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

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

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

VERY IMPORTANT

A. 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 (15 questions in Part-Aand 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-A

1. Q.1 to Q.7 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 3 marks, if you have darkened only the

bubble 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.8 to Q.10 are Paragraph type. Based upon the paragraph 3 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 zero

mark if no bubble are darkened. In all other cases, minus one (1) mark will be awarded.

3. Q.11 to Q.15 are multiple correct type questions.Each question has four choices (A), (B), (C) and (D) out

of which ONE OR MORE may be correct.For each question, you will be awarded 4 marks if you have darkened

only the bubble corresponding to the correct answer andzero mark if no bubble are darkened. No negative marks

will be awarded in this section.

PART-C

4. Q.1 to Q.6 are Integer Type questions. The answer to each question is upto 4 digit ranging from0 to 9999. 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 answer

and 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 number

you 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 point

Pen 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- I


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MATHEMATICS

XIII (VXYZ) Final Test [Paper-I] Code-A Page # 2

Rough Work

PART-A

[SINGLE CORRECT CHOICE TYPE]

Q.1 to Q.7 has four choices (A), (B), (C), (D) out of which ONLY ONE is correct.

Q.1

1

1

xxxxdx6321nx l has the value equal to

(A) 0 (B) ln 6 (C)3

1ln 6 (D)

3

2ln 6

Q.2 Let f : R R be a differentiable function such that f '(x) > f(x) x R and f (x0) = 0, then

(A) f(x) < 0 0xx (B) f(x) 0 0xx (C) f(x) > 0 0xx (D) f(x) 0 0xx

Q.3 Let f(x) =

0x,x

xx1

0x,3

0x,x

5xcos)xsinx1(

x

1

2

3

2

If f(x) is continuous at x = 0, then the value of (2 + 2 + 2 + e2), is(A) 8 (B) 10 (C) 12 (D) 26


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MATHEMATICS


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Q.4 Number of values of x satisfying simultaneously

sin1x = 2 tan1 x and tan1 )1x(x + cosec1 2xx1 =2

, is

(A) 0 (B) 1 (C) 2 (D) 3

Q.5 Tangent drawn to an ellipse 11

y

4

x22

at the point with eccentric angle 30 cuts the director circle

of ellipse at P and Q. The area of triangle OPQ is (where O is origin)

(A)7

194(B)

7

192(C)

7

196(D)

7

198

Q.6 The area bounded by the curve y = sin1x + cos1x + tan1

x

1+ tan1 x, y-axis and

the line 2y = (x + 1) is equal to

(A)sq. units (B)2

sq. units (C)

3

sq. units (D)

4

sq. units

Q.7 The smallest positive root of the equation x1sin = xcos is

(A)2

1

4

3

(B)

2

1

4

7

(C)

2

1

4

11

(D)

2

1

4


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MATHEMATICS


Rough Work

[PARAGRAPH TYPE]


Paragraph for Question no. 8 to 10

Let P1

be a plane containing two lines L1

:1

4z

0

y

3

2x

and L2

:1

2z

0

y

2

7x

P2

be another plane containing a triangle whose vertices are (3, 2, 0), (2, 0, 0) and (0, 5, 0).

P is the point of intersection of L1

= 0 and L2

= 0.

Q.8 If M is the projection of the point P on the line P1

= 0 = P2

then area of triangle OPM is

(where 'O' is the origin)

(A)2

345sq. units (B) 345 sq. units (C)

2

15sq. units (D) 0 sq. units

Q.9 If acute angle between the lines L1

= 0 and P1

= 0 = P2

is cot1 () then is(A) 3 (B) 5 (C) 7 (D) 10

Q.10 Image of the line L1

= 0 in the plane P2

is

(A)1

3z

0

y

3

5x

(B)1

3z

0

y

3

5x

(C)1

z

0

y

3

14x

(D)

1

z

0

y

3

14x


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MATHEMATICS


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[MULTIPLE CORRECT CHOICE TYPE]

Q.11 to Q.15 has four choices (A), (B), (C), (D) out of which ONE OR MORE may be correct.

Q.11 Locus of the centre of the circle which touches the two circles x2 + y2 + 8x9 = 0

and x2 + y28x + 7 = 0 externally, is a conic whose

(A) eccentricity is 2 (B) auxiliary circle is x2 + y2 = 1

(C) length of latus rectum is 30 (D) co-ordinates of focus are (4, 0) and (4, 0)

Q.12 In the given figure AO (O being origin) is the median through the

vertex A of the triangle ABC. Also, given the two upward

parabolas P1

and P2.

y

xO

C

B

A

P1

: y = x2 + 2px + q (p, q R) is passing through A and has its vertex at B.P

2: y = ax2 + 2bx + 1 (a, b R) is passing through A and has its vertex at C.

