SRIGAYATRI EDUCATIONAL INSTITUTIONS

SRIGAYATRI EDUCATIONAL INSTITUTIONS

INDIA

JR MPC Date: 31-03-2020 Time: 3 Hours

MATHS-A SYLLABUS: Sets & Relations, Functions.

1. If 50, 20n A n B and 10n A B then n A B is

1) 50 2) 60 3) 70 4) 40

2. The group of beautiful girls is

1) a null set 2) A finite set 3) not a set 4) Infinite set

3. How many elements has P A , if A

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

4. If 8 7 1:nA n n N and 49 1 :B n n N then

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

5. If sets A and B are defined as , : ,xA x y y e x R , : ,B x y y x x R , then

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

6. If 48, 28, 33n U n A n B and 12n B A , then C

n A B is

1) 27 2) 28 3) 29 4) 30

7. If 60, 21, 43n U n A n B then greatest value of n A B and least value of n A B

are

1) 60, 43 2) 50, 36 3) 70, 44 4) 60, 38

8. If 4 3 1:nX n n N and 9 1 :Y n n N then X Y

1) X 2) Y 3) N 4)

9. Which is the simplified representation of 1 1A B C B C A C where A, B, C are

subsets of set X

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

10. A survey show that in a city that 63 % of the citizens like tea where as 76 % like coffee. If x%

like both tea and coffee, then

1) x =63 2) x =39 3) 50 63x 4) 39 63x 11. The relation R defined on the set A={1,2,3,4,5} by R= {(a, b):| a2 - b 2| < 16; a, b A} is given by

1) { (1,1),(2,1),(3, 1),(4,1),(2,3) } 2) {(2, 2), (3, 2), (4, 2), (2,4)} 3) {(3, 3), (4, 3), (5, 4), (3, 4)} 4) {(1,1),(1,2),(1,3),(1,4),(2,1),(2,2), (2,3), (2,4),(3,1),(3.2),(3,3),(3,4),(4,1), (4,2), (4,3), (4,4),(4,5),

(5,4),(5,5)} 12. Let A be a set of first ten natural numbers and R be a relation on A, defined by (x,y) R x

+ 2y = 10,then domain of R is

1) {1,2,3,......, 10} 2) {2,4,6,8} 3) {1,2,3,4} 4) {2,4,6,8,10}

13. Let 1,3 , 4,2 , 2,4 , 2,3 , 3,1R be a relation on the set 1,2,3,4A .

Then the relation R is

1) not symmetric 2) transitive 3) a function 4) reflexive 14. Which one of the following relations on Z is equivalence relation?

1) 1 | | | |xR y x y 2) 2xR y x y 3) 3 /xR y x y 4) 4xR y x y

15. If 2: 5 6 0A x x x , 2, 4B , 4,5C , then A B C is

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

DPP - I

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

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3) 2,4 , 3,4 , 4,4 4) 2,2 , 3,3 , 4,4 , 5,5

16. A={1,2,3,4,}, relation R on A is defined by R={(x,y) / x<y and 2 2 9x y ;x,y A} then

R=

1) {(1,1) (2,2) (3,3) (4,4)} 2) {(2,1) (3,2) (3,2) (4,3)}

3) {(1,2) (1,3) (2,3) (3,5)} 4) {(1,2) (1,3) (2,3) (3,4)}

17. Total number of equivalence relations defined in the set S a,b,c is

1) 5 2) 3! 3) 23 4) 33 18. Let R {(1,3),(4,2),(2,4),(2,3),(3,1)} be a relation on the set A = {1, 2, 3, 4}. The relation

R is

1) a function 2) transitive 3) not symmetric 4) reflexive

19. On the set of all vectors in space the relation R is defined by .a Rb a b is scalar is

1) symmetric 2) not symmetric 3) not reflexive 4) both 2 and 3

20. Let R1 be a relation defined in the set of real numbers by a1R b 1+ab >0, Then

1R is

1) equivalence relation 2) transitive 3) symmetric 4) anti symmetric

MATHS-B SYLLABUS: - Straight lines

1. In the xy-plane , how many straight lines whose x-intercept is a prime number and whose

y-intercept is a positive integer pass through the point (4,3)?

