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Academic Session: 2017-18

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PART : I MATHEMATICS

SECTION – 1 : (Maximum Marks : 60)

This section contains FIFTEEN questions Each question has FOUR options (A), (B), (C) and (D). ONE OR MORE THAN ONE of these

four option(s) is(are) correct For each question, darken the bubble(s) corresponding to all the correct option(s) in the ORS Marking scheme :

+4 If the bubbles corresponding to the answers are darkened0 If none of the bubbles is darkened

–2 In all other cases

1. Let f(x) =

x

0(5 1 t )dt if x 2

5x 1, if x 2

then the function is

(A) continuous at x = 2 (B) differentiable at x = 2(C) discontinuous at x = 2 (D) not differentiable at x = 2

2. The coordinates of a point on the linex 1 y 1

z2 3

at a distance 4 14 from the point (1, –1, 0)

are

(A) 9, 13, 4 (B) 8 14 1, 12 14 1, 4 14

(C) 7, 11, 4 (D) 8 14 1, 12 14 1, 4 14

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3. For any complex number w = a + bi, where a, b R and i 1 . If w cos40 isin40 , then

| 2 3 9w 2w 3w .... 9w |–1 equals

(A) (1

sin409

)sec(20º) (B)2

sin209

(C)1

cos409

(D)9

cosec 202

4. If locus of z is a curve satisfying )z(Re|)i23(z| and z1 & z2 are two point on the curve such

that

)i23(z

)i23(zarg

2

1 then

(A) locus of z is a parabola

(B) locus of z is an ellipse

(C)2i2z

i2zarg

2

1

for all z1, z2 satisfying given condition

(D)2z

zarg

2

1

for all z1, z2 satisfying given condition

5. Let point P moves in first quadrant while satisfying (given O : (0,0), A : (4, 4 3 ) and B : (4,0))(1) It is closer to x - axis than to line OA, and(2) It is closer to origin than to point B,Then area of the region in which point P can move is greater than or equal to .

(A)2

3(B) 3

4

(C)

10

9(D) 1

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6. Given/ 2 / 2 / 2

0 0 0

I cos(sinx)dx, J sin(cos x)dx, K cos xdx,

then which of the following is wrong

(A) I > K > J (B) I > J > K (C) K > I > J (D) K > J > I

7. Let In = /2

n

0

sin x dx

then which of the following statement (s) is (are) true.

(A) 2I 4

(B) 4

3I

16

(C) 1I 1 (D) 3I 3

8. Ten passengers get into an elevator on the ground floor which stops at 20- different floors above

ground floor then the probability that they will all get out at different floors is

(A) 10

20!

10! 20(B)

10

1.3.5...17.19

10(C)

919!

10! 20(D) 20

10!

10

9. Solution to the equation 13x tan (tanx) for x 0, 2 may contain

(A) (0, / 2) (B) ( / 2, ) (C) ( , 3 / 2) (D) (3 / 2, 2 )

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10. Let2n

e e

2n 1n

alog (2 x ) bx log (4 x )f(x) lim

a bx

where a, b R, ab ≠ 0. Then

(A)x 1limf(x)

exists (B)x 1limf(x)

does not exist

(C)x 1lim f(x)

exists (D)x 1lim f(x)

does not exist

11. Let g(x) be a differentiable function for all x, and f(x) = f() + (x – ).g(x) x R. Then

(A) f(x) is necessarily continuous at x = .

(B) f(x) is necessarily differentiable at x = .

(C) f(x) is necessarily continuous at all x R – {}

(D) f '( ) g( )

12. A fair coin is tossed n times. Then

(A) the probability of getting tails an odd number of times is2

1 when n is odd.

(B) the probability of getting tails an odd number of times is2

1 when n is even.

(C) the probability of getting at least one tail is more than 0.99 for n = 7.

(D) the probability of getting at least one tail is more than 0.99 for n = 8.

