SECTION – I - mentorsmetre.com oscillations and a speed of 8 m/s when 3 m from the centre. Find...

(A) General :

1. The question paper consists of 3 parts (Physics, Chemistry and Mathematics) having total 60 questions, 20questions in each (Physics, Chemistry and Mathematics). Each part consists of three sections.

2. This Question Paper contains 15 pages.

3. Section I contains 10 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out ofwhich ONLY ONE is correct.

4. Section II contains 3 paragraphs each describing theory, experiment, data etc. There are 6 multiple choice

questions relating to three paragraphs with 2 questions on each paragraph. Each question of a particular

paragraph has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

5. Section III contains 4 questions. The answer to each question is a single digit integer, ranging from

0 to 9 (both inclusive).

6. The Question Paper has blank spaces at the bottom of each page for rough work.No additional sheets willbe provided for rough work.

7. Blank papers, clip boards, log tables, slide rule, calculators, cellular phones, pagers and electronic gadgets,in any form, are NOT allowed.

8. This booklet also contains the OMR answer sheet (i.e., A machine gradable Response Sheet).

(B) Answering on the OMR:

9. Each question will have 4 choices in both the Sections, out of which only one choice is correct.

10. Fill the bubble with Ball Pen (Blue or Black) ONLY.

(C) Filling – Name and Registration No.

11. On the OMR sheet, write your Name and Registration No. using ball pen. Also, put your signature in theappropriate box using ball pen.

DO

NO

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RE

AK

TH

E S

EA

LS

ON

TH

IS B

OO

KL

ET,

AW

AIT

INS

TR

UC

TIO

NS

FR

OM

TH

E IN

VIG

ILA

TO

R.

INSTRUCTIONS

S E

A L

(D) Marking Scheme:

12. For each question in Section-I and Section-II, you will be awarded 3 marks if you darken the bubblecorresponding to the correct answer ONLY and zero (0) marks if no bubbles are darkened. In all othercases, minus one (–1) mark will be awarded in these sections.

13. For each question in Section III, you will be awarded 4 marks if you darken the bubble corresponding to

the correct answer ONLY. In all other cases zero (0) marks will be awarded. No negative marks will beawarded for incorrect answer in this section.

Name :.............................................................................................................

Corporate Office : Parus Lok Complex, Boring Road Crossing, Patna-1, Helpline No. : 9569668800 | 75440159934//6/7

Registration No.:

MENTORS EDUSERV TALENT REWARD EXAMINATION

SAMPLE PAPER

(For Class 12 Studying Students & 12 Pass Aspiring for JEE 2017)

(STREAM : ENGINEERING)

Time : 2 hours Maximum Marks: 192

[ 2 ] Sample Paper Class 12 (E)

Corporate Office: Parus Lok Complex, Boring Road Crossing, Patna-1Helpline No.- 9569668800 | Call- 7544015993/4/6/7

PHYSICSSECTION – I

(Single Correct Answer Type)

This section contains 10 multiple choice questions. Each question has four choices (A), (B), (C)and (D), out of which ONLY ONE is correct.

1. Each cell has emf and internal resistance r in the figure. Find the current through resistanceR

(A) r

4(B)

r

3

R

A

B

(C) r

(D) zero

2. In the circuit shown, when the switch is closed, the capacitor charges with a time constant

(A) RC C R

R

+ – B

(B) 2RC

(C) 2

1 RC

(D) RC ln 2

3. What is the average velocity during time interval t = 2 s to t = 5 s in the following position timecurve?

1 2 3 4 5

2

4

6

x(m)

t(s)

P

Q

(A) 2 m/s (B) 2/3 m/s (C) 1.2 m/s (D) 0.4 m/s

4. Two different balls of masses m1 and m

2 are allowed to slide down from rest and from same

height h along two inclined planes having different inclination and . Then

h

m2 m1

(A) The final speed acquired by them will be the same

(B) The final speed acquired by them will be different

(C) The times taken by them to reach the bottom will be the same

(D) None of these

Sample Paper Class 12 (E) [ 3 ]


5. A body constrained to move in y-direction is subjected to a force given by

N)6152( kjiF

. The work done by this force in moving the body a distance of 10m

along the y-axis is

(A) 20 J (B) 150 J (C) 60 J (D) 190 J

6. If a body is to be projected vertically upwards from earth’s surface to reach a height of 10Rfrom surface of earth, (where R is the radius of earth), the velocity required to do so is

