SRIGAYATRI EDUCATIONAL INSTITUTIONS...2020/04/20 · 8. The coefficient of the middle term in the...

SRIGAYATRI EDUCATIONAL INSTITUTIONS

INDIA

SR MPC Date:20-04-2020

Time: 3 Hours Max. Marks : 300

JEE MAIN MODEL MATHEMATICS

Section Question type +Ve Marks

- Ve Marks

No.of Qs

Total marks

Sec – I(Q.N : 01 – 20) Questions with Single Answer Type 4 -1 20 80

Sec – II(Q.N : 21 – 25) Questions with Numerical Answer Type (+/ - Decimal Numbers)

4

0

5

20

Total

25

100

PHYSICS


- Ve Marks

No.of Qs

Total marks



4

0

5

20

Total

25

100

CHEMISTRY


- Ve Marks

No.of Qs

Total marks



4

0

5

20

Total

25

100

JEE MAINS MODEL (UT-1)

S R I G A Y A T R I E D U C A T I O N A L I N S T I T U T I O N S - I N D I A

Page | 2 SENIOR UT-1 :: JEE MAINS MODEL 20-04-2020

SECTION – I

(SINGLE CORRECT ANSWER TYPE) This section contains 20 multiple choice questions. Each question has 4 options (A), (B),

(C) and (B) for its answer, out of which ONLY ONE option can be correct.

Marking scheme: +4 for correct answer, 0 if not attempted and -1 if not correct.

MATHEMATICS

SYLLABUS: ALGEBRA

1. If , , , are roots of 4 3 2100 2 4 10 0,x x x x then 1 1 1 1

is equal to

1) 2

5 2)

1

10 3) 4 4)

2

5

2. Let , ,r s t be the roots of the equation 38 1001 2008 0x x . The value of

3 3 3

r s s t t r is

1) 251 2) 751 3) 735 4) 753

3. The roots of 2

1 1 1 0a x b x c are reciprocal of the roots of the equation 2

2 2 2 0a x b x c if

1) 1 1 1

2 2 2

a b c

a b c 2) 1 1 1

2 2 2

b c a

b a c 3) 1 1 1

2 2 2

a b c

a c b 4)

1 1 1

2 2 2

1 1 1, ,a b c

a b c

4. The quadratic equations 2 6 0x x a and 2 6 0x cx have one root in common. The

other roots of the first and second equations are integers in the ratio 4 :3. The common root is

1) 4 2) 3 3) 2 4) 1

5. Let 2 2 10 3 0x ax a for every real value of ,x then

1) 5a 2) 5a 3) 5 2a 4) 2 5a

6. The coefficient of 7x in the expansion of 6

2 31 x x x is

1) 144 2) 132 3) 144 4) 132

7. 10

20

0

k

k

C

1) 19 20

10

12

2C 2) 192 3) 20

10C 4) 182

8. The coefficient of the middle term in the binomial expansion in powers of x of 4

1 x and

of 5

1 x is the same if equal to

1) 5

3

2)

10

3 3)

3

10 4)

3

5

9. Find the number of numbers which can be formed with digits 0,1,2,3,4 greater than 1000 and

less than 4000 is repetition is allowed

1) 125 2) 400 3) 375 4) 374

10. A shelf contains 20 books, of which 4 are single volume and the others are 8, 5 and 3 volumes

respectively. In two many ways can these books be arranged on the shelf so that the order of

the volumes of same work is maintained?

1) 2.7! 2) 7! 3) 8.7! 4) 6.7!

11. Taking three same and one different letters from the letters of the word “PROPORTION”,

the number of words which can be formed is

1) 18 2) 360 3) 20 4) 21



12. If

2 1

3 2

4 3

x a x x

f x x b x x

x c x x

and 2 1a b c then

1) 50 1f 2) 50 1f 3) 50 501f 4) 50 501f

13. 3 3A is a matrix such that ,A a B adjA such that .B b Find the value of

2 2 1ab a b S where 2 3

3 5....

