oxidized by the oxidizing agent. In case more than one substance are getting oxidized then the

oxidizing agents gets distributed in all the reactions taking place. From this information and the data given

below answer the questions that follow.

Fe+2 Fe+3 + e

EO.P. =

0.77VMnO

4

+ 8H+ + 5eMn2+ 4H

2O E

R.P.= 1.51V

2Cl Cl2

+2e EO.P.

=1.36V

2SO42 S

2O

82 + 2e E

O.P.=2.0V

C2O

42 2CO2 + 2e

EO.P.

=0.77V

Cr2O

72

+ 14 H+ + 6e 2Cr+3 + 7H2O ER.P. = 1.33V

Q.6 Which of the following cannot be used for quantitative estimation of FeC2O

4?

(A) K2Cr

2O

7in presence of dil H

2SO

4. (B) K

2Cr

2O

7in presence of dil. HCl.

(C) KMnO4

in presence of dil. HCl. (D) KMnO4

in presence of dil. H2SO

4

Q.7 Millimoles of FeC2O

4in the solution if 50 ml of 0.1M K

2Cr

2O

7is used for its oxidation in presence of

dil. H2SO

4.

(A) 10 millimoles (B) 30 millimoles

(C) 20 millimoles (D) quantitative estimation can't be made from given data.

Q.8 Millimoles of FeC2O

4in the solution if 50ml of 0.1M KMnO

4is used for its oxidation in presence of

dil. HCl if 3.5 millimoles of Cl2is obtained along with other products.

(A) 25/3 millimoles (B) 6 millimoles

(C) 12.5 millimoles (D) quantitative estimation can't be made from given data.


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CHCH3

OH

H

H

NH2

C CH

CH3

NHCH3

CH3

N

(a)

(d)

(e)

(f)

(g)

(c)

(h)

(b)

Q.9 What is correct order of CH bond energy.

(A) b > c > a (B) c > a > b (C) b > a > c (D) a > c > b

Q.10 Which of the following is correct order of acidic strength.

(A) h > d > g (B) h > g > d (C) g > d > h (D) d > h > g

Q.11 Which of the following is correct order of basic strength.

(A) f > e > d (B) d > f > e (C) e > f > d (D) f > d > e


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PART-B

[MATRIX TYPE]

Q.1 has Four statements (A,B,C,D) given in Column-I and Five statements (P, Q, R, S, T) given in Column-II.

Any given statement in Column-Ican have correct matching with one or more statement(s) given in Column-II.

Q.1 Column I Column II

(Polymer) (Monomers involved)

(A) Nylon-6 (P) 1,3-butadiene

(B) Buna-N (Q) Terephthalic acid

(C) Neoprene (R) Ethylene glycol

(D) Terylene (S) Caprolactum

(T) Chloroprene


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PART-C

[INTEGER TYPE]


Instruction for Q.1 & Q.2

Partial Marks will be awarded (+2) for correct value of 'ab' (+2) for correct value of 'cd' and

(+1) as bonus if both are correct.

Q.1 50ml of a weak monoprotic acid was titrated with 0.1M solution of NaOH. If pH of the solution afteradding 50 ml and 75 ml of base is 4.699 and 5 then calculate a four digit number 'abcd' where :

ab = pKa of the weak acid

cd = pH of the solution when 7.5 millimoles of HCl are added in the solution at the equivalence point

without changing volume.

[Given : log 2 = 0.301]


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Q.2 Dissociation of a salt A2B

3(aq) in water follows first order kinetic in terms of concentration of [A

2B

3] as

A2B

3(aq) 2A+3(aq) + 3B2(aq). Starting from t = 0, solution is taken out at different instant and its

osmotic rise is measured. From the given data calculate 'abcd'

ab = t3/4 of the dissociation of A2B3 in water in minutes.

cd = Osmotic pressure in Pascal after 20 min. if density of solution is 1gm/ml.

Given data : t = 0 t = 10 min

osmotic rise 2 mm 6 mm


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Q.3 The number of ions furnished per molecule of the complex [Cr(NH3)6]Cl

3is / are

If your answer is 2, write the answer as 0002.


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Q.4 A metal 'M' having atomic mass 31.25 crystallizes in cubic close packing and it shows "Schottky defects".

If the edge length of the cubic lattice is 500 pm and density of the metal is 1.6075 gm/ml then calculate

number of moles of metal atom 'M' missing per litre of the crystal.

Given : 1amu = 1.67 1024 gm


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Q.5 If Hund's rule violet then how many unpaired electrons are present in [Cr(H2O)

6]3+



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Q.6 When one 'b' is replaced by 'c' in [M(AB)a2bc]n type of complex, then total number of stereoisomer is

reduced by _______.



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rt solutions-04!03!2012 xiii vxy paper ii final test code a

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