POTENTIAL & CONCEPT EDUCATIONSSpace for rough work Page. 2 AITS-FT # 03 (Dropper Engineering) [SET -...

16
POTENTIAL & CONCEPT EDUCATIONS Most Trusted Institute of North-East Academic Session : 2018 - 19 Date : 27 th January, 2019 | Duration : 3 Hours | Max. Marks : 360 S ET - B Please read the last page of this booklet for the instructions. Potential & Concept Educations Corporate Office : 160, Rajgarh Road, Near Big Bazar, Above Vijaya Bank, 4th Floor, Guwahati - 07 (Assam) Phone No. : +91 92070 - 46780, 96780 - 69546 www. potentialcoaching.in COURSE : Dropper, Fresher, DLP., AITS Note : For Answer keys and accurate Solutions please log on to www.potentialcoaching.in/aits-2018-19 Or Please scan QR code given above. AITS FULL TEST (FT) : FT # 03 (JEE MAIN PATTERN) Target : JEE Main - 2019

Transcript of POTENTIAL & CONCEPT EDUCATIONSSpace for rough work Page. 2 AITS-FT # 03 (Dropper Engineering) [SET -...

Page 1: POTENTIAL & CONCEPT EDUCATIONSSpace for rough work Page. 2 AITS-FT # 03 (Dropper Engineering) [SET - B] - 2018-19 PHYSICS AITS-FT - 03 Engineering 1. The rate of disintegration of

POTENTIAL & CONCEPT EDUCATIONSMost Trusted Institute of North-East

Academic Session : 2018 - 19

Date : 27th January, 2019 | Duration : 3 Hours | Max. Marks : 360

SET - B

Please read the last page of this booklet for the instructions.

Potential & Concept EducationsCorporate Office : 160, Rajgarh Road, Near Big Bazar, Above Vijaya Bank, 4th Floor, Guwahati - 07 (Assam)

Phone No. : +91 92070 - 46780, 96780 - 69546www. potentialcoaching.in

COURSE : Dropper, Fresher, DLP., AITS

Note : For Answer keys and accurate Solutions please log on towww.potentialcoaching.in/aits-2018-19

Or Please scan QR code given above.

AITS FULL TEST (FT) : FT # 03(JEE MAIN PATTERN)

Target : JEE Main - 2019

Page 2: POTENTIAL & CONCEPT EDUCATIONSSpace for rough work Page. 2 AITS-FT # 03 (Dropper Engineering) [SET - B] - 2018-19 PHYSICS AITS-FT - 03 Engineering 1. The rate of disintegration of

Space for rough work Page. 2

AITS-FT # 03 (Dropper Engineering) [SET - B] - 2018-19

PHYSICS AITS-FT - 03Engineering

1. The rate of disintegration of a radioactivesubstance falls from 800 decay/min to 100decay/min in 6 hours. The half-life of theradioactive substance is :(A) 6/7 hour (B) 2 hrs.(C) 3 hrs (D) 1 hr.

2. When a metallic surface is illuminated withmonochromatic light of wavelength , thestopping potential is 5 V0. When the samesurface is illuminated with light of wavelength3, the stopping potential is V0. Then the workfunction of the metallic surface is :

(A) hc6

(B) hc5

(C) hc4

(D) 2hc4

3. A bead of mass m is attached to one end of aspring of natural length R and spring constant

( 3 1)mgKR . The other end of the spring

is fixed at point A on a smooth vertical ring ofradius R as shown in figure. The normal reactionat B just after it is released is :

(A) mg2

(B) 3mg

(C) 3 3mg (D) 3 3mg2

4. In which of the following process the numberof protons in the nucleus increases(A) – decay (B) – decay(C) + decay (D) k – capture

5. In the figure the variation of potential energyof a particle of mass m = 2kg is representedw.r.t. its xcoordinate. The particle moves underthe effect of this conservative force along thex-axis. Which of the following statements isincorrect about the particle :

(A) If it is released at the origin it will move innegative x-axis.