2

S a a a

b b b upto , and 3a

1) 225 2) 0 3) 300 4) +220

14. If matrix

1 0 1

3 4 5

0 6 7

A

and its inverse is denoted by

11 12 13

1

21 22 23

31 32 33

,

a a a

A a a a

a a a

then the value of

23a is equal to _____

1) 21

20 2)

1

5 3)

2

5

4)

2

5

15. If 4

, 14 2

x

xf x f x f x a

and

1 2 96.... ,

97 97 97f f f b

then order pair

,a b is

1) 2,20 2) 1,48 3) 1,24 4) 2,96

16. The function f satisfies the equation 59

3 2 10 301

xf x f x

x

for all real 1.x The value

of 7f is

1) 8 2) 4 3) -8 4) 11

17. Domain of the function

sin 1

1 2

xf x

x x

where x denotes the greatest integer function

less than ,x is

1) all real x 2) 2, 1 3) 2, 1 1,2R 4) 2,2R

18. If A, B and C are three sets such that A B A C and A B A C then

1) A C 2) B C 3) A C 4) A B

19. If : 2A x R x and : 2 3 :B x R x then:

1) 1,2A B 2) 2,5A B R

3) 2,5B A R 4) 2, 1A B

20. If 4 3 1:nX n n N and 9 1 : ,Y n n N where N is the set of natural numbers,

then X Y is equal to

1) N 2) Y X 3) X 4) Y

SECTION-II

(Numerical Value Answer Type)

This section contains 5 questions. The answer to each question is a Numerical values

comprising of positive or negative decimal numbers. Each question has 4 options (1), (2), (3)

and (4) for its answer, out of which ONLY ONE option can be correct. Marking scheme: +4 for correct answer, 0 in all other cases.



21. The least value of n such that 22 8 4 0,n x x n x R where n N is _____

22. The value of 1010 10

10

0 0

12

k kr

r k

CC

_____

23. In a ,ABC if

1

1 0,

1

a b

c a

b c

then the value of 2 2 216 sin sin sinA B C must be _____

24. Let :1 50 .X n N n If : is a multipleof 2 .A n X : is a multipleof 7 ,B n X n

then the number of elements in the smallest subset of X containing both A and B

25. An urn contains 5 red marbles, 4 black marbles and 3 white marbles. Then the number of

ways in which 4 marbles can be drawn so that at the most three of them are red is

SECTION – I


(C) and (D) for its answer, out of which ONLY ONE option can be correct.


PHYSICS

SYLLABUS: MECHANICS

26. The deceleration experienced by a moving motor boat after its engine is out off, is given by

dv/dt 3KV where K is a constant. If v is the magnitude of the velocity at cut-off the

magnitude of the velocity at a time t after the cut-off is

1) 2

0 02 1V V Kt 2) 0

ktV e 3) 0 2V 4) 0V

27. A stone falls freely under gravity. It covers distance 1 2,h h and 3h in the first 5 seconds, the

next 5 seconds and the next 5 seconds respectively. The relation between 1 2,h h and 3h is

1) 1 2 33 5h h h 2) 2 1 3 23 & 3h h h h

3) 1 2 3h h h 4) 1 2 32 3h h h

28. A projectile is given an initial velocity of ˆ ˆ2i j m s where i is along the ground and j is

along the vertical. If 210 ,g m s the equation of its trajectory is.

1) 25y x x 2) 22 5y x x 3) 24 2 5y x x 4) 24 2 25y x x

29. A projectile is fired at an angle of 045 with the horizontal. Elevation angle of the projectile at

its highest point as seen from the point of projection is

1) 060 2) 1tan 1 2 3) 1tan 3 2 4) 045

30. A player stops a football weighing 0.5 kg which comes flying towards him with a velocity of 10

m/s. If the impact lasts for 1/50th

sec. and the ball bounces back with a velocity of 15 m/s, then

the average force involved is

1) 250N 2) 1250N 3) 500N 4) 625N

31. A satellite in a force free space sweeps stationary interplanetary dust at a rate (dM/dt)=av.

The acceleration of satellite is

1) 22 v M 2) 2v M 3) 2 2v M 4) 2v



32. A ball of mass 10g moving perpendicular to the lane of the wall strikes it and rebounds in the

same plane with the same velocity. If the impulse experienced by the wall is 0.54 Ns, the

velocity of the ball is

1) 127ms 2) 13.7ms 3) 1/3 m 4) 1/2 m

33. A bullet is fired from a gun. The force on the bullet is given by 5600 3 10F t , F is in

neuton and t in seconds. The force on the bullet becomes zero as soon as it leaves the barrel.

What is the average impulse imparted to the bullet?

1) 1.8 N-s 2) Zero 3) 9 N-s 4) 0.9 N-s

34. A block of mass m is placed on the surface with a vertical cross section given by 3 6.y x If

the coefficient of friction is 0.5, the maximum height above the ground at which the block can

be placed without slipping is.