13. 1

4n 1

4ntan

n 5

(A)4

+ tan–1 2 (B)

4

3–tan–1 2 (C) tan–13 (D)

4

+ cot–12

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14. Let f : [a, b] R be a function such that for c (a, b), f i(c) = fii(c) = fiii(c) = fiv(c) = fv(c) = 0, then

(fn(c) represents nth derivative of f(x))

(A) f has local extremism at x = c

(B) f has neither local maximum nor local minimum at x = c

(C) f is necessarily a constant function

(D) None of these

15. Which of the following is/are correct

(A) The number of skew symmetric 3×3 matrices than can be formed using elements –1, 0, 1 and 2 is 27

(B) The number of skew symmetric 3×3 matrices than can be formed using elements –1, 0, 1 and 2 is 64

(C) The number of symmetric 3×3 matrices than can be formed using elements –1, 0, 1 and 2 is (12)3

(D) The number of either symmetric or skew symmetric 3 x 3 matrices than can be formed using

elements –1, 0, 1 and 2 is 1754

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SECTION – 2 : (Maximum Marks : 20) This section contains FIVE questions The answer to each question is a SINGLE DIGIT INTEGER ranging from 0 to 9, both inclusive For each question, darken the bubble corresponding to the correct integer in the ORS Marking scheme :

+4 If the bubble corresponding to the answer is darkened0 If none of the bubbles is darkened


16. Let f(x) x sinx be an invertible function in

2

,0 . If area bounded by y = f–1 (x) and y = f(x) in

2

,0 is k then value of [6k] will be ({ } represents GIF)

17. If

2n 2n

r 1 r 1

nn

r 1

1r

rlim

34 r

, then =

18. The domain of definition of the function, f (x) =2

1

2

3x 7x 8cos

x 1

where [.] denotes the greatest

integer function, is (a, b). Then a + b =

19. Let (h, k) be a point with integral co-ordinates from which two tangents drawn to the hyperbola2 2x y

17 3 are perpendicular, then the number of distinct values of (h + k) is

20. The solution of the differential equation1

3(x 1)dy ydx x(x 1)y dx is given by2 2

23 31 2

y A(x 1) (x 1) (x 1),4

then the value of should be


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PART - II : PHYSICS

SECTION – 1 : (Maximum Marks : 60) This section contains FIFTEEN questions Each question has FOUR options (A), (B), (C) and (D). ONE OR MORE THAN ONE of these

four option(s) is(are) correct For each question, darken the bubble(s) corresponding to all the correct option(s) in the ORS Marking scheme :

+4 If the bubbles corresponding to the answers are darkened 0 If none of the bubbles is darkened–2 In all other cases

21. Two series resonant circuits with component values L1, C1 and L2, C2 respectively have the sameresonant frequency. They are then connected in series ; the resonant frequency of the combinationis :

(A)1 1

1

2 L C(B)

2 2

1

2 L C

(C) 1 2 1 2

1

2 L L C C (D)

1 2

1

2 L C

22. A non-relativistic particle of mass m is held in a circular orbit around the origin by an attractive

force. The potential energy of the force is given by U(r) =2kr

2.

Assuming the Bohr quantization of the angular momentum of the particle select correctalternatives.

(A)1/2

2 n kv

m m

(B)

1/2n k

rk m

(C)

1/2

nk

E nm

(D) n

kE n

m


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23. Two half convex lenses of focal lengths f1 = 16 cm and f2 = 21 cm respectively are placed such

that their principal axes coincide. Both the lenses form image of a real point object O on a fixedscreen as shown. The distance between object and screen is 100 cm. Then pick up the correctstatement(s)

O

f =16cm1

f =21cm2

lens1

lens2principal axis

fixed screen

(A) The distance of lens1 from object O can be 20 cm(B) The distance of lens 1 from object O can be 80 cm(C) The distance of lens 2 from object O can be 30 cm(D) The distance of lens 2 from object O can be 70 cm

24. A positive charge q is placed inside a neutral hollow conducting sphere of radius R, as shown infigure. Whole system is placed in uniform external vertical electric field pointing downward(line PCQ is also vertical) then select the correct statement(s) about electric field at point P. PointP is a point of the material inside the conductor.