Which of the following is/are correct?

(A) the sum of all the roots of the equation (x2 + 2px + q) (ax2 + 2bx + 1) = 0 is zero.

(B) ab > 0

(C) p21 = q a

b2

.

(D) ap + b = 0.

Q.13 The value of the constant term in the trinomial

10

2

2 2x

1x

is also equal to

(A) number of different dissimiliar terms in (x1

+ x2

+ ......... + x10

)10.

(B) (10C0)2 + (10C

1)2 + (10C

2)2 + ........ + (10C

10)2

(C) coefficient of x10 in (1 x)20.

(D) number of linear arrangements of 20 things of which 10 alike of one kind and rest all are different.


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MATHEMATICS


Rough Work

Q.14 Let f(x) be a non-constant differentiable function satisfying f(x) = x2 1

0

2dtx)t(f .

Then which of the following is/are correct ?

(A) f(x) is monotonic.

(B) x3cosec

3

4x

)x(fLim

is equal to 1

e .

(C) Derivative of f(x) w.r.t ln x at x = 1 is equal to 3.

(D) Area bounded by f(x) and co-ordinate axes is3

2.

Q.15 Which of the following statement(s) is/are true?

(A) Two disjoint events E and F defined on S are such that P(E) 0 and P(F) 0can be independent.

(B) The events E, FE and FE defined on a sample space S are exhaustive.

(C) If FEP > P(E) then EFP > P(F).

(D) Probability that a positive integer randomly selected will not be divisible by 2 and 3 is21 .


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MATHEMATICS


Rough Work

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 In triangle ABC, ifC =8

, a = 2 and b = 22 , then find the value of (abc)2.

[Note :All symbols used have usual meaning in triangle ABC.]


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MATHEMATICS


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Q.2 Find the number of different non-singular matrices of the form

ww0b11

ca1

where w = ei and a, b, c {z : z41 = 0}.


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MATHEMATICS


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Q.3 PQ, a variable chord of the parabola y2 = 4x subtends a right angle at the vertex. The tangents at P and

Q meet at T and the normals at those points meet at N. If the locus of the mid point of TN is a parabola,

whose length of latus rectum is L, then find the value of 2L.


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MATHEMATICS


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Q.4 Bowl A has 6 red balls and 4 blue balls. 5 balls are drawn simultaneously and kept in a bowl B which

was empty. Now a ball is randomly taken out from the bowl B and found to be blue. If the probability

that 2 red and 3 blue balls were transferred from bowl A to B is nm where m and n arerelatively prime, find (m + n).


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MATHEMATICS


Rough Work

Q.5 Let the complex number z satisfies the inequalities |3z|log|3z|log2

2

1i > 0,

4)1z(amp

i

and | z | 5. If area of common region in which complex number z lies isb

awhere a, b are relatively

prime numbers then find the value of (a + b).


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MATHEMATICS


Rough Work

Q.6 For a positive constant t, let and are the roots of the equation x2 + t2x2t = 0. If the minimum

value of dx11

x1

x

2

1

22

isc

ba . (where b and c are coprime), then find the

value of (a + b + c).


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PHYSICS

XIII (VXY) Final Test [Paper-I] Code-A Page # 13

Rough Work

PART-A



Q.1 A uniform disk, hoop, and sphere each of mass m and radius r are rolled up a ramp without slipping. All

starting with the same center of mass velocity vcm

. Rank the order of the maximum height h that each

object reaches.(A) hdisk

> hhoop

> hsphere

(B) hhoop

> hdisk

> hsphere

(C) hsphere

> hdisk

> hhoop

(D) hhoop

> hsphere

> hdisk

Q.2 A block of mass 1 kg lies on a horizontal surface in a truck. The coefficient of static friction between the

block and the surface is 0.6. If the acceleration of the truck is 5 m/s2, the frictional force acting on the

block is :

(A) 0.5 N (B) 5 N (C) 6 N (D) 10 N

Q.3 A wire of radius R carries a current I uniformly distributed throughout its interior.Which plot best represents

the magnitude of the magnetic field as a function of r, the distance from the center of the wire?