1) 1/6 m 2) 2/3 m 3) 1/3 m 4) 1/2 m

35. A block A of mass 1m rest on a horizontal table. A light string connected to it passes over a

frictionless pulley at the edge of table and from its other end another black B of mass 2m is

suspended. The coefficient of kinetic friction between the block and the table is .k When the

block A is sliding on the table, the tension in the string

1) 2 1 1 2km m g m m 2) 1 2 1 21 km m g m m

3) 1 2 1 21 km m g m m 4) 2 1 1 2km m g m m

36. Water falls from a height 60 m at the rate of 15kg s to operate a turbine. The losses due to

frictional force are 10% of energes, How much power is generated by the turbine?

210g m s

1) 8.1 KW 2) 10.2 KW 3) 12.3 KW 4) 7.0 KW

37. In the figure shown, a particle of mass m is released from the position A on a smooth track.

When the particle reaches at B, then normal reaction on it by the track is

1) mg 2) 2mg 3) 2/3 mg 4) 2m g h

38. A block C of mass m is moving with velocity 0V and collides elastically with block A of mass m

and connected to another block B of mass 2m through spring constant K. What is K if 0X is

compression of spring when velocity of A and B is same ?

1) 2 2

0 0mv x 2) 2 2

0 02mv x 3) 2 2

0 03 2mv x 4) 2 2

0 02 3mv x

39. A vertical spring with force constant k is fixed on a table. A ball of mass m at a height h above

the free upper end of the spring falls vertically on the spring so that the spring is compressed

by a distance d. The net work done in the process is

1) 21

2mg h d kd 2) 21

2mg h d kd 3) 21

2mg h d kd 4) 21

2mg h d kd



40. A body of mass m kg is ascending on a smooth inclined plane of inclination 1

sinx

with

constant acceleration of a 2 .m s The final velocity of the body is v m/s. The work done by the

body during the motion is (initial velocity of a body =0)

1) 21

2mv g xa 2) 2

2

gmv a

3) 1 2t 4) t m

41. A glass marble dropped from a certain height above the horizontal surface reaches the

surface in time t and then continues to bounce up and down. The time in which the marble

finally comes to rest in

1) ne t 2) 2e t 3) 1

1

et

e

4) 1

1

et

e

42. A spring of spring constant 35 10 N m is stretched initially by 5 cm from the unstrutched

position. Then the work required to stretch it further by another 5 cm is

1) 12.50 Nm 2) 18.75 Nm 3) 25.00 Nm 4) 6.25 Nm

43. From a solid sphere of mass M and radius R a cube of maximum possible volume is cut.

Moment of inertia a of cube about an axis passing through its centre and perpendicular to one

of its focus is

1) 24 9 3MR 2) 24 3 3MR 3) 2 32 2MR 4) 2 16 2MR

44. A rings of mass M and radius R is rotating about its axis with angular velocity . Two

identical bodies each of mass M are now gently attached at the two end of a diameter of the

ring. Become of this, the kinetic energy loss will be

1) 2 22m M m

RM

2)

2 2MmR

M m

3)

2 2

2

MmR

M m

4)

2 2

2

M m MR

M m

45. A uniform rod of length l is free to rotate in a vertical plane about a fixed horizontal axis

through O. The rod begins rotating from rest from its unstable equilibrium position. When it

has turned through an angle its angular velocity is given as

1) 6

sing

l 2)

6sin

2

g

l

3)

6cos

2

g

l

4)

6cos

g

l

SECTION- II



comprising of positive or negative decimal numbers. Each question has 4 options (A), (B), (C)

and (D) for its answer, out of which ONLY ONE option can be correct. Marking scheme: +4 for correct answer, 0 in all other cases.



46. A particle tied to a string describes a vertical circular motion of radius r continually. If it has

a velocity 3gr at the highest point then value of ratio of respective tensions in the string

holding it at highest and lowest points is

47. A rain drop of mass 1g falling from height of 1km hits the ground with a speed of 150 .ms If

the resistive force is proportional to the speed of the drop, then the work done by the resistive

force is 2Take 10 msg INS.I Units

48. A track has two surfaces AB and CD each of length 3m and angle of inclination of 030 with

the horizontal and a central horizontal part of length 4m as shown in figure. A block of mass

0.2kg slides from rest from point A. The inclined surface are frictionless. If the coefficient of

friction between the block and the horizontal flat surface is 0.2 where will the block finally

come to rest from point B. (In S.I Units)

49. A boy is pushing a ring of mass 2kg and radius 0.5m with a stick as shown in the figure. The

stick applies a force of 2N on the ring and rolls it without slipping with an acceleration of

-20.3ms . The coefficient of friction between the ground and the ring is large enough that

rolling always occurs. Then the coefficient of friction between the stick and the ring is.