(A)

Rg

11

24(B)

Rg

11

22(C)

Rg

11

20(D)

Rg

11

18

7. A tuning fork of frequency 256 Hz is excited and held at the mouth of resonance column offundamental frequency 254 Hz. Choose the correct statement

(A) 2 beats per second will be heard

(B) 4 beats per second will be heard

(C) 1 beat per second will be heard

(D) No beat will be heard

8. In a parallel-plate capacitor of capacitance C, a metal sheet is inserted between the plates,symmetrically and parallel to them. The thickness of the sheet is half of the separation betweenthe plate. The capacitance now becomes

(A) 4C (B) 2C (C) C/2 (D) C/4

9. A charged particle moves in a uniform magnetic field of induction B

with a velocity v

. The

change in kinetic energy in the magnetic field is zero when the velocity v

is

(A) parallel to B

(B) perpendicular to B

(C) at any angle to B

(D) none of these

10. The material which shows the effect on magnetic lines of force shown in figure, when placedin a uniform magnetic field is called

Magnetic field

Lines

(A) paramagnetic (B) diamagnetic

(C) ferromagnet (D) antiferromagnetic



SECTION – II

(Paragraph Type)

This section contains 6 multiple choice questions relating to three paragraphs with two questionson each paragraph. Each question has four choices (A), (B), (C) and (D) out of which ONLYONE is correct.

Paragraph for Questions 11 and 12

Whenever the flux of magnetic field through the area bounded by a closed conducting loop changes,an emf is induced in the loop. The emf is given by

,d

dt

where B ds

is the flux of the magnetic field through the area.

Now consider a loop as shown in the figure. The loop comprises of two parallel rails connected byan ideal conductor L and a slider of mass m and length l. A uniform external magnetic field B isdirected into the plane of the loop. At t = 0 the slider is imparted a velocity v

0 (as shown).

L

B l v0

From the given information answer the following questions.

11. The current in the circuit as a function of distance (x) travelled by the slider is

(A) Bl

i xLm

(B) Bl

i xL

(C) 2Bl

i xL

(D) Bl

i xm

12. The time period of oscillation of the slider is

(A) 222

lB

LmT (B)

Bl

LmT 2 (C) 22

2lB

mT (D) 2

2Bl

LmT


A solid cylinder of mass m and radius R is kept at rest on a plank of mass 2m lying on a smoothhorizontal surface. Massless and inextensible string connecting cylinder to the plank is passingover a massless pulley. The friction between the cylinder and the plank is sufficient to preventslipping. Pulley A is pulled with a constant horizontal force F.

F

A

2m

m R

13. Acceleration of cylinder with respect to earth is

(A) m

F

21

5(B)

m

F

7(C)

m

F

7

3(D)

m

F

7

2

14. Acceleration of plank with respect to earth is

(A) m

F

21

5(B)

m

F

7(C)

m

F

7

3(D)

m

F

7

2




The figure shows two identical parallel plate capacitors A and B connected to an ideal battery ofemf V volt with the switch S closed. The switch is now opened and the free space between theplates of the capacitors is filled with a dielectric of dielectric constant 3.

V A B

S

15. Find the ratio of charge of the capacitor A before and after the introduction of dielectric

(A) 9 :2 (B) 1: 9 (C) 1 :3 (D) 3 :1

16. Find the ratio of electrostatic energy stored in capacitor A before and after the introduction ofdielectric

(A) 9 :2 (B) 1: 9 (C) 1 :3 (D) 3 :1

SECTION – III

(Integer Answer Type)

This section contains 4 questions. The answer to each of the questions is a single

digit integer, ranging from 0 to 9. The appropriate bubbles below the respective

question numbers in the ORS have to be darkened. For example, if the correct

answers to question numbers X, Y, Z and W (say) are 6, 0, 9 and 2, respectively,

then the correct darkening of bubbles will look like the following:

0

1

2

3

4

5

6

7

8

9

0 0 0

1 1 1

2 2 2

3 3 3

4 4 4

5 5 5

6 6 6

7 7 7

8 8 8

9 9 9

X Y Z W

17. Find the equivalent resistance in between point A and B in the given circuit. If value of R = 4.

R R

R

R

R

R R

R R

R

B A

R

R

18. A liquid cools from 700C to 600C in 5 minute. Calculate the time taken by the liquid to cool from600C to 500C, if the temperature of the surrounding is constant at 300C.