1) 1 2)2 3) 3 4)4 2. The line 2 4y x is shifted 2 units along +y axis , keeping parallel to itself and then 1 unit

along +x axis direction in the same manner, then equation of the line in its new position is

1) 2 6y x 2) 2 5y x 3) 2 4y x 4) none of these

3. A ray of light passing through the point A(2,3) reflected at a pint B on the line 0x y and

then passes through (5,3) .Then the coordinates of B are

1) 1 1

,3 3

2) 2 2

,5 5

3) 1 1

,13 13

4) none of these

4. The straight line 2y x rotates about a point where it cuts the x-axis and becomes

perpendicular to the straight line 0ax by c .Then its equation is

1) 0bx ay c 2) 2 0ax by a 3) 2 0bx ay b 4) 2 0ay bx b

5. A (3,0) and B (6,0) are two fixed points and U 1 1,x y is a variable point of the plane .AU and

BU meet the y-axis at C and D , respectively , and AD meets OU at V. Then for any position of

U in the plane CV passes through fixed point (p,q) , whose distance from origin is (where O is

origin)

1) 1unit 2) 2units 3) 3units 4) 4 units

6. A Variable line L is drawn through O(0,0) to meet lines 1 : 2 3 5L x y and 2 : 2 3 10L x y

at point P and Q, respectively . A point R is taken on L such that 2OP.OQ= OR.OP

+OR.OQ. Locus of R is

1) 9 6 20x y 2) 6 9 20x y 3) 6 9 20x y 4) none of these

7. The set of real values of K for which the lines 3 1 0, 2 2 0 2 3 0x y kx y and x y

from a triangle is

1) 2

4,3

R 2) 6 2

4, ,5 3

R 3) 2

,43

R 4) R

8. Pair of lines through (1.1) and making equal angle with 3 4 1 12 9 1x y and x y intersect x-

axis at 1 2P and P , then 1 2,P P may be



1) 8 9

,0 ,07 7

and 2) 6

,0 8,07

and 3 8 1

,0 ,07 8

and 4) 1

8,0 ,08

and

9. The algebraic sum of distances of the line 2 0ax by from (1.2) ,(2,1) and (3,5) is zero and

the lines bx-ay+4=0 and 3 4 5 0x y cut the co-ordinates axes at concylic points .Then

1) a+b=- 2

7

2) area of the triangle formed by the line ax+by+2=0 with coordinate axes is 14

5

3) line ax+by+3=0 always passes through the point (-1,1)

4) max 5

,7

a b

10. The equation of line which equally inclined to the axis and passes through common points of

family of lines 4acx+y( ab+bc+ca-abc) +abc=0 where a,b,c>0 are in H.P is

1) 7

y-x=4

2) 7

y-x=-4

3) 1

y-x=4

4) 1

y-x=-4

11. The vertices of a triangle are A(-1,-7),B(5,1) and C(1,4) The equation of the bisector of the

angle ABC is:

1) 7 2y x 2) 5 2y x 3) 3 2y x 4) none of these

12. If 1 2 3, ,x x x as well as 1 2 3, ,y y y are in G.P . with same common ratio, then the points (1 1,x y )

(2 2,x y )and ( 3 3,x y ):

1) lie on a straight line 2) lie on an ellipse 3) lie on a circle 4) are vertices of a triangle

13. If in triangle ABC ,A (1,10) , circum centre 1 2

( , )3 3

and orthocentre 11 4

( , )3 3

then the

coordinates of mid –point of side opposite to A is :

1) 11

(1 )3

2) (1,5) 3) (1-3) 4) (1,6)

14. Suppose ABC is a triangle with 3 acute angle A,B and C. The point whose coordinates are

,CosB SinA SinB CosA can be in the:

1) first and 2nd quadrant 2) 2nd and 3rd quadrant 3) third and 4th quadrant 4) 2nd quadrant only 15. A particle begins at the origin and moves successively in the following manner as shown, I

unit to the right ,1/2 unit up , 1/4 unit to the right 1/8 unit down ,1/6 unit to the right etc.