(B) If it is released at x = 2 + where 0then its maximum speed will be 5 m/s andit will perform oscillatory motion

(C) If initially x = – 10 and i. ˆu 6i then it

will cross x = 10(D) x = –5 and x = + 5 are unstable equilibrium

positions of the particle6. A block of mass 10 kg is released on a fixed

wedge inside a cart which is moved withconstant velocity 10 m/s towards right. Takeinitial velocity of block with respect to cart zero.Then work done by normal reaction (withrespect to ground )on block in two second willbe : (g = 10 m/s2).

Page 3: POTENTIAL & CONCEPT EDUCATIONSSpace for rough work Page. 2 AITS-FT # 03 (Dropper Engineering) [SET - B] - 2018-19 PHYSICS AITS-FT - 03 Engineering 1. The rate of disintegration of

Space for rough work Page. 3

AITS-FT # 03 (Dropper Engineering) [SET - B] - 2018-19

(A) zero (B) 960 J(C) 1200 J (D) None of these

7. The diagram shows a solenoid and a loop suchthat the solenoid’s axis lies in the plane of theloop. Both the solenoid and the loop carryconstant currents in the directions as shown inthe diagram. If the system is released from rest,the loop

(A) move towards the solenoid, rotatesclockwise

(B) move towards the solenoid, rotatesanticlockwise

(C) move away the solenoid, rotates clockwise(D) move away the solenoid, rotates

anticlockwise8. The magnetic field at the origin due to the

current flowing in the wire is

(A) 0I ˆ ˆ– (i k)8 a

(B) 0I ˆ ˆ(i k)2 a

(C) 0I ˆ ˆ(–i k)8 a

(D) 0I ˆ ˆ(i – k)4 a 2

9. A vertical wall is in North South direction. Acurrent carrying wire is kept in the wall suchthat to the west of the wall magnetic field istowards South. Then the wire should be(A) vertical and current is upwards(B) vertical and current is downwards(C) Horizontal and current is towards west(D) Horizontal and current is towards east.

10. Magnetic field strength at the centre of regularpentagon made of a conducting wire of uniformcross section area as shown in figure is :

(I) o

05 i 722sin4 a 2

(II) 0(III) Not zero if current 'i' leaves D point instead

of E(IV) Zero even if the current ‘i’ leaves point D

instead of point E(A) I & III (B) II & IV(C) I, II & III (D) None of these

Page 4: POTENTIAL & CONCEPT EDUCATIONSSpace for rough work Page. 2 AITS-FT # 03 (Dropper Engineering) [SET - B] - 2018-19 PHYSICS AITS-FT - 03 Engineering 1. The rate of disintegration of

Space for rough work Page. 4

AITS-FT # 03 (Dropper Engineering) [SET - B] - 2018-1911. In a practical wheat stone bridge circuit as

shown, when one more resistance of 100 isconnected in parallel with unknown resistance‘x’, then ratio 1/2 become ‘2’. 1 is balancelength. AB is a uniform wire. Then value of ‘x’must be :

(A) 50 (B) 100 (C) 200 (D) 400

12. Figure above shows a closed Gaussian surfacein the shape of a cube of edge length 3.0 m.There exists an electric field given byE [(2.0x 4.0)i 8.0 j 3.0k]N/C

, where xis in metres, in the region in which it lies. Thenet charge in coulombs enclosed by the cube isequal to

(A) –54 0 (B) 6 0

(C) –6 0 (D) 54 0

13. Circuit for the measurement of resistance bypotentiometer is shown. The galvanometer isfirst connected at point A and zero deflection isobserved at length PJ = 10 cm. In second caseit is connect at point C and zero deflection isobserved at a length 30 cm from P. Then theunknown resistance X is

(A) 2R (B) R2

(C) R3 (D) 3R

14. A ring of radius R having a linear charge densitymoves towards a solid imaginary sphere of

radius R2 , so that the centre of ring passes

through the centre of sphere. The axis of thering is perpendicular to the line joining thecentres of the ring and the sphere. Themaximum flux through the sphere in thisprocess is :

(A) 0

R (B)

0

R2

(C) 0

R4 (D)