19. A particle moving with SHM in a straight line has a speed of 6 m/s when 4 m from the centreof oscillations and a speed of 8 m/s when 3 m from the centre. Find the amplitude of oscillation?

20. The diameter of a gas bubble formed at the bottom of a pond is d = 4 cm. When the bubblerises to the surface its diameter increases n = 1.1 times. Find the depth of the pond. Surfacetension of water is 0.07 N m-1.



CHEMISTRYSECTION – I



21. Calculate the standard potential for the reaction at 298 K

½ O2 + 2H+ + 2e H

2O

If E° for the reaction, ½O2 + H

2O + 2e 2OH is + 0.4 V

(A) 1.227 V (B) 1.227 V (C) 0.828 V (D) 8.28 V

22. Figure shows a graph of klog10 vs

T

1 where k is rate constant and T is temperature. The

straight line BC has slope, tan = 303.2

1 and an intercept of 5 on Yaxis. Thus E

a, the

energy of activation is:

log 1

0 k

1/T

B

A

C

(A) 2.303 2 cal (B) cal303.2

2(C) 2 cal (D) None of these

23. Which of the following is arranged in order of increasing dipole moment?

(A) BCl3 < NH

3 < H

2O < NF

3(B) BCl

3 < NF

3 < NH

3 < H

2O

(C) NH3 < NF

3 < H

2O < BCl

3(D) H

2O < NF

3 < NH

3 < BCl

3

24. Calculate the enthalpy of formation of OH– ions from the following thermochemical data :

)aq()aq()1(2 OHHOH ; kJ32.57H K298

)l(2)g(2)g(2 OHO2

1H ; kJ83.285H K298

(A) –228.51 kJ (B) –198.51 kJ (C) + 238.5 kJ (D) –238.5 kJ



25. Match the method of concentration of the ore in column I with the ore in column II and selectthe correct alternate:

Column I Column II

X. Magnetic separation A. Ag2S

Y. Froth floatation B. FeCr2O

4

Z. Gravity separation C. Al2(SiO

3)

3

X Y Z

(A) A B C

(B) B A C

(C) C A B

(D) B C A

26. Which of the following is optically active?

(A) (B)

(C) (D)

27.

N

O conc. HNO3

conc. H2SO4 X

O major products ‘X’ will be

(A)

O

O

NO2 (B)

O

O

O2N

(C)

O

O

NO2 (D)

O

O

O2N



28. The reaction of cyclooctyne with HgSO4 in the presence of aq. H2SO4 gives

(A) (B)

(C) (D)

29. Consider the following statements and pick up the incorrect statements:

(A) CH – Br2MeO will react more readily than CH Br2O N2 for 1SN

reaction

(B)

Br

will react more readily than

Br

for 1SN reaction

(C)

Cl

N

H

will react more readily than

Cl

N

for 1SN reaction

(D) 1SN reaction occurs in polar protic solvent

30. In which of the following cases, the major product has been incorrectly shown?

(A) H O2

Br

(B)Br

Me CO K 3

(C)EtO

EtOH

Br(D) Br

C H OH2 5



SECTION – II

(Paragraph Type)



Consider the following energy level diagram :

6C(s) + 6H (g) + 9O (g)2 2

C H O + 6O (g)6 12 6 2

x

y z

6CO (g) + 6H O ( )l2 2

Energy

Answer the following questions on the basis of the given diagram :

31. The heat of formation of glucose is

(A) –x (B) –y (C) x – y (D) –x + z

32. In the given diagram z refers to

(A) 0f 26 H of CO (B) 0

f 6 12 6H of C H O

(C) 0c 6 12 6H of C H O (D) 0 0

c (s) f 2H of C H of H O


Ortho boric acid is a white crystalline solid. It is soluble in water. It can be prepared by acidifyingaqueous solution of borax on heating. Borax first loses water molecules and swells up. On furthestheating it turns into a transparent liquid, which solidifies into glass like material known as boraxbead.