The length of each move is half of the previous move and movement continues in the ‘Zigzag

‘manner indefinitely. The coordinates of the point to which the ‘Zigzag’ converges is :

1) 4 2

,3 3

2) 4 2

,3 5

3) 3 2

,2 3

4) 2

2,5

16. The orthocentre of the triangle ABC is ‘B’ and the circumcentre is ‘S’ (a,b) .If A is origin

then the coordinate of C are :

1) (2a,2b) 2) ,2 2

a b 3) 2 2( ,0)a b 4) none of these



17. Let 1 denotes the area of the triangle formed by the vertices

2 2 2

1 1 2 2 3 3( ,2 ), ( , 2 ), ( , 2 )am am am am am am and 2 denotes the area of the triangle formed by the

vertices 2

11 2 1 2 2 3 2 3 3 1 3 1[ . ( )], [ , ( )] [ , ( )].am m a m m am m a m m and am m a m m Find .

1) 1 2) 2 3) 3 4) 4 18. A point P(x,y) moves so that the sum of the distance from P to the coordinates axes is equal to

the distance from P to the point A(1,1) .The equation of the locus of P in the first quadrant is:

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

19. Each member of the family of parabolas Y= 2 2 3ax x has a maximum or a minimum point

depending upon the value of a . The equation to the locus of the maximum or minimum for all

possible value ‘a’ is :

1) a straight line with slope 1 and Y-intercept 3 2) a straight line with slope 2 and Y-intercept 2

3) a straight line with slope 1 and X-intercept 3 4) ) a straight line with slope 2 and Y-intercept 3

20. A and B are any two points on the positive X and Y axes respectively satisfying 2(OA)+3(OB)

=10.If P is the middle point of AB then the locus of P is:

1) 2 3 5x y 2) 2 3 10x y 3) 3 2 5x y 4) 3 2 10x y

PHYSICS

SYLLABUS: Kinematics, Newton’s Laws of motion

1. Velocity of the river with respect to ground is given by 0v .Width of the river is d. A swimmer

swims (with respect to water) perpendicular to the current with acceleration 2a t (where t is

time) starting from rest from the origin O at t=0. The equation of trajectory of the path

followed by the swimmer is

v0

X0

d

Y

1) 3

3

03

xy

v 2)

2

2

02

xy

v 3)

0

xy

v 4)

0

xy

v

2. The relation between time t and displacement x is 2t x x , where and are constants.

The retardation is

1) 32 v 2) 32 v 3) 32 v 4) 2 32 v

3. A particle of mass m moves on positive x-axis under the influence of force acting towards the

origin given by 2ˆkx i . If the particle starts from rest at x=a, the speed it will attain when it

crosses the origin is

1) k

ma 2)

2k

ma 3)

2

ma

k 4) None of these

4. A particle is moving along a straight line whose velocity displacement graph is as shown in the

figure. What is the magnitude of acceleration when displacement is 3 m?

v

s3m

4 ms-1

600



1) 24 3ms 2) 23 3ms 3) 23ms 4) 24

3ms

5. A ball is thrown vertically upwards from the ground. If T1 and T2 are the respective time

taken in going up and coming down, and the air resistance is not ignored, then

1) 1 2T T 2)

1 2T T 3) 1 2T T 4) Nothing can be said

6. Identify the correct statement related to the projectile motion.

1) It is uniformly accelerated everywhere 2) It is uniformly accelerated everywhere except at the highest position where it is moving with

constant velocity 3) Acceleration is never perpendicular to velocity 4) None of the above