0

R3

15. The given figure gives electric lines of forcedue to two charges q1 and q2. What are thesigns of the two charges?

Page 5: POTENTIAL & CONCEPT EDUCATIONSSpace for rough work Page. 2 AITS-FT # 03 (Dropper Engineering) [SET - B] - 2018-19 PHYSICS AITS-FT - 03 Engineering 1. The rate of disintegration of

Space for rough work Page. 5

AITS-FT # 03 (Dropper Engineering) [SET - B] - 2018-19(A) Both are negative(B) Both are positive(C) q1 is positive but q2 is negative(D) q1 is negative but q2 is positive

16. Figure shows three circular arcs, each of radiusR and total charge as indicated. The net elecricpotential at the centre of curvature is :

(A) 0

Q2 R (B)

0

Q4 R

(C) 0

2QR (D)

0

QR

17. The figure shows a charge q placed inside acavity in an uncharged conductor. Now if anexternal electric field is switched on :

(A) only induced charge on outer surface willredistribute.

(B) only induced charge on inner surface willredistribute.

(C) both induced charge on outer and innersurface will redistribute.

(D) force on charge q placed inside the cavitywill change.

18. A diatomic ideal gas undergoes athermodynamic change according to the P–Vdiagram shown in the figure. The total heat givenof the gas is nearly :

(A) 2.5 P0V0 (B) 1.4 P0V0

(C) 3.9 P0V0 (D) 1.1 P0V0

19. Logarithms of readings of pressure and volumefor an ideal gas were plotted on a graph asshown in Figure. By measurring the gradient, itcan be shown that the gas may be

(A) monoatomic and undergoing an adiabaticchange

(B) monoatomic and undergoing an isothermalchange

(C) diatomic and undergoing an adiabaticchange

(D) triatomic and undergoing an isothermalchange.

Page 6: POTENTIAL & CONCEPT EDUCATIONSSpace for rough work Page. 2 AITS-FT # 03 (Dropper Engineering) [SET - B] - 2018-19 PHYSICS AITS-FT - 03 Engineering 1. The rate of disintegration of

Space for rough work Page. 6

AITS-FT # 03 (Dropper Engineering) [SET - B] - 2018-1920. A particle moves along the parabolic path y = ax2

in such a way that the x component of thevelocity remains constant, say c. Theacceleration of the particle is

(A) ˆack (B) 2ˆ2ac j

(C) 2 ˆac k (D) 2 ˆa cj

21. Two masses are connected by a spring asshown in the figure. One of the masses wasgiven velocity = 2 k, as shown in figure where‘k’ is the spring constant. Then maximumextension in the spring will be

(A) 2 m (B) m

(C) 2mk (D) 3mk22. The centre of mass of a non uniform rod of

length L whose mass per unit length varies

as 2k.x

L where k is a constant & x is the

distance of any point from one end, is (fromthe same end)

(A) 3 L4

(B) 1 L4

(C) kL

(D) 3kL

23. A person P of mass 50 kg stands at the middleof a boat of mass 100 kg moving at a constantvelocity 10 m/s with no friction between waterand boat and also the engine of the boat is shutoff. With what velocity (relative to the boatsurface) should the person move so that theboat comes to rest.

(A) 30 m/s towards right(B) 20 m/s towards right(C) 30 m/s towards left(D) 20 m/s towards left

24. A ball of mass m approaches a moving wall ofinfinite mass with a speed ‘v’ along the normalto the wall. The speed of the wall is ‘u’ towardthe ball. The speed of the ball after ‘elastic’collision with wall is :(A) u + v away from the wall(B) 2u + v away from the wall(C) |u – v| away from the wall(D) |v – 2u| away from the wall

25. A force of constant magnitude F acts on aparticle moving in a plane such that it isperpendicular to the velocity v(| v | v)

of thebody, and the force is always directed towardsa fixed point. Then the angle turned by thevelocity vector of the particle as it covers adistance S is :(take mass of the particle as m)