R/2C

Qq

P

E

(A) Electric field due to outer surface of sphere at point P is zero

(B) Magnitude of electric field due to inner surface of sphere at point P is2

0

q

9 R(C) Magnitude of electric field at point P, due to hollow sphere is less than E(D) Direction of resultant electric field at point P due to charge q and hollow sphere is verticallyupward



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25. The range of voltage of a meter used as a voltmeter can be changed to n times its original valuewith the help of a 27 multiplier. Using the same meter as an ammeter, its range of current can bechanged to n times its original value using a 3 shunt. The power dissipated by the moving-coil ofthe meter when giving a full-scale reading is 9 × 10–4 W. Select the correct statement(s).(A) The resistance of the coil is 9 (B) The resistance of the coil is 81 (C) The full deflection current is 9 mA(D) The full deflection current is 10 mA

26. A tightly-wound rigid solenoid coil has been partly inserted into another. They are connected to aconstant current source so that the same current I flows through them ; both generate a magnetic

field in the same direction. The solenoids have N turns both, their length is , their cross-sectional

areas are A1 and A2. It may be assumed that A1, A2 < 2. The centers of the coils are at a distance

x < along their common axis [A1, A2 << (x – )2, x2].

(A) Total energy of the magnetic field in the system is 2 2

01 22

N[A A 3 2x ]

2

(B) The electromotive forces generated in the inner coils is2

0 22

A N

(C) The electromotive forces generated in the outer coils is2

0 22

A N

(D) The electromotive forces generated in the outer coils is zero

27. When no current is passed through a conductor(A) the free electrons do not move(B) the average speed of a free electron over a large period of time is zero(C) the average velocity of a free electron over a large period of time is zero(D) the average of the velocities of all the free electrons at an instant is zero


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28. In the given circuit all ammeters are ideal. Then choose correct statement.

A4

A3

A2

A1

A5

10V

5V

10V

8V

(A) Reading of A2 = Reading of A5.(B) Reading of A2 and Reading of A4 both are zero.(C) Reading of A1 is 5 amp(D) Reading of A1 = 2.5 times reading of A3.

29. Two capacitors of capacitance 1 µF and 2 µF are separately charged by a common battery. Thetwo capacitors start discharging through equal resistances separately at t = 0.(A) The current in each of the two discharging circuit is zero at t = 0(B) The currents in the two discharging circuits at t = 0 are equal but not zero(C) The currents in two discharging circuits are equal at all times(D) Capacitor of 1 µF capacity loses 50% of its charge earlier than capacitor of capacity 2 µF

30. The radii of a spherical capacitor are equal to a and b (b > a). The space between them is filledwith a dielectric of dielectric constant K and resistivity . At t = 0, the inner electrode is given acharge q0. Choose the correct option(s) :

(A) Charge q on the inner electrode as a function of time is given by 0

t

K0q q e

(B) In a short time, the charge on the inner electrode will become zero(C) After a long time, the charge on the outer sphere will become q0

(D) The total amount of heat generated during the spreading of charge will be given by2

0

0

q1 1H

a b 8



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31. A small current element of length ‘ d’ and carrying current is placed at (1, 1, 0) and is carrying

current in ‘ + z ’ direction. If magnetic field at origin be 1B

and at point (2, 2, 0) be 2B

then :

(A) 1 2|B | |B |

(B) 1 2B B

(C) 1 2| ||B | 2B

(D) 1 2B 2B

32. A charged particle is projected in magnetic field B

= 10 k̂ from origin in x-y plane. The particle moves in a

circle and just touches a line y = 5 m at x = 5 3 m. Then (mass of particle = 5 × 10–5 kg, charge = 1µc) -

(A) The particle is projected at an angle 60° with x-axis

(B) The radius of circle is 10 m

(C) speed of particle is 2m/s

(D) workdone by magnetic force on the particle is zero.

33. A neutron beam, in which each neutron has same kinetic energy, is passed through a sample of

hydrogen like gas (but not hydrogen) in ground state and at rest. Due to collision of neutrons with

the ions of the gas, ions are excited and then they emit photons. Six spectral lines are obtained in

which one of the lines is of wavelength (6200/51) nm. The mass of neutron and proton can be

assumed to be nearly same. Use hc = 12400 eVÅ.

(A) The gas is helium

(B) This gas is lithium

(C) minimum possible value of kinetic energy of the neutrons for this to be possible is 63.75 eV

(D) minimum possible value of kinetic energy of the neutrons for this to be possible is 12.75 eV


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34. In a decay process A decays to B,

AB

Two graphs of number of nucli of A and B versus time is given then :

(A) t2 – t1 = 4 (B) t2 – t1 = 2 (C) t1 = 2 log25 (D) t2 = log2100

35. Graph shows variation of source emf V and current i in a series RLC circuit, with time.

i

V

t

V/i

(A) The current leads the emf in the circuit.

