SRIGAYATRI EDUCATIONAL INSTITUTIONS MPC PPT...2020/02/04 · 27. A street car moves rectilinearly from station A to the next station B (from rest to rest) with an acceleration varying

SRIGAYATRI EDUCATIONAL INSTITUTIONS

INDIA

JR MPC Date: 02-04-2020 Time: 3 Hours Max Marks : 300

SECTION – I

(SINGLE CORRECT ANSWER TYPE) This section contains 20 multiple choice questions. 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 if not attempted and -1 if not correct.

MATHS

SYLLABUS: Sets & Relations, Functions, Straight lines

1. If the set of factors of a whole number ‘n’ including ‘n’ itself but not ‘1’ is denoted by F(n). If

16 40F F F x then ‘x’ is

1) 4 2) 8 3) 6 4) 10

2. Let 1, 2,3 then the number of subsets of A is

1) 2 2) 4 3) 8 4) 0

3. Let 25 , 2n A B X n B A X and 2n A B X . If 2n A n B then ‘X’ is

1) 4 2) 5 3) 6 4) 7

4. Suppose 1 2 30, .......,A A A are thirty sets each with five elements and 1 2, ,....... nB B B are n sets each

with three elements such that 30

1 1

n

i j

i j

A B S

. If each elements of S belongs to exactly ten of the

'iA s and exactly 9 of the 'jB s , then the value of n is

1) 15 2) 135 3) 45 4) 90

5. In a battle 70 % of the combatants lost one eye, 80 % an ear, 75% an arm, 85% a leg, x% lost

all the four limbs the minimum value of x is

1) 10 2) 12 3) 15 4) 5

6. In the set 1,2,3,4,5 ,A a relation R is defined by , : , ,R x y x y A x y . Then R is

1) reflexive 2) symmetric 3) transitive 4) equivalence

7. If A ={ 1,2,3} ,R ={ (1,2),(1,1),(2,3)} Then minimum number of elements may be adjoined with

the elements of R so that it may become transitive is

1) 0 2) 1 3) 2 4) 3 8. The period of cosx x is

1) 2 2) 3) 2

4) non periodic

9. A real valued function f(x) satisfies the functional equation ( ) ( ) ( ) ( ) ( )f x y f x f y f a x f a y where a is a given constant and (0) 1f , (2 )f a x is

equal to 1) ( )f x 2) ( ) ( )f a f a x 3) ( )f x 4) ( )f x

10. The range of 2

2

1f(x) x

x 1

is

1) [1, ) 2) [2, ) 3) 3

[ , )2 4) R

11. If the coordinates of the points A,B,C be (-1,5) ,(0,0) and (2,2) respectively , and D be the

middle point of BC, then the equation of the perpendicular drawn from B to the line AD is

1) 2 0x y 2) 2 0x y 3) 2 0x y 4) 2 0x y

JEE MAINS MODEL

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 JEE MAINS MODEL 02 APR 2020

12. If AD,BE and CF are the altitudes of a triangle ABC Whose vertex A is the point (-4,5) .The

coordinates of the points E and F are(4,1) and (-1-4) respectively , then equation of BC is

1) 3 4 28 0x y 2) 4 3 28 0x y 3) 3 4 28 0x y 4) 2 7 0x y

13. ABC is an equilateral triangle whose centroid is origin and base BC is along the line

11 60 122x y .Then

1) Area of the triangle is numerically equal to the perimeter

2)Area of triangle is numerically double the perimeter

3) Area of triangle is numerically three times the perimeter

4) Area of triangle is numerically half of perimeter

14. A straight line passes through the point of intersection 2 2 0 2 6 0x y and x by and

the origin .Then the complete set of values of b for which the acute angle between this line

and y=0 is less than 45o is

1) ,4 7, 2) ,5 7,

3) ,4 5,7 7, 4) ,4 4,5, 7,

15. The set of lines 0, 3 2 4 0ax by c where a b c , is concurrent at the point:

1) 1

,02

2) 1 1

,2 2

3) 1 1

,4 4

4) 3 1

,2 2

16. The orthocentre of the triangle formed by the lines xy=0 and 1x y is :

1) 1 1

,2 2

2) 1 1

,3 3

3) (0,0) 4) 1 1

,4 4

17. Locus of the image of the point (2,3) in the lines 2 3 2 3 4 0x y x y is( where

R )