(A) 2

FS2mv (B) 2

2FSmv

(C) 2FS

mv(D) 2

FSmv

Page 7: POTENTIAL & CONCEPT EDUCATIONSSpace for rough work Page. 2 AITS-FT # 03 (Dropper Engineering) [SET - B] - 2018-19 PHYSICS AITS-FT - 03 Engineering 1. The rate of disintegration of

Space for rough work Page. 7

AITS-FT # 03 (Dropper Engineering) [SET - B] - 2018-1926. A long horizontal rod has a bead which can slide

along its length, and initially placed at a distanceL from one end of A of the rod. The rod is setin angular motion about A with constant angularacceleration . If the coefficient of frictionbetween the rod and the bead is µ and gravityis neglected, then the time after which the beadstarts slipping is :

(A)

(B)

(C) 1 (D) infinitesimal

27. A non-ideal voltmeter and a non-ideal ammeterare connected as shown in the figure. Thereading of the voltmeter is 20 V and that of theammeter is 4 A. The value of R is :

(A) 5 (B) less than 5 (C) greater than 5 (D) may be less than 5

28. Two circular rings of identical radii andresistance of 36 each are placed in such away that they cross each others centre C1 andC2 as shown in figure. Conducting joints aremade at intersection points A and B of the rings.An ideal cell of emf 20 volts is connected acrossAB. The power delivered by cell is

(A) 80 watt (B) 100 watt(C) 120 watt (D) 200 watt

29. A battery of internal resistor ‘r’ and e.m.f. isconnected to a variable external resistance AB.If the sliding contact is moved from A to B,then terminal potential difference of battery will:

(A) remain constant & is independent of valueof external resistance

(B) increase continuously(C)decrease continuously(D)first increase and then will decrease

30. A uniform wire of resistance R is stretcheduniformly n times & then cut to form fiveidentical wires. These wires are arranged asshown in the figure. The effective resistancebetween A & B will be :

(A) nR5

(B) 2R

5n

(C) 2n R5

(D) 2n R2

Page 8: POTENTIAL & CONCEPT EDUCATIONSSpace for rough work Page. 2 AITS-FT # 03 (Dropper Engineering) [SET - B] - 2018-19 PHYSICS AITS-FT - 03 Engineering 1. The rate of disintegration of

Space for rough work Page. 8

AITS-FT # 03 (Dropper Engineering) [SET - B] - 2018-19

CHEMISTRY31. Which one of the following is most reactive for

hydrogenation reaction ?

(A)

(B) CH3 – CH = CH2(C) CH3 – CH = CH – CH3

(D)

32. What is the Product (A) of following reaction

(A) (B)

(C) (D)

33. In the give reaction (A) is :

(A)

(B)

(C) Both (a) and (b)(D) None of these

34. In the structure of NaCl given below, ratio

Na Clr / r is

(A) 0.414 (B) 0.681(C) 0.745 (D) 0.520

35. There is formation of Prussian blue when Fe3+

reacts with [Fe(CN)6]4–. Two solutions as shownare separated by a semipermeable membraneAB. Due to osmosis, there is

(A) blue colour formation in side X(B) blue colour formation in side Y(C) blue colour formation in both the sides X

and Y(D) no blue colour forrnation

36.

The reagent [X] may be(A) aq.NaOH (B) alc. KOH(C) (C2H5)3N (D) Both (B) and (C)

AITS-FT - 03Engineering

Page 9: POTENTIAL & CONCEPT EDUCATIONSSpace for rough work Page. 2 AITS-FT # 03 (Dropper Engineering) [SET - B] - 2018-19 PHYSICS AITS-FT - 03 Engineering 1. The rate of disintegration of

Space for rough work Page. 9

AITS-FT # 03 (Dropper Engineering) [SET - B] - 2018-1937. What is the major product of the following

reaction ?