(A)

O R 2R

Field

r

(B)

O R 2R

Field

r

(C)

O R 2R

Field

r

(D)

O R 2R

Field

r


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PHYSICS


Rough Work

Q.4 Sudbury's Creighton mine is one of the deepest in the world (2.07 km). In this mine the conditions as

compared to those at the surface are,

(A) lower air pressure, higher acceleration due to gravity

(B) higher air pressure, lower acceleration due to gravity

(C) higher air pressure, higher acceleration due to gravity

(D) lower air pressure, lower acceleration due to gravity

Q.5 A 5 106 coulomb electric charge is placed midway between two parallel metal plates connected to a

9-volt battery. If the electric charge experiences a force of 1.5 104 newtons, what is the separation of

the metal plates?

(A) 2.7 104 m (B) 3.7 103 m (C) 0.30 m (D) 3.3 m

Q.6 Four very long straight wires carry equal electric currents in the +z direction. They intersect the x-y plane

at (x, y) = (a, 0), (0, a), (a, 0) and (0, a). The magnetic force exerted on the wire at position

(a, 0) is along

(A) +y (B)y (C) +x (D)x

Q.7 Two beams of light having intensities I and 4I interfere to produce a fringe pattern on the screen. Phase

difference between the beams is 2

at point A and at point B. Then the difference between resultant

intensities at A and B is

(A) I (B) 2I (C) 3I (D) 4I


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PHYSICS


Rough Work

[PARAGRAPH TYPE]


Paragraph for question nos. 8 to 10

The energy-level scheme for the hypothetical one electron element Bansalium is shown in figure. The

potential energy is taken to be zero for an electron at an infinite distance from the nucleus.

2eVn = 45eVn = 3

10eVn = 2

20eVn = 1

Q.8 A sample of atoms Bansalium are in all the 3 excited state shown above. What is the possible wavelength

that can be emitted by atom in visible range ?

(A) 414 nm (B) 620 nm (C) 124 nm (D) 920 nm

Q.9 If a Bansalium atom is in ground state, which of the following photons cannot excite the atom to a higher

state ?

(A) 10 eV (B) 15 eV (C) 18 eV (D) 12 eV

Q.10 If photons emitted from Bansalium transitions n = 4 n = 2 and from n = 2 n = 1 will eject

photoelectrons from an unknown metal but the photon emitted from the transition n = 3n = 2 will not,

what are the limits (maximum and minimum possible values) of the work function of the metal ?

(A) 8 eV < < 10 eV (B) 5 eV < < 10 eV

(C) 5 eV < < 8 eV (D) 5 eV < < 12 eV


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PHYSICS


Rough Work

[MULTIPLE CORRECT CHOICE TYPE]


Q.11 In the given circuit,

~

R = 5 V =30 voltC

V =20 voltL1A

(A) current leads the voltage in phase (B) voltage leads the current in phase.

(C) power factor of the circuit is5

1(D) Applied voltage is 15 V.

Q.12 A satellite of mass m orbits a planet of mass M in a circular orbit of radius R. The time required for one

revolution is

(A) independent of M (B) proportional to m

(C) proportional to R3/2 (D) proportional to R2

Q.13 A ray of light from a denser medium strikes the plane boundary of a rarer medium at an angle of incidence

I. The angle of refraction is r. If the reflected and the refracted rays are mutually perpendicular, the criticalangle of the medium is

(A) sin1(cot I) (B) sin1(tan I) (C) sin1(cot r) (D) sin1(tan r)

Q.14 A particle on a spring executes simple harmonic motion. When the particle is found at x =2

xmax

then

(A) speed= vmax

/ 2 (B) speed= 3 vmax / 2

(C) acceleration = 3 amax / 2 (D) acceleration = amax / 2

Q.15 According to the principles of newtonian physics, which of the following depend on the frame of reference?(A) Real Force (B) Time elapsed (C) Work (D) Kinetic energy


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PHYSICS


Rough Work

PART-C

[INTEGER TYPE]


Q.1 An air bubble of radius r = 3mm moves up in a viscous liquid with a constant velocity v = 0.7 cm/sec.

If the density of the liquid is 1.75 gm/cc. Find the viscosity of liquid (in poise). Neglect the density of air

in comparison to that of the liquid.


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PHYSICS


Rough Work

Q.2 A solid Hemisphere rests in equilibrium on a rough ground and against a smooth wall. The curved

surface touches the wall and the ground. The angle of inclination of the circular base to the horizontal is

30, Find minimum coefficient of friction required between ground and hemisphere. Fill 32 in OMR

sheet.