1) 2 2 3 4 7 0x y x y 2) 2 22 3 2 4 7 0x y x y

3) 2 2 2 4 4 0x y x y 4) 2 2 2 4 3 0x y x y

18. AB is the diameter of a semi circle K,C is an arbitrary point on the semicircle (other than A

or B ) and S is the centre of the circle inscribed into triangle ABC , then measure of:

1) angle ASB changes as C move on K

2) angle ASB is the same for all positions of C but it cannot to be determined with out knowing

the radius

3) angle ASB = 0135 for all C 4)angle ASB= 0150 for all C

19. The equation of 1L and 2L are y=mx and y=nx, respectively . suppose 1L makes twice as

larger of an angles with the horizontal (measured counter clock wise from the positive x-axis )

as does 2L and that 1L has 4 times the slope of 2L .If 1L is not horizontal , then the value of

the product (mm) equals :

1) 2

2 2)

2

2 3) 2 4) -2

20. The line x/3+y/4=1 meets the y-and x- axis at A and B , respectively. A square ABCD is

constructed on the line segment AB away from the origin .The co-ordinates of the vertex of the

square farthest from the origin are

1) (7,3) 2) (4,7) 3) (6,4) 4) (3,8)

SECTION-II

(Numerical Value Answer Type)

21. Let ,f x y be a periodic function satisfying the condition



, 2 2 ,2 2 ,f x y f x y y x x y R and let g x be a function defined as 2 ,0xg x f .

If T is period of g x then find the value of T/4.

22. If ‘f’ is a polynomial function satisfying the condition

tan cot tan . cotf x f x f x f x

, 02 2

x

and 2 9f then the value of

' 2

6

f is.

23. If 2 2( ) cos[ ] cos[ ]f x x x where [x] stands for greatest integer function, then

22

f f k

, then 10

k=_______.

24. A line with gradient 2 intersects a line with gradient 6 at the point (40,30). The distance

between X-intercepts of these lines is________

25. Distance of the origin from the line (1 3) (1 3)y x=10 along the line y= 3x k is____

PHYSICS

SYLLABUS: Kinematics, Newton’s Laws of motion

26. Two particles A and B are placed in gravity free space at (0, 0, 0)m and (30, 0, 0)m

respectively. Particle A is projected with a velocity 1ˆˆ ˆ5 10 5i j k ms , while particle B is

projected with a velocity 1ˆˆ ˆ10 5 5i j k ms simultaneously. Then,

1) They will collide at (10, 20, 10)m 2) they will collide at (10, 10, 10)m

3) they will never collide 4) they will collide at 2s

27. A street car moves rectilinearly from station A to the next station B (from rest to rest) with an

acceleration varying according to the law f a bx , where a and b are constants and x is the

distance from station A. The distance between the two stations and the maximum velocity are

1) max

2,

a ax v

b b 2) max,

2

b ax v

a b 3) max,

2

a bx v

b a 4) max,

a ax v

b b

28. When a man moves down the inclined plane with a constant speed 5 ms-1

which makes an angle of 37

0 with the horizontal, he finds that the rain is falling vertically downward. When he

moves up the same inclined plane with the same speed, he finds that the rain makes an angle

1 7tan

8

with the horizontal. The speed of the rain is

1) 1116ms 2) 132ms 3) 5 ms-1

4) 173 ms

29. A particle is falling freely under gravity. In first t second it covers distance x1 and in the next t second, it covers distance x2, then t is given by

1) 2 1x x

g

2) 2 1x x

g

3) 2 12 x x

g

4) 2 12 x x

g

30. A packet is released from a rising balloon accelerating upward with acceleration a. The acceleration of the stone just after the release is

1) a upward 2) g downward 3) (g-a) downward 4) (g+a) downward 31. The length of a seconds hand in watch is 1 cm. The change in velocity of its tip in 15s is