7. A particle has initial velocity, ˆ ˆ3 4v i j and a constant force ˆ ˆ4 3F i j acts on it. The path

of the particle is

1) straight line 2) parabolic 3) circular 4) elliptical 8. A body is projected at an angle 600 with the horizontal with kinetic energy K. When the

velocity makes an angle 300 with the horizontal, the kinetic energy of the body will be

1) K/2 2) K/3 3) 2K/3 4) 3K/4 9. A particle is fired horizontally from an inclined plane of inclination 300 with horizontal with

speed 50 ms-1. If 210g ms , the range measured along the incline is

1) 500 m 2) 1000

3

m 3) 200 2 m 4) 100 3 m

10. A particle is dropped from a height h. Another particle which is initially at a horizontal

distance d from the first is simultaneously projected with a horizontal velocity u and the two particles just collide on the ground. Then

1) 2

2

2

u hd

h 2)

22 2u h

dg

3) d h 4) 2 2gh u h

11. If 1T and

2T are the times of flight for two complementary angles, then the range of projectile

R is given by

1) 1 24R gTT 2)

1 22R gTT 3) 1 2

1

4R gTT 4)

1 2

1

2R gTT

12. Two stones are projected with the same speed but making different angles with the horizontal.

Their horizontal ranges are equal. The angle of projection of one is 3

and the maximum

height reached by it is 102m. Then the maximum height reached by the other in metres is

1) 76 2) 84 3) 56 4) 34 13. Two balls A and B of same size are dropped from the same point under gravity. The mass of

A is greater than that of B. If the air resistance acting on each ball is same, then

1) both the balls reach the ground simultaneously 2) the ball A reaches earlier 3) the ball B reaches earlier 4) nothing can be said 14. In the figure a block of mass 10 kg is in equilibrium. Identify the string in which the tension is

zero.

1) B 2) C 3) A 4)None of the above

15. At what minimum acceleration should a monkey slide a rope whose breaking strength is 2

3 rd

at weight?

1) 2

3

g 2) g 3)

3

g 4) zero

16. 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 17. The time taken by a body to slide down a rough 450 inclined plane is twice that required to

slick down a smooth 450 inclined plane. The coefficient of kinetic friction between the object and rough plane is given by

1) 1

3 2)

3

4 3)

3

4 4)

2

3

18. The force required to just move a body up the inclined plane is double the force required to

just prevent the body from sliding down the plane. The coefficient of friction is . If is the

angle of inclination of the plane than tang is equal to

1) 2) 3 3) 2 4) 0.5 19. A force F1 accelerates a particle from rest to a velocity v. Another force F2 decelerates the

same particle from v to rest, then 1) F1 is always equal to F2 2) F2 is greater than F1 3) F2 may be smaller than, greater than or equal to F1 4) F2 cannot be equal to F1 20. 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

CHEMISTRY

SYLLABUS : Atomic structure and Periodic table.

1. 1

3, 2, 2,2

n l m s . The element could be in its +2 oxidation state.

1) Zn 2) Cu 3) Cr 4) Ni

2. In 2nd period the element that can exhibit highest oxidation state is______

1) N 2) O 3) F 4) C

3. The shortest wavelength of Balmer series in hydrogen spectrum is_______

1) 6566 A0 2) 3648A0 3) 4104A0 4) 5464A0

4. Which of the following obey Heisen Berg’s uncertainty principle?

1) Electron 2) - ray 3) Positron 4) All these

5. The number of waves produced by electron moving in an orbit with circumference is 8 r is ____

1) 1 2) 4 3) 3 4) 8 6. The number of radial nodes for 5s- orbital is

1) 1 2) 2 3) 4 4) Infinity 7. The ratio of energies of 10000A0 and 2000A0 wavelength radiations is _______

1) 1:1 2) 2:1 3) 5:1 4) 1:5 8. The correct set of quantum numbers among these:

1) 1

2, 0, 0,2

n l m s 2) 1

3, 0, 2,2

n l m s

3) 1

5, 3, 4,2

n l m s 4) 1

3, 3, 0,2

n l m s

9. Which of the following requires more energetic radiation to cause photo electric effect?

1) Cs 2) K 3) Pt 4) Cu



10. The best reducing agent among these:

1) Be 2) Al 3) B 4) Cl

11. Which of the following can form Interstitial hydrides?

1) Ca 2) Cs 3) Sr 4) Sc 12. Which of the following orbital has maximum number of angular nodes?