(B) The circuit is more inductive than capacitive.

(C) To increase the rate at which energy is transferred to the resistive load, L should be decreased.

(D) To increase the rate at which energy is transferred to the resistive load, L should be increased.


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This section contains FIVE questions

The answer to each question is a SINGLE DIGIT INTEGER ranging from 0 to 9, both inclusive

For each question, darken the bubble corresponding to the correct integer in the ORS

Marking scheme :+4 If the bubble corresponding to the answer is darkened 0 If none of the bubbles is darkened–1 In all other cases

36. A parallel beam of light falls on a quarter cylinder of radius 9 cm, as shown in figure (A). Refractive

index of the material of the cylinder is 3 . Maximum value of OP (in cm ), as shown in figure (B),

so that rays don’t suffer TIR at the curved surface is (consider refractive index of surroundingmedium equal to 1)

(B)

PO

(A)

O600

37. Light of wavelength 6000Å falls normally on a thin wedge shape film of refractive index 1.5, fringesthat are 2mm apart. The angle of the wedge is nearly P × 10–4 rad. Find the value of P.

38. The K line has a wavelength for an element with atomic number Z = 19. The atomic number of

an element with has wavelength /4 for the K line is 10P + Q. Find the value of Q – P ?


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39. The electric field in a region is radially outwards with magnitude E = r/. In a sphere of radius R

centered at the origin, calculate the value of charge in coulombs if5

V/m2 and

1/ 33

R m10

.

40. In the L–C circuit, the capacitor C1 is charged to a potential of 1 volt, and the capacitor C2 and the

inductor were initially uncharged. Now switch S1 is closed at t = 0, and at t =1.5

100

sec. switch S2 is

closed and S1 is opened. After0.5

100

sec. , S2 is also opened. Find final potential difference across

the capacitor C2 in volt.


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PART - III : CHEMISTRYAtomic masses : [H = 1, D = 2, Li = 7, C = 12, N = 14, O = 16, F = 19, Na = 23, Mg = 24, Al = 27, Si = 28,

P = 31, S = 32, Cl = 35.5, K = 39, Ca = 40, Cr = 52, Mn = 55, Fe = 56, Cu = 63.5, Zn = 65, As = 75,

Br = 80, Ag = 108, I = 127, Ba = 137, Hg = 200, Pb = 207]


This section contains FIFTEEN questions

Each question has FOUR options (A), (B), (C) and (D). ONE OR MORE THAN ONE of these

four option(s) is(are) correct

For each question, darken the bubble(s) corresponding to all the correct option(s) in the ORS

Marking scheme :

+4 If the bubbles corresponding to the answers are darkened

0 If none of the bubbles is darkened


41. For the endothermic reaction

3A(g) B(g) + C(g)

select the option(s) by which equilibrium concentration of A(g) can be increased ?

(A) Decreasing the temperature

(B) Increasing the volume of the container

(C) Decreasing the volume of the container

(D) Adding B(g) at equilibrium

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42. Which of the following statement(s) is/are correct ?

(A) Diamond have dangling bonds

(B) Fullerenes are cage-like molecules.

(C) Graphite is thermodynamically most stable allotrope of carbon.

(D) Graphite is slippery and therefore is used as dry lubricant in machines.

43. Which of the following is/are correctly matched for given species ?

(A) XeO3 : Three (p-d) bonds (B) H2SO3 : One (p-d) bonds

(C) SO3 : Three (p-d) bonds (D) HClO3 : Two (p-d) bonds

44. At Boyle’s temperature, the graph of Z v/s P is drawn for H2. Select incorrect graph(s) :

(A)

P 200 atm

(B)

200 atm

(C)

200 atm

(D)

Z

P 200 atm

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45. An amount of 20g potassium sulphate was dissolved in 150 cm3 of water. The solution was then

electrolysed. After electrolysis the content of potassium sulphate in the solution was 15% by mass.