1) Zero 2) 30 2

cm/s 3)

30

cm/s 4)

2

30

cm/s

32. When a ball is thrown up vertically with velocity v0, it reaches a maximum height of h. If one wishes to triple the maximum height then the ball should be thrown with velocity



1) 03 v 2) 03 v 3) 09 v 4) 0

3

2v

33. A train is moving on a track at 30 ms-1

. A ball is thrown from it perpendicular to the direction of motion with 30 ms

-1 at 45

0 from horizontal. Find the distance of ball from the point of

projection on train to the point where it strikes the ground.

1) 90 m 2) 90 3 m 3) 60m 4) 60 3 m

34. A fixed mortar fires a bomb at an angle of 530 above the horizontal with a muzzle velocity of

80 ms-1

. A tank is advancing directly towards the mortar on level ground at a constant speed of 5 m/s. The initial separation (at the instant mortar is fired) between the mortar and tank, so that the tank would be hit is [Take g = 10 ms

-2]

1) 662.4 m 2) 526.3 m 3) 486.6 m 4) None of these 35. A ball is projected from point A with velocity 10 ms

-1 perpendicular to the inclined plane as

shown in figure. Range of the ball on the inclined plane is

900

A

300

1) 40

3m 2)

20

3m 3)

12

3m 4)

60

3m

36. A gun is firing bullets with velocity 0v by rotating it through 3600 in the horizontal plane. The

maximum area covered by the bullets is

1) 2

0v

g

2)

2 2

0v

g

3)

4

0

2

v

g

4)

2 4

0v

g

37. A grass hopper can jump maximum distance 1.6m. It spends negligible time on ground. How

far can it go in 10 2 s? 1) 45m 2) 30 m 3) 20 m 4) 40 m 38. A ball is projected upward from the top of a tower with a velocity 50 ms

-1 making an angle 30

0

with the horizontal. The height of tower is 70m. After how many seconds from the instant of throwing, will the ball reach the ground. (g = 10 ms

-2)

1) 2s 2) 5s 3) 7s 4) 9s 39. Three equal weights A, B and C of mass 2 kg each are hanging on a string passing over a fixed

frictionless pulley as shown in the figure. The tension in the string connecting weights B and C is approximately

1) zero 2) 13 N 3) 3.3 N 4) 19.6 N 40. A block of mass m is placed at rest on an inclined plane of inclination to the horizontal. If

the coefficient of friction between the block and the plane is , then the total force the inclined

plane exerts on the block is 1) mg 2) cosmg 3) sinmg 4) tanmg

41. For the arrangement shown in the figure, the reading of spring balance is

1) 50 N 2) 100 N 3) 150 N 4) None of these 42. A particle is placed at rest inside a hollow hemisphere of radius R. The coefficient of friction

between the particle and the hemisphere is 1

3 . The maximum height up to which the

particle can remain stationary is



1) 2

R 2) 3

12

R

3) 3

2R 4) 3

8

R

43. A smooth inclined plane of length L having inclination with the horizontal is inside a lift which is moving down with a retardation a. The time taken by a body to slide down the inclined plane from rest will be

1)

2

sin

L

g a 2)

2

sin

L

g a

3) 2

sin

L

a 4) 2

sin

L

g

44. A block of mass m is placed at rest on a horizontal rough surface with angle of friction . The

block is pulled with a force F at an angle with the horizontal. The minimum value of F required to move the block is

1) sin

cos

mg

2)

cos

cos

mg

3) tanmg 4) sinmg

45. A heavy body of mass 25 kg is to be dragged along a horizontal plane 1

3

. The least

force required is (1 kgf = 9.8 N)

1) 25 kgf 2) 2.5 kgf 3) 12.5 kgf 4) 6.25 kgf

SECTION- II

(Numerical Value Answer Type) 46. During the first 18 min of a 60 min trip, a car has an average speed of 11 ms

-1. What should be

the average speed for remaining 42 min so that car is having an average speed of 21 ms-1

for

the entire trip________ ms-1

47. A stone is dropped from the top of a tower and one second later, a second stone is thrown

vertically downward with a velocity 20 ms-1

. The second stone will overtake the first after

travelling a distance of (g=10 ms-2

)______ m.