50. Two masses 1m =1kg and 2m =2kg are connected by a light inextensible string and suspended

by means of a weightless pulley as shown in the figure. Assuming that both the masses start

from rest, the distance travelled by centre of mass in two seconds is ______ in S.I system

2take g=10 ms



SECTION – I


(C) and (D) for its answer, out of which ONLY ONE option can be correct.


CHEMISTRY

SYLLABUS: FIRST YEAR IN ORGANIC CHEMISTRY

51. Among 2 3 2 2 3, ,Al O SiO PO and 2SO the correct order of acid strength is

1) 2 3 2 2 3 2Al O SiO PO SO 2) 2 2 3 2 3SO PO SiO AlO

3) 2 2 2 3 2 3SiO SO Al O PO 4) 2 3 2 2 2 3Al O SiO SO PO

52. The electronic configuration of four elements are given below. Arrange these elements in the

correct of the magnitude (without sign) of their electron affinity.

(I) 2 52 2s p (II) 2 53 3s p (III) 2 42 2s p (IV) 2 43 3s p

Select the correct answer using the codes given below:

1) III<IV<II<I 2) III<IV<I<III 3) I<II<IV<III 4) II<I<IV<III

53. The electron affinity of chlorine is 3.7 eV. How much energy in kcal is released when 4 g of

chlorine is completely converted into Cl ion in gaseous state. (Given: 1 eV = 23.06 kcal 1mol )

1) 9.6 kcal 2) 19.6 kcal 3) 4.8 kcal 4) 11.6 kcal

54. 10 mL of 2 2H O solution on treatment with KI and titration of liberated 2 ,I required 10 mL of

1 N hypo. Thus 2 2H O is.

1) 1N 2) 5.6 volume 3) 117g L 4) all are correct

55. 2D O (heavy water) and 2H O differ in following except in.

1) freezing point 2) density

3) ionic product of water 4) its reaction with sodium

56. H, D and T (isotopes of hydrogen) have nuclear spin quantum number respectively as:

1) 1 1

,1,2 2

2) 1 1

, ,12 2

3) 1 3

,1,2 2

4) 1 1 1

, ,2 2 2

57. Among the following species, identify the isostructural pairs:

3 3 3 3 3, , , ,NF NO BF H O HN

1) 3 3,NF NO and 3 3,BF H O 2) 3 3,NF HN and 3 3,NO BF

3) 3 3,NF H O and 3 3,NO BF 4) 3 3,NF H O and 3 3,HN BF

58. Four diatomic species are listed below in different sequences. Which of these presents the

correct order of their increasing bond order?

1) 2

2 2 2C He NO O 2) 2

2 2 2He O NO C

3) 2

2 2 2O NO C He 4) 2

2 2 2NO C O He

59. Which of the following types of bonds are present in 4 2,5 ?CuSO H O

I. Electrovalent II. Covalent III. Coordinate

Select the correct answer using the code given below:

1) I and II only 2) I and III only 3) I, II and III 4) II and III only

60. The enamel of teeth is.

1) 2CaF 2) 3 4 2Ca PO 3) 3 4 22

3 .Ca PO CaF 4) 4CaSO



61. 2 2 :Na O

1) is diamagnetic in nature 2) is a salt of dibasic acid 2 2H O

3) oxides 3 greenCr to 2

4CrO (yellow) 4) all are correct properties of 2 2Na O

62. Which cannot be used to generate 2 ?H

1) Al NaOH 2) Zn NaOH 3) Mg NaOH 4) 2LiH H O

63. 3 4 aq

B OH NaOH Na B OH

Which of the following is the best catalyst to take this reaction in forward direction

1) cis-1,2 diol 2) trans-1,2 diol 3) borax

4) 2 4Na HBO

64. 1273

2 3 2

KAl O C Cl X Y . Correct statements regarding X & Y

1) Both X and Y contain dative bonds in one of their forms

2) Both contains Ionic bond

3) Both contains Oxygen 4) Both contains chlorine

65. Which of the following is the correct order of reducing power of hydrides?

1) 4 4 4 4 4CH < SiH <GeH < SnH < PbH 2) 4 4 4 4 4CH > SiH >GeH > SnH > PbH

3) 4 4 4 4 4CH >GeH > SiH > PbH > SnH 4)