(A) (B)

(C) (D)

38. Product (A) is

(A) (B)

(C) (D)

39. Compare rate of reaction with OH– :

(A) i > ii > iii (B) i > iii > ii(C) iii > ii > i (D) ii > i > iii

40. Given, (Scm2 mol–1) for different electrolytes

Thus, of CH3COOH is(A) 516.5 (B) 420.3(C) 172.9 (D) 390.7

41. Which of the following is non-existent accordingto molecular orbital theory ?(A) 2H (B) 2O

(C) He2 (D) 2O

42. The molecular formula of diphenyl methane,

How many structural isomers are possible whenone of the hydrogen is replaced by chlorine atom(A) 4 (B) 8(C) 7 (D) 6

43. The structures given below are :

(A) Enantiomers(B) Diastereomers

Page 10: POTENTIAL & CONCEPT EDUCATIONSSpace for rough work Page. 2 AITS-FT # 03 (Dropper Engineering) [SET - B] - 2018-19 PHYSICS AITS-FT - 03 Engineering 1. The rate of disintegration of

Space for rough work Page. 10

AITS-FT # 03 (Dropper Engineering) [SET - B] - 2018-19(C) Geometrical isomers(D) Homomers

44. Maximum enol content is in :

(A) (B)

(C) (D)

45. Which is the correct matched forthe followingreactions

(A) Free Radical

reaction

(B) Electrophilic

add ition

(C) Electrophilic

substitution

(D) Nucreophitic

substitution46. Which one of the following anions is NOT

stabilised by delocalisation

(A) (B)

(C) (D)

47. An ideal gas expands in volume from 1 × 10–3

m3 to 1 × 10–2 m3 at 300 K against a constantpressure of 1 × 105 Nm–2. The work done is(A) – 900 J (B) – 900 kJ(C) 270 kJ (D) + 900 kJ

48. Given that, Ka(HCN) = 4.9 × 10–10, Ka(HNO2)= 4.5 × 10–4

Thus, which of the following reaction is favouredin forward direction ?(A) HNO2(aq ) + CN– (aq ) 2NO (aq)

+ HCN(aq )(B) 2NO (aq )+ HCN(aq) HNO2(aq )

+ CN–(aq )(C) Both are favoured in forward direction(D) None is favoured in for-ward direction

49. Given,H3PO4 + H2O 2 4H PO + H3O+,

1apK = x

2 4H PO + H2O 24HPO + H3O+,

2apK = y24HPO + H2O 3

4PO + H3O+, 3apK = z

Thus, pH of 0.1 M K2HPO4 solution is

(A) 2.0 (B)x y

2

(C) y z2

(D) x y z2

50. The pKa of a weak acid HA is 4.80 The pKb ofa weak base BOH is 4.78. The pH of an aqueoussolution of the corresponding salt BA will be(A) 9.58 (B) 4.79(C) 7.01 (D) 9.22

Page 11: POTENTIAL & CONCEPT EDUCATIONSSpace for rough work Page. 2 AITS-FT # 03 (Dropper Engineering) [SET - B] - 2018-19 PHYSICS AITS-FT - 03 Engineering 1. The rate of disintegration of

Space for rough work Page. 11

AITS-FT # 03 (Dropper Engineering) [SET - B] - 2018-1951. For the two moving particles A and B, following

values are givenParticle Velocity MassA 0.1 ms–1 m kgB 0.05 ms–1 5m kgRatio of de-Broglie wavelength associated withthe particles A and B is(A) 2 : 5 (B) 3 : 4(C) 6 : 4 (D) 5 : 2

52. The wave number of the spectral line in theemission spectrum of H-atom will be equal to89

times the Rydberg's constant if the electronjumps from(A) n = 3 to n = l (B) n = 10 to n = 1(C) n = 9 to n = 1 (D) n = 2 to n = 1

53. In the redox reaction,xKMnO4 + NH3 yKNO3 + MnO2 + KOH+ H2O(A) x = 4, y = 6 (B) x = 3, y = 8(C) x = 8, y = 6 (D) x = 8, y = 3

54. The correct decreasing order of oxidation numberof oxygen in compounds BaO2, O3, KO2 andOF2 is :(A) BaO2 > KO2 > O3 > OF2