48. Three equal weights A, B and C of mass 2 kg each are hanging on a string passing over a fixed

frictionless pulley as shown in the figure. The tension in the string connecting weights B and C

is ______ N

A

B

C

49. In order to raise a block of mass 100 kg a man of mass 60 kg fastens a rope to it and passes the

rope over a smooth pulley. He climbs the rope with an acceleration 5

4

g relative to rope. The

tension in the rope is 210g ms .

50. A suitcase is gently dropped on a conveyor belt moving at a velocity of 3 m/s. If the coefficient

of friction between the belt and the suitcase is 0.5, find the displacement of the suitcase

relative to conveyor belt before the slipping between the two is stopped (g= 10 m/s2)

CHEMISTRY

SYLLABUS : Atomic structure and Periodic table.

51. The number of subatomic particles present in an isotope of hydrogen with half life 12.5 years

is _______



1) 2 2) 3 3) 4 4) 10

52. The best oxidizing agent among the following is______

1) N2 2) O2 3) F2 4) I2

53. The number of spectral lines observed when electron falls from 8th

to 2nd

energy level is ____

1) 15 2) 16 3) 18 4) 21

54. The quantum number that reflects 3Cr ion among these:

1) 1

3, 2, 0,2

n l m s 2) 1

3, 2, 0,2

n l m s

3) 1

4, 0, 0,2

n l m s 4) 1

3, 2, 2,2

n l m s

55. The number of electrons present in 4

C CN is____

1) 20 2) 30 3) 48 4) 58

56. The most acidic oxide among these:

1) 2ClO 2) 2Cl O 3) 2 6Cl O 4) 2 7Cl O

57. An element with 4 electrons in the valence shell combines with another element having 6

electrons in the valence shell. The molecular formula of the substance among these:

1) C2O 2) C2O2 3) C2O3 4) CO2

58. A metal absorb which of the following frequencies?

1) 1/2hv 2) ¾ hv 3) 1/8hv 4) 1hv

59. Quick silver among these:

1) z= 80 2) z= 47 3) z =82 4) z= 41

60. Which of the following is a bridge element?

1) Li 2) Al 3) Mg 4) Hg

61. The elements with stable + 8 oxidation states in their compounds among these:

1) Hg,Zn,Cd 2) Os, Ir, Pt 3) Ru, Os, Xe 4) Cr, Mo, W

62. According to Moseley a straight line graph is obtained in plotting?

1) V vs Z 2) 2V Vs Z 3) V Vs Z 4) 1

Vs ZV

63. A hydrogen molecule at 4000C moves at a velocity of 52.2 10 / seccm . Its de-Broglie

wavelength is in the order

1) 4 010 A 2) 01A 3) 3 010 A 4) 010 A

64. Kinetic energy of an electron in an orbit of H-atom is 241.82 10 J , the wavelength associated

with the electron is

1) 4200 A0 2) 3600 A

0 3) 2800 A

0 4) 7250 A

0

65. If the value of energy in Bohr orbit is -78 Kcal/mole. Then the angular momentum of on

electron in that orbit is

1) 2

h

2)

h

3)

1.5h

4)

2h

66. The velocity of an electron in the Bohr’s orbit with radius 0.529 A0 is _____

1) 82.18 10 / seccm 2) 82.18 10 / secm 3) 162.18 10 / seccm 4) 836559 10 / seccm

67. Number of electrons with 1

2 spin in n= 4 is

1) 32 2) 16 3) 8 4) 9

68. Photo electric emission is observed from surface for frequencies V1 and V2 the K.E in the two

cases are in the ratio 1:K , then the threshold frequency V0 is given by

1) 2 1

1

V V

K

2) 1 2

1

KV V

K

3) 2 1

1

KV V

K

4) 2 1V V

K

69. The ejection of the photo electron from the silver metal in the photo electric effect experiment

can be stopped by applying 0.35 V. When the radiation of 256.7 nm is used, W of the silver

metal is _____

1) 4.48 eV 2) 3.35 eV 3) 44.8 eV 4) 22.4 eV



70. Which of the following condition is incorrect for a well behaved wave function ?

1) must be finite 2) must be single valued

3) must be infinite 4) must be continuous

SECTION- II

(Numerical Value Answer Type)