Determine volume of the gases obtained at NTP ? ( OH2d = 1 g cm–3)

(A) 45.6 L H2 gas (B) 22.8L O2 gas

(C) 42 L H2 gas (D) None of these

46. Titanium metal is extensively used in aerospace industry because the metal imparts strength to

structures but does not unduly add to their masses. The metal is produced by the reduction of

TiCl4() which in turn is produced from mineral rutile TiO2(s). The following reaction for production

of TiCl4() be carried out at 25ºC: TiO2(s) + 2Cl2(g) TiCl4()+O2(g)

Given that ºfH for TiO2(s), TiCl4(), Cl2(g) and O2(g) is –944.7, –804.2, 0.0, 0.0 KJ mol–1. Sº for

TiO2 (s), TiCl4 (), Cl2 (g) and O2(g) is 50.3, 252.3, 233.0, 205.1 Jmol–1K–1 respectively. Select

correct option(s) :

(A) ºrH 0

(B) ºrS 0

(C) ºrG 0

(D) Reaction is not possible under standard conditions

47. A buffer solution can be prepared by mixing solution of :

(A) Potassium chloride and Potassium hydroxide.

(B) Ammonium hydroxide and Ammonium chloride.

(C) Acetic acid and Sodium acteate.

(D) Boric acid and borax.

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48. Sodium thiosulphate is prepared by ?

(A) Boiling Na2SO3 solution with S in acidic medium.

(B) Boiling NaOH solution with S.

(C) Neutralising H2SO3 solution with NaOH.

(D) Boiling Na2SO3 with S in absence of air.

49. Choose the correct statement(s) from the following :

(A) Beryllium is not readily attacked by acids because of the presence of an oxide film on the

surface of the metal.

(B) Beryllium sulphate is readily soluble in water as the greater hydration enthalpy of Be2+

overcomes the lattice enthalpy factor.

(C) Beryllium exhibits Co-ordination number more than four.

(D) Beryllium oxides is purely acidic in nature.

50. In a cubic unit cell, atoms A are present at all corner, B atoms are present at non-adjacent face

center and also at edge centers which are not common to the faces containing B atoms at the

centres. C atoms are present at body centre & remaining face centers. The formula of given solid

cannot be:

(A) AB2C3 (B) AB2C2

(C) ABC (D) AB2C

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51. Which of the following is the correct option/s of reagent for the given conversion

COOHCH4

(A) Br2/h(1eq.) , MgCl, Br2/h(1eq.), HCOOH

(B) Br2/h(1eq.) , MgCl, Br2/h(1eq.), Mg/dry ether, CO2/H3O

(C) Cl2/h(1eq.) , MgCl, Br2/h(1eq.), KCN/H3O

(D) Cl2/h(1eq.),CH3–MgBr, Br2/h(1eq.), CH3–COOH

52. Observe the following reaction & choose the correct option/s :

XY + Z

KOHHO

OK

O(formed from Z)

(A) X is KMnO4/H (B) Y is

O

O

(C) Z isCH=O

CH=O(D) X is O3/Zn–H2O

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53. Observe the following reaction

(1) CH3–C–Cl/AlCl3

O

(2) Zn-Hg/HCl XNBS/

YNaOH

ZMnO2/

W

Choose the correct options

(A) W gives +ve test with 2,4-DNP (B) W gives +ve test with tollens reagent

(C) W gives iodoform with I2/NaOH (D) W is acetophenone

54. In which of the following reaction's, carbocation is involved as intermediate

(A) O—H/H2O (B)

Cl

Na,dry acetone

(C)HBr(1eq.)

(D)HCl/Peroxide

55. The structures of the compound that gives a tribromo derivative on treatement with bromine water

is/are:

(A)

CH3

OH

(B)

CH3

OH

(C)

SO3H

OH

(D)

COOH

OH

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This section contains FIVE questions

The answer to each question is a SINGLE DIGIT INTEGER ranging from 0 to 9, both inclusive

For each question, darken the bubble corresponding to the correct integer in the ORS

Marking scheme :

+4 If the bubble corresponding to the answer is darkened

0 If none of the bubbles is darkened


56. Orbital angular momentum of an electron ish

3 , then the number of possible orientations of this

orbital in space is:

57. How many of the following underlined element are sp3 hybridized.

[Cu(NH3)4]+2 , 3PCl , 3BCl , [Pt(en)2]

+2 , [Ni(CO)4], 2CS ,

24SO , 2SnCl 4SnCl , 2HgCl , 4ClO , 42C H , 3CH , 3CH ,

4NH , 3C F , 3NO , 3ClO , 3PH , 2

4Ni CN

, 5PCl ,

2CH O , 6SF , 2Cl CO , 3

, 2H S

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58. When pyrolusite is heated with KOH in presence of air, a green colored compound results. What is

the oxidation number of Mn in this compound ?