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PHYSICS


Rough Work

Q.3 The figure shows two circuits with a charged capacitor that is to be discharged through a resistor as

shown. The initial charge on capacitors is1

2

q

q= 2. If both switches are closed at t = 0, the charges

become equal at 104ln2 sec. Find the resistance R (in).

q1

q1 5F

5q

2

q2 10/3F

R


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PHYSICS


Rough Work

Q.4 A wooden block of mass 0.6 kg of size 10 cm 10 cm 10 cm is floating over an unknown liquid as

shown in the figure

4 cm

How much minimum mass (in gm) should be kept on the wooden block so that it completely submerges

into liquid ?


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PHYSICS


Rough Work

Q.5 A spherical black body of diameter 0.10 m is held at constant temperature. If the power radiated by the

body is 5.67 102 Js1 , the temperature of the body (in K) is


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PHYSICS


Rough Work

Q.6 A uniformly wound solenoidal coil of self-inductance 1.8 104 henry and resistance 6 ohms is broken

up into two identical coils. These identical coils are then connected in parallel across a 12 volt battery of

negligible resistance. The time constant for the current in the circuit is _______ 105 seconds.


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CHEMISTRY


Rough Work

PART-A



Q.1 Which of the crystal system has none of the interfacial angle equal to 90.

(A) Hexagonal (B) Trigonal (C) Monoclinic (D) Orthorhombic

Q.2 The minimum number of 90 angles between hybrid orbitals is observed in

(A) sp3d2 (B) d2sp3 (C) dsp2 (D) sp3d

Q.3

OO||||

HCCCl

)excess(NaOH

(A) COONaCH

||O

(B) COONa

|COONa

+ COONa|

OHCH2

(C)

O||

COONaCCl +

O||

OHCHCCl 2 (D)

OH|

COONaCH|Cl

Q.4 Which of the following ideal aqueous solutions will show maximum boiling point.

(A) 0.5 M NaCl showing 50% dissociations

(B) 0.3 M K2Fe[Fe(CN)

6]

(C) 1 M Glucose solution

(D) 1 mole of AgCl is mixed with 0.5 l of H2O


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CHEMISTRY


Rough Work

Q.5equivalent1

/SOHHNO 423

(A)

ONaCH3

(B).

Product (B) is

(A) (B) (C) (D)

Q.6 Statement-1 : 7N15 is a emitter.

Statement-2 : emission decreases n/p ratio and increases stability if n/p is greater than 1 for lower

atomic number.

(A) Statement-1 is true, statement-2 is true and statement-2 is correct explanation for statement-1.

(B) Statement-1 is true, statement-2 is true and statement-2 is NOT the correct explanation for statement-1.

(C) Statement-1 is true, statement-2 is false.

(D) Statement-1 is false, statement-2 is true.

Q.7 Incorrectstatement about given carbohydrate is

OH OH

H HH

OH H

CH OH2

O

OOH

H OH

H OH

HO

H

CH OH2

(A) Above compound is a reducing sugar (B) Above compound undergo mutarotation

(C) Above compound is a non-reducing sugar (D) Above compound has a glycosidic linkage


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CHEMISTRY


Rough Work

[PARAGRAPH TYPE]


Paragraph for question nos. 8 to 10

Covalent compounds undergo in hydrolysis via SN

1 (unimolecular nucleophilic substitution) or SN2

(Bimolecular nucleophilic substitution) mechanism, for SN2 mechanism within the molecule atom should

have at least one vaccant orbital, if it is not there then hydrolysis takes place via SN1 mechanism (dissociative

step) in drastic condition.

Q.8 What are the hydrolysed products of BeCl2 formed during hydrolysis(I) [Be(OH)

4]2 (II) Be(OH)

2(III) HCl (IV) BeH

2

(A) I, II, III (B) II, III (C) I, III (D) II, III and IV

Q.9 Least probable product formed on hydrolysis of BCl3

(A) [B(OH)4] (B) HCl (C) B(OH)

3(D) None of these

Q.10 CCl4

is inert towards hydrolysis under ordinary condition because

(I) No vaccant orbital on attacking site of C-atom.

(II) H2O molecule can not approach to the anti-bonding M.O. of CCl bond due to steric crowding

(III) Bond dissociation energy of CCl bond is highest.