71. How many of the following require more energy to remove an electron than in He.

(1) H (2) Li (3) Li+ (4) Be

+2 (5) Al (6) Ne (7) Na

+ (8) Mg (9) C (10) F (11) O

72. How many of the following have negative electron gain enthalpies?

(1) O- (2)N

-H (3) N

-2 (4) P

-1 (5) P

-2 (6) S

-

73. Calculate the electro negativity of silicon using Allred –Rochow method, covalent radius of

silicon is 1.175 A0.

.

20.359 0.744

effZX

r

.

74. If the uncertainty in position of electron is 105 10 M . Then the uncertainity in momentum is 2510A Kg m/sec. What is the value of A?

75. The magnetic moment of an element with z=26 in its + 3 oxidation state is __________B.M.

SRIGAYATRI EDUCATIONAL INSTITUTIONS

INDIA

JR MPC Date: 02-04-2020 Time: 3 Hours

KEY SHEET

MATHS

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

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

21) 3 22) 2 23) 0.3 24) 2 25) 0

PHYSICS

26) 3 27) 1 28) 2 29) 1 30) 2 31) 4 32) 1 33) 1 34) 4 35) 1

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

46) 25.3 47) 11.25 48) 13 49) 1218 50) 0.9

CHEMISTRY

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

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

71) 2 72) 6 73) 1.82 74) 1.05 75) 5.92

HINTS & SOLUTIONS

MATHS-A

1. F 16 2,4,8,16 ,

F 40 2,4,8,20,40

F 16 F 40 2,4,8 F 8

F x F 8 x 8

2. no of subsets = 2n

3. n A B 25 x,n B A 2x

n A B 2x

n A n A B n A B

25 x 2x 25 3x

n B n B A n A B 2x 2x 4x

n A 2n B 25 3x 2 4x

5x 25 x 5

4. 30

1

15 30 15

10i

iS A n S

Again, 1

13 .

9 3

n

jj

nS B n S n

Thus 15 453

nn

5. Minimum value of

6. xRy, yRz xRz

7. (1,3) need to be adjoined to make the

relation transitive

8. no value of T exist such that

f x T f x

9. ( ) ( ) ( ) ( ) ( )f x y f x f y f a x f a y

JEE MAINS MODEL



0, 0 (0 0) (0) (0) ( 0) ( 0)x y f f f f a f a

2 2(0) ( (0)) ( ( ))f f f a

2 2 21 (1) ( ( )) ( ( )) 0 ( ) 0f a f a f a

Now (2 ) ( ( ))f a x f a x a

( ) ( ) ( ) ( )f a f x a f a a f a x a

10. 1

2xx

11. Here D(1, 1) therefore equation of line

AD is given by 2 3 0x y .

Thus the line perpendicular to AD is

2 0x y k and it passes through B, so

k= 0.

Hence required equation is 2 0x y .

12. Slope of 5 4 9

34 1 3

AF

Slope of 1

3CF

Equation of CF is

3 11 0x y ……………(i)

Slope of 5 1 4 1

4 4 8 2AE

Slope of BE= 2

Equation of BE is

2 7 0x y …………….(ii)

Solving (i) and (ii), we get point O = (2, -

3)

Equation of AC is

2 6 0x y ……………..(iii)

Solving (i) and (iii), we get point C(8, -1)

Also slope of AO is 4/ 3

Slope of BC is ¾

Equation of BC is 3 4 28 0x y

13. Let h be the length of the altitude from A,

Distance from centroid to

2 2

122 1222

3 6111 60

hBC

6h is height of ABC

Area is 2

12 33

h

Perimeter , 2

3 12 33

hP .