33. Boric acid crystallizes in a layer structure in which H3BO

3 are bonded together by

(A) Dative bond (B) Hydrogen bond

(C) Van der waal’s force (D) Ionic and Dative bonds

34. 375K 375 K Red heat3 3

acid acidH BO X Y Z

X, Y and Z are

(A) B2O

3, HBO

2 and H

2B

2O

4(B) HBO

2, H

2B

2O

7, B

2O

3

(C) HBO2, B

2O

3, H

2B

4O

7(D) B

2O

3, H

2B

4O

7, B(OH)

3




A chemist performs the following reactions:

(i) K2[PtCl

4] + 2NH

3 A + 2KCl

(ii) [Pt(NH3)

4](NO

3)

2 + 2KCl B + 2NH

3 + 2KNO

3

She finds both A and B are white, diamagnetic, crystalline compounds that give elementalanalyses for the formula PtCl

2(NH

3)

2. However A is more soluble in polar solvents, such as

ethanol, while B is soluble in petroleum ether and CCl4.

Another chemist who reads a report of this experiment and immediately identifies A and B.Since nickel is in the same group of the periodic table as platinum, he decides to perform thesame experiment with Ni(II) but is unsuccessful. He obtains some K

2NiCl

4, but when he attempts

to run reaction (i), the only products he is able to isolate are Ni(NH3)

6Cl

2 and KCl. When

tripheyl phosphine, Ph3P, is used in place of ammonia as one of the ligands (chloride ion is still

the second ligand), compound C is isolated. This compound analyses for the empirical formulaNiCl

2(Ph

3P)

2, and is greenish, paramagnetic, and soluble in organic polar solvents. Regardless

of the reaction conditions or concentrations chosen, only C is found; no other isomers areobserved.

35. The structure of A is

(A)

Cl

NH3

NH3

Cl

Pt(B)

Cl

Cl

NH3

NH3

Pt

(C)

ClNH3

NH3

Cl

Pt(D)

NH3NH3

Cl

Cl

Pt

36. Compound C is

(A)

Cl

Ph3P

Ph3P

Cl

Ni(B)

Cl

Cl

Ph3P

PPh3

Ni

(C)

ClPh3P

PPh3

Cl

Ni(D)

Cl

PPh3

Cl

Ni

PPh3

Ni

ClCl



SECTION – III


This section contains 4 questions. The answer to each of the questions is a single digit integer,

ranging from 0 to 9. The appropriate bubbles below the respective question numbers in the ORS

have to be darkened. For example, if the correct answers to question numbers X, Y, Z and W (say)

are 6, 0, 9 and 2, respectively, then the correct darkening of bubbles will look like the following:

0

1

2

3

4

5

6

7

8

9

0 0 0

1 1 1

2 2 2

3 3 3

4 4 4

5 5 5

6 6 6

7 7 7

8 8 8

9 9 9

X Y Z W

37. Two substance 1/ 2A t 5min and 1/ 2B t 15 min follow first order kinetics and are taken

in such a way that initially [A] = 4[B]. The time after which the concentration of Both thesubstance will be equal is 5x min. Find the value of x.

38. How may no bond resonance structure of

MeMe

.

39. Number of complexes which shows geometrical isomer as well as optically active

2 24 4 4PtCl , AuCl , PdCl

; 3 2 33 2Rh PPh Cl , PtCl NH

; 2 3Pd NO CN Py NH ,

3Zn Py NH Cl F , K CoFClBr I , 24FeCl

40. How many stereoisomers of

CH = CH – CH3

Me



MATHEMATICSSECTION – I



41. The function (x) = x

x x

2e – 1 + 1 is

(A) an odd function (B) an even function

(C) neither an odd nor an even function (D) a periodic function

42. The solution of the equation dy x (2logx 1)

dx sin y ycos y

is

(A)2

2 xy siny x logx c

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

(C)2

2 xycos y x logx c

2 (D) 2y sin y x log x c

43. Let f(x) = ax5 + bx3 + cx – 5, where ba, and c are constants. If 7)7( f , then )7(f equals

(A) –17 (B) –7 (C) 14 (D) 21

44. Let f :R R be a differentiable function satisfying f(y)f(x y) f(x) x,y R and

f '(0) p, f '(5) q, then f '( 5) is

(A)2p

q(B)

p

q(C)

q

p(D) q

45. If tan x tan y, R , then maximum value of 2sec (x y) is equal to

(A)2( 1)

2

(B)

2( 1)

(C)

2( 1)

2

(D)

2( 1)