4 4 4 4 4SiH <CH < SnH <GeH < PbH

66. The correct order of increasing “ C O ” bond length of and -2

3 2CO, CO CO is

1) -2

3 2CO , CO , CO 2) -2

2 3CO , CO , CO 3) -2

3 2CO, CO , CO 4) -2

2 3CO , CO , CO

67. Name the structure of silicates in which three oxygen atoms of 4

4SiO

are shared is

1) pyrosilicate 2) sheet silicate

3) linear chain silicate 4) three dimensional silicate

68. 500 ml of a sample COD of water required 19 .6 mg of K2Cr

2O

7 of water sample is

1) 8 ppm 2) 6.4 ppm 3) 16.8 ppm 4) 4.9 ppm

69. The gas leaked from a storage tank of the Union Carbide plant in Bhopal gas tragedy was.

1) Methylamine 2) Ammonia 3) Phosgene 4) Methylisocyanate

70. A water sample has ppm level concentration of following anions

2

4 310; 100; 50F SO NO

The anion/anions that make/makes the water sample unsuitable for drinking is/are?

1) only 2

4SO 2) only 3NO 3) both 2

4SO and 3NO 4) only F

SECTION-II



comprising of positive or negative decimal numbers. Each question has 4 options (A), (B), (C)

and (D) for its answer, out of which ONLY ONE option can be correct.

Marking scheme: +4 for correct answer, 0 in all other cases. 71. Number of hydrogen bonds in H9O4

+ species is

72. A 1 g sample of 2 2H O solution containing x per cent 2 2H O by weight required x mL of 4KMnO

for complete oxidation in acidic medium. Calculate normality of 4KMnO solution.

73. A student suggested that calcium should be made if calcium oxide is reacted with aluminum

powder. Was the student correct?

0 1604.2fG CaO kJ mol

0 1

2 3 1582.4fG Al O kJ mol

74. How many oxygen atoms of 4

4SiO

are shared in three dimensional sheet silicate?

75. How many units of SiO44–

will be required for the formation of pyrosilicates?

******



SRIGAYATRI EDUCATIONAL INSTITUTIONS

INDIA

SR MPC Date:20-04-2020

Time: 3 Hours Max. Marks : 300

KEY SHEET

MATHEMATICS

1) 4 2) 4 3) 2 4) 3 5) 3 6) 4 7) 1 8) 3 9) 4 10) 3

11) 3 12) 1 13) 1 14) 1 15) 2 16) 2 17) 3 18) 2 19) 3 20) 4

21) 5 22) 1 23) 144 24) 29 25) 490

PHYSICS

26) 1 27) 1 28) 2 29) 2 30) 4 31) 2 32) 1 33) 4 34) 1 35) 2

36) 1 37) 1 38) 4 39) 1 40) 4 41) 3 42) 2 43) 1 44) 3 45) 3

46) 0.2

5

47) -8

.

7

5

48) 0.

5

49) 0.

4

50) 2.2

2

CHEMISTRY

51) 1 52) 2 53) 1 54) 4 55) 4 56) 1 57) 3 58) 2 59) 3 60) 3

61) 4 62) 3 63) 1 64) 1 65) 1 66) 4 67) 2 68) 2 69) 4 70) 4

71) 3 72) 0.59 73) 230.2 74) 4 75) 2

JEE MAINS MODEL (UT-1)



HINTS & SOLUTIONS

MATHS

1. 1 1 1 1

, , ,

4 3 2

1 1 100 2 410 0x

x x x x x

4 3 210 4 2 100 1 0x x x x

1 1 1 1 4 2

10 5

2. 1 0S r s t

0r s s t t r

3 3 3

3r s s t t r s r s t t r

3 t r s 3trs

2008

3 7538

3. 2

1 1 1 0a x b x c

, are roots of equation

1 1

......