1) s 2) p 3) g 4) f 13. The e/m highest for

1) - rays 2) -rays 3) Neutron 4) - rays

14. Which of the following effect photographic filon to great extent?

1) - rays 2) - rays 3) -rays 4) neutrons.

15. An element M has 1 2 3, ,I I I and 4I as 20, 40, 60 and 400 eV. It combines with z=16. The

generally expected formula of the substance among these: (Based on general valence rules)

1) 2 2M S 2)

2 4M S 3) 2 3M S 4) MS

16. The element present in 3rd period and 5th group among these in long form of periodic table

according IUPAC system is

1) Ca 2) Cr 3) Mn 4) None

17. Which of the following is amphoteric in nature?

1) BeO 2) ZnO 3) 2 3Al O 4) All these

18. Smallest size species among these:

1) 2Fe 2) 3Fe 3) 3Co 4) 3Sc

19. The species that are isoelectronic among these are:

1) 4 3 3 2, , ,C N Al Mg 2) 2 3, ,S P Ar Cl 3) 2 3 4, , ,Na Mg Al Si 4) All these

20. How many of the following pairs have nearly same polarizing power.

a) 2,Li Mg b) 2 3,Be Al c) ,Na K d) 3 4,B Si

1) a, b 2) a, b, c 3) a, b, d 4) b, c, d



SRIGAYATRI EDUCATIONAL INSTITUTIONS

INDIA

JR MPC Date: 31-03-2020 Time: 3 Hours

KEY SHEET

MATHS-A

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

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

MATHS-B

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

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

PHYSICS

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

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

CHEMISTRY

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

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

HINTS & SOLUTIONS

MATHS-A

1. n A B n A B n A B

n(A) n(B) 2n A B =50

2. Beautiful is a relative term but not well

defined.

3. n(A)=0, n 0n p(A) 2 2 1

4. 8 7 1nn

1 2

0 1 2 17 7 ........ 7 7n n n n n n n

n n nc c c c c

1

0 1 27 7 ........ 49 7 1n n n n n

nc c c n

2 3

0 1 28 7 1 49 7 7 ....n n n n n n

nn c c c

8 7 1n n is a multiple of 49 for all n N

A contains elements which are multiple

of 49 and clearly B contains all multiples of 49.

A B

5. The graph of xy e and y x do not

intersect

6. n U 48,n A 28,n B 33

n(B – A) = 12

n A B n B n B A 33 12 21

C

n A B n U n A B 48 21 27

7. n U 60,n A 21,n B 43

Greatest value ofn A B n U 60

Least value ofn A B n B 43

DPP - I



8. 4 3 1nn

1 2

0 1 2 13 3 ...... 3 3n n n n n n n

n n nc c c c c

1

0 1 23 3 ...... 9 3 1n n n n n

nc c c n

2 3

0 1 24 3 1 9 3 3 ...n n n n n n

nn c c c

4 3 1n n is a multiple of 9

X Contains elements, Which are

multiple of 9

Clearly Y contains elements, which are all

multiples of 9

X Y X Y Y

9. 1 1A B C B C A C C

draw venn diagram.

10. Let the population of the city be 100

Let A denote the set of citizens who like tea and B denote the set of citizens who like coffee.

63n A and 76n B

n A B n A n B n A B and

100 63 76 100n A B n A B

63 76 100n A B

39 1n A B

Also n A B n A and

n A B n B

63n A B and 76n A B

63 2n A B

From (1) and (2) : 39 63n A B

39 63x .