(B) OF2 > O3 > KO2 > BaO2

(C) KO2 > OF2 > O3 > BaO2

(D) BaO2 > O3 > OF2 > KO2

55. The pair of amphoteric hydroxides is(A) LiOHOHAl ,)( 3 (B) 22 )(,)( OHMgOHBe

(C) 23 )(,)( OHBeOHB (D) 22 )(,)( OHZnOHBe

56. If 500 mL of gas A at 400 torr and 666.6 mL ofB at 600 torr are placed in a 3 litre flask, thepressure of the system will be(A) 200 torr (B) 100 torr(C) 550 torr (D) 366 torr

57. Volume of an ideal gas is to be decreased by10% by increase of pressure by x% underisothermal condition. Thus, x is

(A) 1009 (B) 9

100

(C) 10 (D)1

1058. An ideal gas is at 300 K and 1 atm. Then volume

remains constant if(A) temperature is doubled and pressure is

halved(B) temperature is halved and pressure is

halved(C) only temperature is doubled(D) None of these

59. Which of the following is least ionic ?(A) AgCl (B) KCl(C) BaCl2 (D) CaCl2

60. The number and type of bonds between carbonatoms in calcium carbide are(A) Two sigma, one pi(B) Two sigma, two pi(C) One sigma, one pi(D) One sigma, two pi

Page 12: POTENTIAL & CONCEPT EDUCATIONSSpace for rough work Page. 2 AITS-FT # 03 (Dropper Engineering) [SET - B] - 2018-19 PHYSICS AITS-FT - 03 Engineering 1. The rate of disintegration of

Space for rough work Page. 12

AITS-FT # 03 (Dropper Engineering) [SET - B] - 2018-19

61. f is an odd function. It is also known that f(x)is continuous for all values of x and is periodicwith period 2.

If x

0g(x) f (t) dt, then :

(A) g(x) is odd(B) g(n) = 0, n N

(C) g(2n) = 0, n N(D) g(x) is non-periodic

62. The absolute value of

/ 2 sin x

0/ 2 cos x

0

(x cos x 1)e dx

(xsin x 1)e dx

is equal to(A) e (B) e

(C)e2

(D)e

63. Area bounded by the curves y = loge x andy = (loge x)2 is :(A) e – 2 sq. units (B) 3 – e sq. units(C) e sq. units (D) e – 1 sq. units

64. The solution of the equationdy x(2 log x 1)dx (sin y ycos y

is :

(A)2

2 xysin y x log x c2

(B) 2ycos y x (log x 1) c

(C)2

2 xycos y x log x c2

(D) y sin y = x2 log x + c65. The differential equation of the family of

curves y = ex (A cos x + B sin x), where Aand B are arbitary constants is :

(A)2

2d y dy2 2y 0

dxdx

(B)2

2d y 2dy 2y 0

dxdx

(C)22

2

d y dy y 0dxdx

(D)2

2d y dy7 2y 0

dxdx

66. If a, b

are the vectors forming consecutivesides of a regular hexagon ABCDEF, then thevectors representing side CD is :

(A) a b

(B) a b

(C) b a

(D) a b

67. If a

and b

are two unit vectors inclined at an

angle such that a b 1,

then :

(A)3

(B)23

(C)2

3 3 (D)

23

MATHEMATICS AITS-FT - 03Engineering

Page 13: POTENTIAL & CONCEPT EDUCATIONSSpace for rough work Page. 2 AITS-FT # 03 (Dropper Engineering) [SET - B] - 2018-19 PHYSICS AITS-FT - 03 Engineering 1. The rate of disintegration of

Space for rough work Page. 13

AITS-FT # 03 (Dropper Engineering) [SET - B] - 2018-1968. If non-zero vectors a

and b

are equally

inclined to vector c

, then c

is :

(A)a b

a ba 3 b a b

(B)b a

a ba b a b

(C)a b

a ba 3 b a 3 b

(D) None of these69. If from the point P(a, b, c) perpendicular PQ,

PR be drawn to yZ and Zx-planes then, theequation to the plane oQR is :

(A)x y z 0a b c (B)

x y z 0a b c

(C)x y z 0a b c (D) None of these

70. Find the value of 't' for which the lines

x 1 y 3 z 52 4 7

and x t y 2 z 1

1 3 1

intersect.