59. Observe the following reaction

(1) CH3–CH=CH2/H

CH3O(2) KMnO4/

(3) H

Major product

Number of –COOH functional groups are present in major product

60. (P)

NH2

OH

Number of chiral carbon in P = x

(Q)

CH=CH–CH3

CH=CH–CH3

Number of geometrical isomers in Q = y

The value ofy

xis :

Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose.GENERAL %1. The sealed booklet is your Question Paper. Do not break the seal till you are instructed to do so.2. The question paper CODE is printed on the right hand top corner of this sheet and the right hand top corner of the back cover of

this booklet.3. Use the Optical Response Sheet (ORS) provided separately for answering the question.4. Blank spaces are provided within this booklet for rough work.5. Write your Name and Roll Number in the space provided on the below cover.6. After the open booklet, verify that the booklet contains all the 60 questions along with the options are legible.

QUESTION PAPER FORMAT AND MARKING SCHEME :7. The question paper has three parts : Mathematics, Physics and Chemistry. Each part has two sections.8. Each section as detailed in the following table :

Full Marks Partial Marks Zero MarksNegative

Marks

1

One orMore

CorrectOption(s)

15

+4If only the bubble(s)corresponding to allthe correct option(s)

is(are) darkened

–

0If none of

the bubblesis darkened

–2In all other

cases60

2Single digitInteger (0-9)

5

+4If only the bubbles

corresponding to thecorrect answer is

darkened

–0

if notattempted

–1In all other

cases20

SectionQuestion

TypeNumber ofQuestions

Category-wise Marks for Each Question MaximumMarks of

the Section

OPTICAL RESPONSE SHEET :9. Darken the appropriate bubbles on the original by applying sufficient pressure.10. The original is machine-gradable and will be collected by the invigilator at the end of the examination.11. Do not tamper with or mutilate the ORS.12. Write your name, roll number and the name of the examination centre and sign with pen in the space provided for this purpose on

the original. Do not write any of these details anywhere else. Darken the appropriate bubble under each digit of your rollnumber.

DARKENING THE BUBBLES ON THE ORS :13. Use a BLACK BALL POINT to darken the bubbles in the upper sheet.14. Darken the bubble COMPLETELY.15. Darken the bubble ONLY if you are sure of the answer.

16. The correct way of darkening a bubble is as shown here :

17. There is NO way to erase or "un-darkened bubble.18. The marking scheme given at the beginning of each section gives details of how darkened and not darkened bubbles are

evaluated.

Resonance Eduventures Ltd.CORPORATE OFFICE : CG Tower, A-46 & 52, IPIA, Near City Mall, Jhalawar Road, Kota (Raj.) - 324005

Ph.No. : +91-744-3012222, 6635555 | Toll Free : 1800 258 5555Reg. Office : J-2, Jawahar Nagar, Main Road, Kota (Raj.) 324005 | Ph. No.: +91-744-3192222 | FAX No. : +91-022-39167222

Website : www.resonance.ac.in | E-mail : [email protected] | CIN: U80302RJ2007PLC024029

MMAAJJOORR TTEESSTT--11 ((MMTT--11)) ((JJEEEE AADDVVAANNCCEEDD PPAATTTTEERRNN))CCOOUURRSSEE :: VVIIJJEETTAA ((0022JJPP)) CCOODDEE -- 0

0

NAME OF THE CANDIDATE : ………………………………………………………………..………………………

ROLL NO. : ………………………..………………………

I have read all the instructions I have verified the identity, name and roll numberand shall abide by them of the candidate.

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Signature of the Candidate Signature of the Invigilator

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P21-17 PPAAPPEERR--11

PAPER-1 Academic Session: 2017-18 C 0 MAJOR TEST-1 (MT-1) · MATHEMATICS MATHEMATICS Space for...

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