14. Line passes through the point of

intersection of 2 2 0x y and

2 6 0x by

So, its equation is given by

2 2 2 6 0x y x by

As it passes through the origin

2 6 0 3

Equation of the line is

6 0x b y

Its slope is 1

6 b.

As its angle with 0y is less than 4

1

1 16 b

6 1 1b or

5 7b or b

But 4b (as the lines intersect)

,4 4,5 7,b

15. 0;3 2 4 0ax by c a b c

3 2

04

a bax by

4 4 3 2 0ax by a b

4 3 4 2 0a x b y

3 1

,4 2

x y

16. As OAB is a right angle triangle

So orthocenter is at origin.

17. 2 3 0x y

2 3 4 0x t they intersect at 1,2 .

Eq. of line of slope m passing through (1,

2).

2 1y m x let the image of (2, 3) be

(h, k) so, 3 1

2

k

h m

and

2 3,

2 2

h k lies

on the line.

21.

2 3 2

hk h

k

2 1 3 0h h k k

2 22 4 3 0h h k k

2 22 4 3 0h k h k

2 2 2 4 3 0h k h k



18. As incircle S divides the angle BAC

into two parts.

Ao, 2

SAB

090

2SAB

0

0 9045

2SAB SBA

0180ASB SAB SBA

0 0 0180 45 135 for all C.

19. Slope of 1L m

Slope of 2L n : given that 4m n

tan 2 , tanm n

2

2

1

nm

n

So, 2

24

1

nn

n

2

12

1 n

Thus, 22 2 1n

22 1n

2 24 2.2 2mn n n

20. The coordinates of A are (0, 4) and those

of B are (3, 0).

2 23 4 5BC AB

Or BL = BC sin and cosCL BC or

45 4

5BL

And 3

5 35

CL .

Similarly, MD=4 and AM= 3. So, the

coordinates of C are

, 7,3OB BL CL and those of D are

(MD, OA+ AM) (4,7).

The coordinates of the vertex farthest

from the origin are (4, 7).

21. , 2 2 ,2 2 (2 2 2 2 2 2 ,2 2 2 2 2 2f x y f x y y x f x y y x y x x y

= 8 , 8f y x

=

8 8 , 8 8 64 , 64f x y f x y

64 64 , 64 64f x y

12 122 ,2f x y

12 12, 2 ,2f x y f x y

12,0 2 ,0f x f x

122 ,0 2 2 ,0x xg x f f

= 122 ,0xf 12g x

12g x g x

period of g x 12is T 34

T

22. Putting tan x t , we get f t is a

polynomial function of the form,

1nf t t

When t =2, 2 9 3f n

3 1f t t

' 2 12f ' 2

26

f

23. ( ) cos9 cos10f x x x

(2 ) 1 1 0 1 32

f f

24. Line 1, 30 2 40y x put

0, 25y x

Line 2, 30 6 40y x put

0, 35y x

Thus, distance between X-intercepts

35 25 10 unit.

25. The angle between both the lines is 450.

Hence,

5

' 2 2 52

OP OP

PHYSICS

26. For collision, A Br r (at same instant)

i t i tA Br v r v

ˆ ˆˆ ˆ ˆ ˆ ˆ5 10 5 30 10 5 5i j k t i i j k t

Equating the coefficients of x 5 30 10t t

t ve

So, they will never collide.

27. .dv

f v a bxdx



Or 0 0

v x

vdv a bx dx

22v ax bx …………..(i)

At other station, 0v

2a

xb

.

Further acceleration will change its

direction when, 0f or 0a bx or

ax

b

At this x, velocity is maximum.

Using eq. (i), 2

max 2a a a

v a bb b b

.

28. Let velocity of rain is

ˆ ˆRv ai bj

In first case, ˆ ˆ4 3Mv i j

ˆ ˆ4 3RM R Mv v v a i b j

It appears vertical

4 0a

or 4a

In second case, ˆ ˆ4 3Mv i j

ˆ ˆ4 3RM R Mv v v a i b j

ˆ ˆ8 3i b j

It appears at 1 7tan

8

3 7b

4b

And speed of rain 2 2a b

32 /m s .