(A)4

17(B)

1017

(C)1417

(D) None of these

71. If RR is given by f(x) = x3 + 3, then f –1(x)is equal to :

(A)13x 3 (B) 1/3x 3

(C) 1/3(x 3) (D) 1/3x 372. Find the interval of 'x' satisfying the equation

1 [sin x [sin x [sin x ....n

upto n terms] =

[cos x] where x (0, 2 ). (where [ ] denotesG.I.F.)

(A) 0,2

(B) ,2

(C)3 , 22

(D) None of these

73. Let tan(x + y) = a and y = tan–1 b, then findthe value of x.

(A)1 a btan

1 ab

(B)1 a btan

1 ab

(C)1 a btan

ab

(D) None of these

74.

nn n

n

p qlim ,

2

p, q > 0 equals :

(A) 1 (B) pq

(C) pq (D)pq2

Page 14: POTENTIAL & CONCEPT EDUCATIONSSpace for rough work Page. 2 AITS-FT # 03 (Dropper Engineering) [SET - B] - 2018-19 PHYSICS AITS-FT - 03 Engineering 1. The rate of disintegration of

Space for rough work Page. 14

AITS-FT # 03 (Dropper Engineering) [SET - B] - 2018-1975. The following functions are continuous on

(0, ) :

(A) tan x

(B)x

0

1t sin dtt

(C)

xsin x,0 x2

sin ( x), x2 2

(D) None of these

76. If x = t3 + t + 5 and y = sin t then 2

2d ydx

is equal

to:

(A)2

2 3

(3t 1)sin t 6t cos t(3t 1)

(B)2

2 2(3t 1) sin t 6t cos t

(3t 1)

(C)2

2 2(3t 1)sin t 6t sin t

(3t 1)

(D) 2cos t

(3t 1)

77. The curve y = x3 + x2 – x has two horizontal

tangents. The distance between these two

horizontal lines, is pq (where p,q I and

H.C.F. of p and q is unity). Find (p + q) :(A) 58 (B) 59(C) 60 (D) 61

78. The range of values of m for which the line

y = mx and the curve 2

xyx 1

encloses a

region , is :(A) (–1, 1) (B) (0, 1)

(C) [0, 1] (D) 1,

79. The bottom of the legs of a three legged tableare the vertices of an isosceles triangle withsides 5, 5 and 6. The legs are to be traced atthe bottom by three wires in the shape of a Y.The minimum length of the wire needed forthis purpose, is :

(A) 4 3 3 (B) 10

(C) 3 4 3 (D) 1 6 2

80. Evaluate 2(2x 41x 91) dx.

(x 1)(x 3)(x 4)

(A) ln (x–1) + 3 ln (x + 3) + C(B) ln (x–1) + 2 ln (x + 3) + 3 ln (x – 4) + C(C) ln (x+1) + 4 ln (x – 4) + C(D) 4 ln (x–1) – 7 ln (x + 3) + 5 ln (x – 4) + C

81. A survey shows that 63% of the Americanslike cheese whereas 76% like apples. If x% ofthe Americans like both cheese and apples,then we have(A) x 39 (B) x 63

(C) 39 x 63 (D) None of these

Page 15: POTENTIAL & CONCEPT EDUCATIONSSpace for rough work Page. 2 AITS-FT # 03 (Dropper Engineering) [SET - B] - 2018-19 PHYSICS AITS-FT - 03 Engineering 1. The rate of disintegration of

Space for rough work Page. 15

AITS-FT # 03 (Dropper Engineering) [SET - B] - 2018-1982. Four numbers are in arithmetic progression.