11. We have (a, b) R | a2 - b 2| < 16.

a = 1 0< b2 < 17 b= 1, 2, 3, 4.

If a = 2 we get b= 1, 2, 3, 4.similary a =3

we get

b =1,2,3,4,a=4 we get b=1,2,3,4,5,a=5 we

get b=4,5

Then R={(1,1),(1,2),(1,3),(1,4),(2,1),(2,2),

(2,3),(2,4),(3,1),(3.2),(3,3),(3,4), (4,1),(4,2),(4,3), (4,4),(4,5),(5,4),(5,5)}

Clearly, option (4) is correct.

12. x 2y 10 x 10 2y

A {1,2,3,...10}

Domain of R {2,4,6,8}

R {(2,4),(4,3),(6,2),(8,1)}

13. 3,2 R

14. We observe that 1R is reflexive,

symmetric and transitive relation on Z.

Relations 2R , 3R and

4R are not

symmetric on Z.

15. We have, 2,3A , 2, 4B and

4,5C

4B C

2,4 , 3,4A B C

16. Since x<y and 2 2x y 9

R {(1,2),(1,3),(2,3),(3,4)}x<y

17. The smallest equivalence relation is the

identity relation 1R a,a , b,b , c,c .

Then two ordered pairs of two distinct

elements can be added to give three more equivalence relation

2R a,a , b,b , c,c , a,b , b,a

Similarly R3 and R

4. Finally the largest

equivalence relation i.e., the universal relation R

5 = {(a, a), (b,b), (c,c),(a, b),(b,

a),(a, c),(c,a), (b,c), (c,b)}.

18. 2,4 , 2,3 2R has two images

R is not a reflexive

1,1 R R is not reflexive

2,3 , 3,2R R R is not symmetric

19. . .a b b a

20.

Leta R 21 . 1 0a a a

1,a a R

1R is reflexive on R.

Let 1, .a b R 1 0ab 1 0ba

1( , )b a R 1R is symmetric on R.

Since 1

11,

2R and 1

1, 1

2R but

11, 1 R

1R is not transitive on R.



MATHS-B

1. The line 1x y

p q, where ‘p’ is a prime

and ‘q’ is a positive integer, passes

through (4,3).

4 3

1p q

3 12

34 4

pq

p p

Since, q is a positive integer, p> 4 and (p-4) divides 12, there are only two such prime numbers,

P =5 and p = 7

2. Any point 1 1,x y after shifting 2 units

along +y axis becomes 1 1, 2x y and

after shifting along +x axis it will be

1 21, 2x y , which satisfy the same

equation.

3. Let A’ is image of A(2, 3) on x +y =0

' 3, 2A

Now , B is the point of intersection of

'PA with 0x y

Equation of line 'PA is

3 5/8 5y x or 5 8 1 0x y .

1 1

,13 13

B .

4. Slopes of the line in the new position is

b/a, since it is perpendicular to the line

0ax by c and it cuts the x-axis.

Hence the required line passes through (2, 0) and its slope is b/a.

The required is 0 2b

y xa

or

2ay bx b .

5. Equation of AU is 11 1

1

0

3

yy y x x

x

So that the coordinates of C are

1 10,3 / 3y x

Similarly, the coordinates of D are

1 10,6 / 6y x

Now, equation of AD is

1

1

61

3 6

y xx

y…………(i)

And equation of OU is

1 1y x x y ……………….(ii)

Solving (i) and (ii), we get

11

1 1

61

3 6

y xx y

y y

Therefore, equation of CV is

1 1

1 1 1

11

1

6 3

3 6 30

630

6

y y

y x xy x

xx

x

1

1

31

3 2

y xy

x.

6. Let the line L be cos sin

x y.