1

x

1 112

0a b

cx x

2

1 1 1 0 1a b x c x

1 1 1

2 2 2

c b a

a b c

2

2 2 2 0 2a x b x c

1 1

,

are roots in equation

4. Common root

, 4 are root of 2 6 0x x a

4 6

1

4 6 2

,3 are roots of 2 6 0x cx

3 6

2

d integer

5. 0, 0, 0a y D

2 3 10 0a a

5 2a

6. 66 62 21 1 1 1x x x x x

1

6 1611

r r

rC x

2

2

66 21r r

rC x

1 2 1 2

1 2

26 6 1 1r r r r

r rC C x

6 6 6 6 6 6

1 3 3 2 5 11C C C C C C

132

1 22 7r r

0r x

1 21, 3r r

1 23, 2r r

1 25, 1r r

7. 20 20 20

0 1 10....C C C

20 20 20 20 20 20

0 1 10 0 1 10.... .... 2C C C C C C

20 20 20 20 20 20 20

0 1 10 11 19 20 10.... .... 2C C C C C C C

20 20

1020 20C

19 20

10

12

2C

8. 4 4 2 24

21 1x C x

6 6 3 36

31 1x C x

34 2 6

2 3C C

3

10

9. _ _ _ _ _

3 5 5 5 375 1 374

10. P C M B 1 2 8 1 5 1 2 3...... .....H H H G G F F F

7! 2 2 2 8 7!

11. PP, RR, OOO T I N

3 same and one different

1 5

1 1

4!20

3!C C

12. 1 1 3 22R R R R

2 2 2 0 0

3 2

4 3

x a c x b

f x x b x x

x c x x

2

3 4 2f x x x x

1f x

50 1f

13. B adjA

3 1 2b A a

2

1312 11 27

aS b

a

b

3,a b a 9

13s



2 2 1 225ab a b s

14. 23

cofactorof 6 21 21

20 20a

A

15. 4

4 21 1 1

4 2 2 4

x

xa f x f x a

1 2 2 1.... 1 1

97 97 97 97b f f f f

48 48b a 1, 48a b

16. 7 3 7 2 1 100 1x f f

11 3 11 2 7 140 2x f f

1 3 2 2

5 7 20f

7 4f

17. Not defined if 1 0x or 2 0x

1x 2x

1 2x 2 1x

1,2 2, 1R

18. B A B B A C

B B A B C

= A C B C

A B C

B A C C C B C

19. 2 2A x

2 3 5

2 3 1

x xB

x x

: 2, 1A B x x

: ,2 5,A B x x

: 1,2A B x x

: , 2 5,B A x x

20. Set x contains elements of the form

4 3 1 1 3 3 1nn n n

2 1

1 29 3 3 .....n n n n

nC C

Set x has natural numbers which are

multiplies of 9 set y has all multiplies of 9

X Y Y

21. 2 1 0ax bx 0 0a D

2 0 1 0n D

64 4 2 4 0n n

24 2 24 0n n

2 2 24 0n n

6 4 0 2n n

From (1) and (2) 4 5n n

22. 10 10

10 10

0 0

1

2

k

r k

r k

C C

10

10 12 1

2

1

23. 21 0c ab a c a b b c

2 2 2 0a b c ab bc ca

2 2 2

0a b b c c a

Which is possible when only when

3a b c A B C

2 2 216 sin sin sin 1443 3 3

24. 50; 25; 7; 3n X n A n B n A B

n A B n A n B n A B

25 7 3 29

25. 0Red 1Red 2Red 3Red

Number of ways 7 5 7 5 7 5 7

4 1 3 2 2 3 1. . .C C C C C C C

35 175 210 70 490

1x 1x

PHYSICS

26. 3dvkv

dt (or)

3

dvkdt

v

Integrating we get, 2

1..... 1

2kt c

V

At 0 2

0

10,

2t v v c

v

Putting in (1)

2 2 2 2

0 0

1 1 1 1

2 2 2 2kt or kt

v v v v

(or)