29. 2 2

1

10.5

2x gt gt

2 2

1 2

12 2

2x x g t gt

2 2

2 12 1.5x gt x gt

2 2 12 1

x xx x gt or t

g

.

30. Packet comes under gravity. Therefore

only force is mg.

F mg

a gm m

(downwards)

31. 2 12

/60 30

Rv cm s

T

In 15s, velocity vector (of same

magnitude) will rotate 900

2 2 02 cos90f iv v v v v vv

2

2 /30

v cm s

32. 2

2

uh or u h

g

33. Velocity of train in the direction of train is

also 30 m/s. So there is no relative motion

in this direction. In perpendicular direction,

2 sin 2u

d Rg

2 030 sin 9090

10m

34. 02 8 sin532 sin

1.2810

uT s

g

2 02 80 sin 106sin 2615.2

10

uR m

g

Distance travelled by tank,

5 5 1.25 6.4d T m

Total distance 615.2 6.4 m

621.6m

35. 2

2sin 2 sin

cos

uR

g

2 010 / , 10 / , 30u m s g m s and 060

36. 2

00max 45

vR at

g

R

2

max maxA R

37. Maximum range is obtained at 450

2

1.6 4 /u

or u m sg

0 2 4 1/ 22 sin 45

10

uT

g

0.4 2s



Number of jumps in given time,

10 225

0.4 2

tn

T

Total distance travelled

1.6 25 10m

38. Using 21

2s ut at in vertical direction

0 2170 50sin30 10

2t t

On solving this equation, we get t =7s.

39. Maximum value of friction between A and

B

1 1max Af N m g

0.3 50 10

150N

Maximum value of friction between B and

ground

2 2max A Bf N m m g

0.3 120 10 360N

Force diagram is as shown below

2 1 max

150T f N

1 2 1 2max max2T T f f

300 150 360 810N

1 cT m g

1 81081

10c

Tm kg

g

40. During motion of block, a component of its

acceleration comes in the direction of

cosmg .

Therefore,

cosmg N

41. x y constant

0dx dy

dt dt

Or dx dy

dt dt

1 0 2v v v

Or 1 2 0v v v .

42. 2 2z x c

Now, w y z l

Or 2 2w y x c l

2 2

. 0dw dy x dx

dt dt dtx c

Or dw x dx dy

dt z dt dt

…………..(i)

2

dw dxv

dt dt

1

dyv

dt

And sinx

z

Substituting these values in Eq.(i) we have

2 11 sinv v .

43. With respect to trolley means, assume

trolley at rest and apply a pseudo force (

=ma, towards left) on the bob.

sin cos

net

mg maa

m

sin cosg a

44. If they do not slip, then net force on system

= F

Acceleration of system 3

Fa

m

T F

FBD of m 3

FF mg ma



a

mg

T=F

2 2

3 3

F Fmg or

mg

45. Just at the time of tipping, normal reaction

at 1 will become zero.

(moments of all forces about point 2) =0

1 24w w x

Or

1

2

4 104 1

80 2

gwx m

w g .

46. 1 2

1 2

av

d d dv

t t t

18 11 42

2160

v

25.3 /v m s

47. 221 1

20 1 12 2

gt t g t

Solving this equation we get,

1.5t s

Now, 21

20 1 12

d t g t

11.25cm .

48. For 1 1 1,A T m a m g

For B, 2 3 2 2 3m m g T m m a

1 2 3

netFa

m m m

; For C, 3 2 3m g T m a

49. 60 , 100m Bm kg m kg

‘a’ be acceleration of rope.

5

, ;4

rel rel m m rel

ga a a a a a a

5

4m

ga a

B BT m g m a ……………………(i)

m m mT m g m a …………………...(ii)

Solving (i) & (ii), we get

100 100T g a …………(iii)

5

60 604

gT g a

………………(iv)

(iii) – (iv) , 40 100 75 60g a g a

235160 350

16a a ms

35100 100 1000 100 1218

16T g a N

.