Then 5

2cos 3sinOP and

10

2cos 3sinOQ

And let OR r

Then according to condition

20 6 cos 9 sinr r

locus is 6 9 20x y

7. Lines form triangle. Therefore,

3 1 0x y is not parallel to

2 2 0kx y

1 2

2 3 3

kk

Also line 2 3 0x y is not parallel to

2 2 0kx y

2 42

kk

Further lines must not be concurrent

1 3 16

2 2 05

2 1 3

k k

8. Lines making equal angle with given two lines are always parallel to angle bisectors.

Equation of angle bisectors

3 4 1 12 9 1

5 15

x y x y

So bisectors have slope 1

7,7

Equation of required lines 1 7 1y x

and 1

1 17

y x



Which intersect x-axis at 6

,07

and

8,0 .

9. Line 2 0ax by always passes through

the point 8

2,3

6 8 6 0a b

Or 3 4 3 0a b …………….(i)

Noe 4 0bx ay and 3 4 5 0x y

meet axis in concyclic points.

So, 1 2 1m m

3

. 14

b

a

4 3 0a b ……………….(ii)

Solving (i) and (ii), we get

9/ 7. 12/ 7a b

Line 3 0ax by always passes

through the point 1,1 .

10. 4 0acx y ab bc ca abc abc

Dividing by abc, we get

4 3 2 1 11 0x y

b b b a c

1

4 3 1 0x y yb

Lines are concurrent at point of intersection of lines 4 3 0x y and

1 0y or 3/ 4,1

Hence the required line in 7

4y x .

11. 1, 7 , 5,1A B and 1,4C

2 28 6 10AB

2 23 4 5BC

2 2

,1 1

AB ARso

BC RC

Point

2.1 1. 1 2.4 1 7 1 1, ,

2 1 2 1 3 3R

Straight line BR,

11

231 5 51 14

53

y x x

7 7 5y x

7 2y x

12.

1 1

2 2

3 3

1

1

1

x y

x y

x y

1 1

1 1

2 2

1 1

1

1

1

x y

x r y r

x r y r

where r is the common

ratio.

1 1

2 2

1 1 1

1 0

1

x y r r

r r

Thus, points are collinear, lie on a straight line.

13.

2 11 2 42.

83 3 3 3, 1,2 1 2 1 9

G .

Now let ,D h k

2 1

1 , 13

hso h

8 2 10 8

, 10 29 3 3

kso k

22 11

2 ,3 3

k so k

11

, 1,3

D h k

14. cos sin ,sin cosB A B A

Let 0 0 061 , 30 , 89B A C

0 0cos sin cos61 sin30 0B A

0 0 0sin cos sin61 cos30 0B A

So, second quadrant,

Let 0 030 , 61B A

0 0cos sin cos30 sin61 0B A

0 0sin cos sin30 cos61 0B A

So, first quadrant.

15. X-coordinate

1 1 1 41 ....

14 16 31

4



Y-coordinate

1 11 1 1 22 2.....

512 8 32 51

44

.

16. ABC is right angled at B. Midpoint of AC is S(a, b).

As A is origin (0, 0) so, C will be (2a, 2b).

17.

2 2

1 1 1 1

2 2 2

1 2 2 2 2

2 2

3 3 3 3

2 1 11 1

2 1 2 12 2

2 1 1

am am m m

am am a m m

am am m m

2

1 2 2 3 3 1

12

2a m m m m m m

1 2 1 2

2 2 3 2 3

3 1 3 1

11

12

1

am m a m m

am m a m m

am m a m m

1 2 1 2

2

2 2 3 2 3

3 1 3 1

11

12

1

m m m m

a m m m m

m m m m

2

1 2 2 3 3 1

1

2a m m m m m m

Thus, 1

2

2 .

18. 2 2

1 1x y x y

Square both sides and in first quadrant,

,x x y y

2 2 2 22 1 2 2 1x y xy x x y y

2 2 2 2 0x y xy

1 0x y xy

1 1 2x y

19. Vertex of the parabola, 2 2 3y ax x .

,2 4

b D

a a where 2 4D b ac .