(IV) CCl4 is non polar and does not react with polar H2O moleculeSelect correct code:

(A) I, II and IV (B) I and IV (C) I and II (D) I, II, III and IV

MULTIPLE CORRECT CHOICE TYPE]


Q.11 Which of the following statements is/are correct with respect to surface phenomenon?

(A) Potassium ferrocyanide can cause greater coagulation in a basic dye as compared to Na2HPO

3.

(B) A starch aqua-sol can act as a protective colloid for Fe(OH)3

sol.

(C) The slope of the Freundlich Isotherm (log m

x

vs log P) keeps on changing for a long range ofpressure and is constant over a limited range of pressure.

(D) On mixing AgNO3

with large amount of KI and subjecting the colloidal state to electrophoresis,

coagulation is obtained at cathode.


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CHEMISTRY


Rough Work

Q.12 Which of the following specie(s) is / are having only one corner shared per tetrahedron.

(A) 672OSi (B)

272OCr (C)

272OS (D)

693OSi

Q.13 H

H

Me

Me

Incorrect statement about this compound is:

(A) It shows geometrical isomerism (B) It posses centre of symmetry(C) It posses plane of symmetry (D) It shows optical isomerism

Q.14 Which of the following statements is / are correct with respect to behaviour of real gas.

(A) For every Vander Waal gas at critical condition, attractive forces will be dominant.

(B) The liquid and gaseous state can be distinguished only if the temperature is below the gas's critical

temperature.

(C) At very high pressures, real gases occupy greater volume as compared to ideal gas having same

moles at same temperature and exerting same pressure.

(D) For a real gas the 'y' intercept of

T

PVmvs P curve where 'P' represents pressure (in atm) , V

m

represents molar volume and 'T' represents temperature in kelvin is equal to 0.0821 atm-litre/mol-

Kelvin.

Q.15 Suitable reagent(s) to carry out following conversion is / are

N

CH3

CCH3

O

N Et

CH3

(A)SHCH

|SHCH

2

2

/ H2/ Ni followed by OH (B) N

2H

4/ H

2O

2

(C) N2H

4/ EtONa (D) Zn / Hg / HCl


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CHEMISTRY


Rough Work

PART-C

[INTEGER TYPE]


Q.1 1 l H2O

2solution having 1 M concentration was left open causing first order decay of H

2O

2with rate

constant equal to 6.93 102 sec1. If after 20 sec, the solution is reacted with excess of I(aq) forming

I2

(g) with water then calculate the amount of energy released in kJ.

[Assume no change in volume of H2

O2

solution]

Given Data : mole/kJ200)aq(OHH 22of

; mole/kJ60)aq(IHof

mole/kJ60)g(IH 2of

; kJ290OHH 2of


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CHEMISTRY


Rough Work

Q.2 How many geometrical isomer(s) is / are formed by the complex of the type [Ma2bcde] where, M is the

central metal and a,b,c,d ande are unidentate Ligands?

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


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CHEMISTRY


Rough Work

Q.3 Number of different carbonyl compounds formed during reactions are


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CHEMISTRY


Rough Work

Instruction for Q.4

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.4 0.5 l of a saturated solution of Ag2CrO

4is mixed with 0.5 l of 2 106 M AgNO

3. If concentration of

[CrO42] after mixing is M

2

106

and none of the ions undergo hydrolysis, then calculate a four digit

number abcd, where

ab = 1942sp

10

CrOAgofK

and cd = conductivity of final solution in terms of 1081cm1.

[Assume Temperature of the solution to be 298 K]

Given data : Molar conductance at infinite dilution in 1 cm2 mol1 are

100CrO,50Ag,75NO,200OH,350H24mm3mmm


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CHEMISTRY


Rough Work

Q.5 How many complexes have number of geometrical isomers less than or equal to two?

[CoCl2Br

2]2, [Rh(en)

3]3+, [Cr(en)

2Br

2]+, [Pt(en)Cl

2], [Co(NH

3)3(NO

2)3],

[Pt(NH3)2(SCN)

2], [Cr(NH

3)2

Br2Cl

2]

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


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CHEMISTRY

Rough Work

Q.63

HN

CH(R)CO2H has its Ka

1= 107. The isoelectric point of the -amino acid occur at

pH = 8.2. If pKa2

of the conjugate acid of-amino acid is equal to X, what will be 10X.

[Hint: If pKa2

is 2.4 write 0024 in OMR sheet]

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

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