4

46. Let the complex numbers z1, z

2 and z

3 be the vertices of an equilateral triangle. Let z

0 be the

circumcenter of the triangle, then 2 2 21 2 3z z z is equal to

(A) 2

0z (B)2

0z3 (C)2

0z9 (D) 0

47. The number of into functions from A to B, where A = {1, 2, 3, 4, 5}, B = {a, b}

(A) 32 (B) 30 (C) 2 (D) 25

48. The coefficient of x53 in the expansion, m

0

100100C

m (x 3)100 m . 2m is

(A) 100C47

(B) 100C50

(C) 100C53

(D) 100C100



49. If each critical point of f(x) = 31 2 nn n(x ) (x ) (x ) , where 1 2 3n , n , n I+ is either local

maximum or local minimum then

(A) n1, n

2, n

3 are even integer

(B) n1 is odd , n

2 is even , and n

3 is even

(C) n1, n

2 , n

3 are prime numbers

(D) n1, n

2, n

3 are odd integers

50. Let P(x) be a polynomial of least degree whose graph has three points of inflexion (–1, –1),(1, 1) and a point with abscissa 0 at which the curve is inclined to the axis of abscissas at an

angle of 60°. Then 1

0

)( dxxP equal to

(A)7

2

14

33 (B) 12

(C) 122 (D)7

2

14

33

SECTION – II

(Paragraph Type)



Let 1

f(x)x i

, where x R and let f ) , f( ) , f( ) , f( ) be four points on the argand plane.

Now answer the following questions:

51. The maximum value of f f is

(A) (B)1 1

(C) 1 (D) 2

52. If a triangle is formed by joining the points f( ) , f( ) and f( ) , then maximum value of area of

the triangle is

(A) 3 3 (B)3 3

4(C)

3 3

16(D) none of these




Integration plays a vital role in proving identities involving binomial coefficients whose algebraicmethod of proving is, in general, cumbersome and requires the help of Mathematical Induction. Ifwe apply both integration and induction/recursion techniques, several elegant binomial identitiesare proved. For instance

n 1n1 2 n

00

C C ( 1) C 1C ... (1 x) dx

2 3 n 1 n 1

where nr rC C ,r 0,1,2,....,n

53. If k kn m

n m1 k 2 k

k 0 k 0

( 1) ( 1)S C ,S C ,

k m 1 k n 1

where m > n then,

(A) 12 Snm

nmS

(B)

12 SS

(C)12 SS (D) 021 SS , for all m and n

54. The compact value of series 12

)1(.......

753321

0

n

CCCCC n

n

must be equal to

(A) 2

2

)!(

)!12(2

n

nn (B)

)!12(

)!(2 22

n

nn

(C) 22 )!(2 nn (D)12

2

n

n


A continuous function )(xf satisfying 3224 2)(4 xxxfxx for all ].2,0[x Such that the area

bounded by ,4),( 24 xxyxfy the y-axis and the line tx ( )20 t is k times the area bounded

by ,2),( 32 xxyxfy y-axis and the line x = t (0 t 2). Then

55. The function )(xf , is given by :

(A) ])2(2[1

1 234 xkkxxk

(B) ])2(2)2([1

1 234 xkxkxk

(C) ])2(2)2([1

1 34 xkxkxk

(D) ])2(2[1

1 34 xkkxxk

56. If k = 0; then )(xf is symmetric about :

(A) origin (B) y-axis (C)x-axis (D)y = x



SECTION – III


This section contains 4 questions. The answer to each of the questions is a single digit integer,

ranging from 0 to 9. The appropriate bubbles below the respective question numbers in the ORS

have to be darkened. For example, if the correct answers to question numbers X, Y, Z and W (say)

are 6, 0, 9 and 2, respectively, then the correct darkening of bubbles will look like the following:

0

1

2

3

4

5

6

7

8

9

0 0 0

1 1 1

2 2 2

3 3 3

4 4 4

5 5 5

6 6 6

7 7 7

8 8 8

9 9 9

X Y Z W

57. If the graph of 3 2f x 2x ax bx a,b N cuts the x axis at three distinct points, then the

minimum possible value of ba is

58. The number of roots of equation |f(|x|)| = 2 (where f(x) = x2 – 4x + 3) is

59. Let a1, a

2,..., a

10 be in A.P. and h

1, h

2, ..., h

10 be in H.P. If a

1 = h

1 = 2 and a

10 = h

10 = 3, then a

4 h

7

is

60.

2

0

cosθ - sinθdθ

(1+cosθ)(1+sinθ) = cos–1( ) , then the value of is

SECTION – I - mentorsmetre.com oscillations and a speed of 8 m/s when 3 m from the centre. Find...

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Transcript of SECTION – I - mentorsmetre.com oscillations and a speed of 8 m/s when 3 m from the centre. Find...