2 2

0

1 1

2 2kt

v v

or

22 00 2

1 2v

v ktv

or

2

2 0

2

01 2

vv

v kt

or 0

2

01 2

vv

v kt

27. 21

2h gt

2

1

15 125

2h g

2

1 2

110 500

2h h g

2 375h



2

1 2 3

115 1125

2h h h g

3 625h

2 1 3 13 , 5h h h h

or 2 31

3 5

h hh

28. ˆ ˆ ˆ2 cos 1, sin 2x yu i j u i u j u u

2

2

1tan

2 x

gxy x

u

2 212 2 5

2y x gx x x

29. 2 2 0 2sin 45

... 12 4

u uH

g g

2 2sin90u u

Rg g

2

... 22 2

R u

g

tan

2

H

R

2

1

2

1 14tan

2 2

2

u

g

u

g

30. Here m =0.5 kg; u=-10m/s; t=1/50s;

v=+15 1ms

force 0.5 10 15 50 625m v u t N

31. Thrust on the satellite,

2vdmF v v v

dt

Acceleration 2F m v M

32. As the ball, m=10g =0.01 kg rebounds after

striking that wall

Change in momentum

2mv mv mv

Impulse =Change in momentum =2mv

1Impulse 0.5427

2m 2 0.01

Nsv ms

Kg

33. Given 5600 2 10F t

The force is zero at time t, given by 50 600 2 10 t

3

5

6003 10

2 10t

seconds

Impulse 33 10

5

0 0

600 2 10

t

Fdt t dt

33 105 2

0

2 10600

2

tt

2

3 5 3600 3 10 10 3 10

1.8 0.9 0.9 Ns

34. At limiting equilibrium, tan

2

tandy x

dx z (from question)

Coefficient of friction 0.5

2

0.52

x 1x

Now, 3 1

6 6

xy m

35. For the motion of both the blocks

1 1km a T m g

2 2m g T m g

2 1

1 2

km g m ga

m m

2 12 2

1 2

km g m gm g T m

m m

Solving we get tension in the string

1 2

1 2

1 km m gT

m m

36. Given, 260 , 10h m g ms

Rate of flow of water 15kg s

Power of the falling water

1 215 10 60 900kgs ms m watt

Loss in energy due to friction



10

9000 900100

watt

Power generated by the turbine

9000 900 watt 8100 watt 8.1kw

37. By conservation of energy

213 2

2mg h mg h mv (v=velocity at B)

21; 2

2mgh mv v gh

From free body diagram of block at B

2

2 ;mv

N mg mg N mgh

38. When C strikes A

2 2 2 1

0 0

1 1 1velocity of A

2 2 2mv mv kx v

2 2 2

0 0 ......kx m v v i

2 2

0

1 12

2 2mv kx

(When A and B block attains K.E)

2 2

0

1......

2Kx mv ii

From (i) and (ii)

2 2 2 2 2

0 0 0 02

kkx mv mv mv x

2 2 2

0 0 02

kkx x mv

2 2

0 0

3

2kx mv

2

0

2

0

2

3

vk m

x

39. Gravitational potential energy of ball gets

converted into elastic potential energy of the

spring 21

2mg h d kd

Net work done 210

2md h d kd

40. 1

sinx

From free body diagram of the body

sinF mg ma

sin ..... 1g

F m g a m ax

Displacement of the body till its velocity

reaches v

2

2 0 22

vv as s

a

Now, work done

2

0cos2

m xvFs g ax

x a

2

2

mvg ax

ax

41. 2

AB

ht

g

122BC CB

ht t

g

22 2

2 2e h h

eg g

2 22BD DB

ht t e

g

Total time taken by the body in coming to

rest

22 2 22 2 .....

h h he e

g g g

22 22 1 ....

h he e e

g g

2 2 1 2 1 12

1 1 1

h h h e ee t

g g e g e e

42. 35 10k N M



2 23 2 3

2 1

1 15 10 0.1 0.05

2 2w k x x

5000

0.15 0.05 18.75 .2

Nm

43. Here 2

3a R

Now,

3

3

4

3

'

RM

M a

3

3

43 23 . '

2 32

3

RM

M

R

Moment of inertia of the about the given

axis,

2

2 2

2 2

' 43 3.

6 6 9 3

MR

M a MRI

44. Kinetic energy (rotational) 21

2RK I

Kinetic energy (translational) 21

2TK MV

M.I. (initial) I(ring) 2 2 .MR mR

'

2system

M

M m

Solving we get loss in

2 2..

2

M mK E R

M m

45. 211

2 Loss of potential energy

2

211 cos

2 3 2

ml mgl

2 23 62cos cos

2 2

g g

l l

46. 2

2 3top top

mvT mg mg V gr

r

2 6 8bottomT mg mg mg

: 1: 4 0.25top bottomT T

47. 2 21 1

2 2gravitational frictionw w mv mu

21

2friction gravitational forcew mv w

212

2mv mgh

1.25 10

8.75 Joule

48. At point A, the energy of the block is intirely

potential =mgh, where h is the height of A

from surface sin 3sin3 1.5h AB m

When the block is released, it reaches point B

where the entire PE is converted into KE. It

will, move on tack BC. On reaching „C‟ it

will rise on the surface CD to a point E and

will then return to C moving towards B and

the process goes on until the block loses all

its energy and comes to rest. The body loses

energy while moving on the horizontal part

BC of the track.