The sum of first and last term is 8 and theproduct of both middle terms is 15. The leastnumber of the sequenc is(A) 4 (B) 3(C) 2 (D) 1

83. The sum of 10 terms of the sequence 1, 6, 27,108, ... is(A) 280481 (B) 280482(C) 280484 (D) 280483

84. Let a, b and c be real numbers, a 0. If is aroot of a2x2 + bx + c = 0, is the root of

a2x2 – bx – c = 0 and 0 < < , then theequation a2x2 + 2bx + 2c = 0 has a root thatalways satisfies

(A)2

(B)

2

(C) (D)

85. If b > a, then the equation (x–a)(x–b)–1=0 has(A) both roots in (a, b)(B) both roots in ( , a)(C) both roots in (b )(D) one root in ( , a) and the other in

(b, )

86. If the angles of elevation of the top of a towerfrom three collinear points A, B and C on aline leading to the foot of the tower are 30o,45o and 60o respectively, then the ration AB :BC is

(A) 3 :1 (B) 3 : 2

(C) 1: 3 (D) 2 : 387. A line L intersects the three sides BC, CA and

AB of a ABC at P, Q and R respectively..

Then, BP CQ AR. .PC QA RB

is equal to

(A) 1 (B) 0(C) –1 (D) None of the above

88. A variable straight line drawn through the point

of intersection of lines x y 1a b and

x y 1,b a meets the coordinate axes in A and

B. Then, the locus of the mid-point of AB is(A) xy (a + b) = ab (x + y)(B) 2xy (a – b) = ab (x + y)(C) 2xy (a – b) = ab (x – y)(D) 2xy (a + b) = ab (x + y)

89. Tangents PA and PB drawn to x2 + y2 = 9from any arbitrary point P on the line x + y =25. Locus of mid-point of chord AB is(A) 25 (x2 + y2) = 9 (x + y)(B) 25 (x2 + y2) = 3 (x + y)(C) 5 (x2 + y2) = 3 (x + y)(D) None of these

90. Radius of the largest circle that can be drawnto pass through the point (0, 1), (0, 6) andtouching X-axis, is

(A)52

(B)32

(C)72

(D)92

Page 16: POTENTIAL & CONCEPT EDUCATIONSSpace for rough work Page. 2 AITS-FT # 03 (Dropper Engineering) [SET - B] - 2018-19 PHYSICS AITS-FT - 03 Engineering 1. The rate of disintegration of

Date : 27 - 01 - 2019 SET - B

IMPORTANT INSTRUCTIONS

1. Immediately fill the particulars on this page of the Test Booklet with Blue/Black Point Pen. Use of Pencil isstrictly prohibited.

2. When you are directed, fill in the particulars of the Answer Sheet carefully.

3. The test is 3 hours duration.

4. The Test Booklet consists of 90 questions. The maximum marks are 360.

5. There are three parts in the question paper Physics, Chemistry and Mathematics having 30 questions each.

6. For each question, you will be awarded 4 marks if you darken all the bubble(s) correspondind to thecorrect answer(s) and zero mark if no bubbles are darkened. In all other cases, 1 (one) marks will bededucted.

7. There is only one correct response for each question. Filling up more than one response in any questionwill be treated as wrong response and marks for wrong response will be decucted accordingly as perinstructions 6 above.

Filling the ORS (Optical Response Sheet) :

Use only Black ball point pen only for filling the ORS. Do not use Gel/lnk pen as it might smudge the ORS.

8. Write your Roll no. in the books given. Also darken the corresponding bubbles with Black ball point penonly. Also fill your roll no in the space provided.

9. Fill your Paper Code as mentioned on the Test Paper.

10. If student does not fill his/her roll no. and paper code correctly and properly, then his/her marks will notbe displayed and 5 marks will be deducted (paper wise) from the total.

11. Since it is not possible to erase and correct pen filled bubble, you are advised to be extremely careful whiledarkening the bubble corresponding to your answer.

12. Neither try to erase/rub/scratch the option nor make the Cross(X) mark on the option once filled. Do notscribble, smudge, cut, tear, or wrinkle the ORS. Do not put any stray marks or whitener anywhere on theORS.

13. If there is any discrepancy between the written data and the bubbled data in your ORS the bubbled data willbe taken as final.

Name of the candidate

I have read all the instructions and shall abideby them

.............................................................................Signature of the Candidate

Roll Number :

I have read all the instructions and shall abideby them

.............................................................................Signature of the Candidate

AITS FULL TEST (FT) : FT # 03(JEE MAIN PATTERN)

Target : JEE Main - 2019