50. 2

1 2

1, , ,

2a g v u at s ut at s vt

1 2rels s s

CHEMISTRY

51. t ½ is 12.57 for Tritium 3

1 H 1e +1-p +2-n

= 4 subatomic pasticles

52. F2 has highest E.N and has highest

standard reduction potential of + 2.89 V. It

implies the highest oxidizing capacity of

the element.

53.

8 2 6 1 2 3 4 5 6 21n

lines.

54. 3 3 13 3 2 0

2Cr d n l m s

55. 4

C CN Tetra cyano methane

5 4 5 6 4 7 30 28 58C N

56. In 2 7Cl O Cl is in its highest oxidation

state. 2 7 2 42Cl O H O HClO .

It is most acidic.

57. 4e in valence shell reflects 4th

group and

general covalence as 4.0

6e in valence shell reflects 6th

group and

general covalence as is 2

4 2

2 4 2.C O C O CO

58. It absorbs in whole number quanta i.e

,2 ,3 ,4hv hv hv hv etc.

59. quick silver is mercury 80z .

60. Mg as it resembles IIA and IIB group

elements i.e, Ca, Sr, Ba, Ra, and Zn, Cd,

Hg

61. 4 4 4,RuO OsO and XeO in them Ru, Os,

and Xe have + 8 oxidation state.

62. Moseley equation V a z b

V Vs Z .

63. 27

24 5

6.625 10

2.016 1.66 10 2.2 10

h

mv

8 80.5998 10 1 10cm cm

0 81 10A cm



01A .

64.

34

24 31

6.6 10

2 . 2 1.82 10 9.11 10

h

K Em

34 6

0

28 10

6.6 10 0.36 103600

3 6 10 10A

65. 2

313.6/nE Kcal mole

n

2 313.6 313.64.02 4

78n

nE

4 2n

2

2 2

nh h hMvr

66. 82.18 10 Z

Vn

on see

2

nhmvr

20.529nr n 2

nhv

mr

0 20.529 0.529 1A n n

8

82.18 10 12.18 10 / sec

1V cm

67. Total number of electron in 2 22 2 4 32n u n

Half of them will have -1/2 as they will be

Paired 32

162

.

68. 1 0 1 0 1 01 1hv hv hv hv h v v

2 0 2 0 2 0hv hv k k hv hv h v v

1 0 1 0

2 0 2 0

1 h v v v v

k h v v v v

1 0 2 0k v v v v

1 0 2 0kv kv v v

1 2 2 0 0 1kv v v kv v k

1 20

1

kv vv

k

.

69. 1240 1240

4.83256.7

KE eV

4.83TE eV TE W KE

0.35KE eV

4.83 0.35 4.48W TE KE eV

70. cannot be infinite it should be finite to

measure amplitude of wave function.

71. 2 2 2 2 2 2 61 1 1 2 2Li s Be s Na s s p .

21He s I.P of 24.6He eV

2IP of He = 54.4 eV

2 75.63Li IP eV

2

3 153.9Be IP eV

2 47.27Na IP eV

Li and 2Be require more energy than

in He based on electronic configuration

and effective nuclear change.

72. All these species require energy to add on

electron which is read as negative electron

affinity or electron gain enthalpy.

73. 2 2 6 2 214 . 1 2 2 3 3Si Z E C s s p s p

effZ Z (shielding constant)

1.4 0.35 3 8 0.85 2 1.00effZ

14 9.85 4.15

2

4.150.359 0.744 1.82

1.175

74. .4

hx p

4

hp

x

34

10

6.625 10

4 3.14 5 10

240.10549 10

251.0549 10

251.05 10

75. 2 2 6 2 676 . 1 2 2 3 3Z Fe E C s s p s p

2 64 3s d

3 5 03 4Fe d s

It has 5- unpaired electron

14 4 7 .n B M

5 5 2 35 5.916 5.92 B.M.

Documents

SRIGAYATRI EDUCATIONAL INSTITUTIONS MPC PPT...2020/02/04 · 27. A street car moves rectilinearly from station A to the next station B (from rest to rest) with an acceleration varying