If S is the total distance travelled on

horizontal part, the work done against

friction is RS mgs

From the principle of conservation of energy,

we have mgh mgs

1.5

7.50.2

hs m

i.e., the block travels a total distance of 7.5m

on the horizontal track BC before coming to

rest. Starting from B. It travels 4m from B to

C and 3.5m from C to a ppoint P where it

comes to rest. Hence the block comes to rest

at point P at a distance of 0.5m from B.

49. 12 f Ma

1 2 2 2 0.3f Ma

1 1.4f N



Taking torque about C

1 2 cf R f R I

2

1 2 2

a af f MR

R R

1 2f f Ma

2 1f f Ma

1.4 2 0.3

2 0.8 2f N

0.8

0.42

50. Acceleration of each block 2 1

1 2

m ma g

m m

blocks move in opposite directions.

1 1 2 2

1 2

1 2 10

1 2 9cm

a am a m aa

m m

221 1 10 20

2 2.222 2 9 9

cms a t m m

CHEMISTRY

51. As acidic nature increases left to right in a

period with increase in electronegativity.

52. Conceptual

53. 35.5 3.7 23.06

3.7kcal

Cl e Cl eV

As energy released for conversion of 4g

gaseous chlorine into Cl ions

3.7 23.06

4 9.635.5

kcal

54. 2 2 22H O I I

2 2

2 2 3 4 62 2I S O S O I

2

2 2 2 2 32H O I S O

1 1 2 2N V N V

2 2H O hypo

1 2 2

10 11

10N H O N

(a) True

Conc. 117N E gL

(c) True “Volume” conc.

5.6 "5.6"N Volume

Thus, (b)

Thus all correct (d)

55. Conceptual

56. Conceptual

57. 3 3,NF H O are pyramidal in shape while

3 3,NO BF are planar molecules.

58. 2

2 2 2He O NO C

Bond order 0.5 1.5 2.5 3.0

59. 4 25CuSO H O

2.5Cu O S O H O

O

O

Here, ionic and covalent bonds are present in

4CuSO while 2H O molecules are attached

by coordinate bonds.

60. Conceptual

61. 2 2Na O has peroxide on 2

2 18O e and is

isoelectronic of 2.F It has all paired electrons

and is thus diamagnetic.

2

2 2 22H O H O

Thus, it is also salt of dibasic acid 3

2 2.H O Cr

is oxidized to 2

4CrO in acidic medium.

3 2 2

2 4 22Cr O H CrO H O

Thus, (d)

62. Mg does not react with .NaOH

2 2 22 2 2 2 3Al NaOH H O NaAlO H

2 2 22Zn NaOH Na ZnO H

2 2LiH H O LiOH H

63. Boric acid is a very weak acid. It does not

react with alkali explicitly. However, the

weak orthoboric acid may be converted into

comparatively strong monobasic acid by

addition of any cis-1,2 diol to pull the

reaction in forward direction significantly.

64. 1273

2 3 2 33 3 2 3KAl O C Cl AlCl CO

65. Reducing Power 1

bond strength

66.

67. In sheet silicates, three out of four oxygen of 4

4SiO unit are shared as shown in below :

Three oxygens of every tetrahedra are shared

with others

In pryosilicates, there is only one shared

oxygen, in linear chain silicates, two oxygen



per tetrahedra are shared while in three

dimensional silicates, all four oxygens are

shared.

68. -3

2 2 7 219.6×10 g K Cr O ................500ml of H O ?

............. 62

10 ml of H O

2 2 7 249g of K Cr O =8g of O

2 2 739.2g of K Cr O =?

COD = 6.4 ppm

69. It was methyl isocyanate 3CH NCO

70. Water becomes harmful if

F concentration greater than 10 ppm

2

4SO greater than 500 ppm

3NO greater than 50 ppm

71.

O

H H

H

O

H

HO

H

H

O

HH

72. Pure 2 2100 1700

x xH O g equivalent

41000

xNKMnO equivalent

1000 1700

Nx x

10

0.5917

N N

73. 2 33 2 3CaO Al Al O Ca

0 0 0

2 3 3f f fG G Al O G CaO

1582.4 3 604.2

230.2kJ

+ve sign indicates that reaction is no

spontaneously; thus student‟s suggestion is

incorrect.

74. These silicates involve all four oxygen atom

in sharing with adjacent 4

4SiO tetrahedral

units.

75.

Si

OO

O

OSi

OO

O

SRIGAYATRI EDUCATIONAL INSTITUTIONS...2020/04/20 · 8. The coefficient of the middle term in the...

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