,2 4

b Dh k

a a

4 4. .32

,2 4.

ah k

a a

1 1

; 3h ka a

3; 3k h y x

20. 2OA h

2OB k

2 2 3 2 10h k

2 3 5h k

2 3 5x y

PHYSICS

1. 2ydv

tdt

2 2

y

dyv t or t

dt

Or 3

3

ty ………..(1)

And 0

0

xx v t t

v

Substituting in Eq.(1) we have 3

3

03

xy

v

2. 2dt

xdx

1

2

dxv

dt x

2

12 .

2

dv dxa

dt x dt

2 32 2v v v

3. 2F kx

am m

2

.dv kx

vdx m

Or

0 2

0

v

a

kxv dv dx

m

2 3

2 3

v ka

m

32

3

kav

m

4. 0. 4 tan 60dv

a vds

24 3 /m s

5. Air resistance (let F) is always opposite to

motion (or velocity) Retardation in upward journey

1 11

F mg Fa g

m m



Acceleration in downward journey

2 22

mg F Fa g

m m

Since, 1 2 1 2a a T T

6. a =g = constant for small heights. 7. . 0F v F v

Hence path is parabola.

8. x xv u

0 0cos30 cos60v u

Or 3

uv

Velocity has become 1

3 times. Therefore,

kinetic energy will become 1/3 times.

9. 2

2sin 2 sin

cos

uR

g

2 050 / , 10 / , 0u m s g m s

2

0

2 0

50sin 2 0 30 sin30

10cos 30R

2500 1 1

10 3/ 4 2 2

1000

3m

10. 2h

Tg

2h

g u T ug

2

2 2hud

g

11. 1 2

2 sin 2 cos,

u uT T

g g

2 sin cosu u

Rg

1 222 2

gT gT

g

1 2

1

2gTT .

12. 2 2

1

sin

2

uH

g

2 2 0sin 60102

20

u

52.2 /u m s

Other stone should be projected at 090

or 030 from horizontal.

2 2 0

2

sin 30

2

uH

g

252.2 1/ 4

20

34m

13. ˆ ˆ8 4dv

a i tjdt

At 1s ˆ ˆ ˆ ˆ1 8 4 8 4netF ma i j i j

W F Where F= force on cube

ˆ8 4F i j w

ˆ ˆ ˆ8 4 10i j j

ˆ ˆ8 6i j

Or 2 2

8 6F

=10 N

14. Maximum friction available to 2m is

max 2f m g

Therefore maximum acceleration which

can be provided to 2m by friction, (without

the help of normal reaction from 1m ) is

maxmax

2

fa g

m

If a g , normal reaction from 1m (on

2m ) is non zero.

15. cota

g

cota g

16. x y constant

0dx dy

dt dt

Or dx dy

dt dt

1 0 2v v v



Or 1 2 0v v v .

17. 221

1 2

30/

7

m ga m s

m m

1 2

2

1 2

m m ga

m m

210/

7m s

0

2 13

1 2

sin 30m g m ga

m m

210/

7m s

1 2 3a a a

18. T mg ma

T mg ma

F T mg ma

F mg ma mg ma

Or 2

Fa g

m

19. 1

2

sina

a

1 2 sina a

20. 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 .

CHEMISTRY

1. Zn z= 30 has 2 104 3 2s d oxidation state

indicates 103d .

1

3, 2 2,2

n l m s .

2. Nitrogen shows + 5 oxidation state under

normal conditions. 3. Limiting wave length

2 0 2 0

1912 912 2 3648n A A .

4. All of them they are sub-atomic particles

with negligible mass and have very high velocity.

5. 2n r 2 r is circum ference

84

2

rn

r

6. Number of radial nodes

1 1 5 0 1 4n Between two orbits one radial node exists.

7. 1 21 2

2 1

2000 1: 1:5

10000 5

EE E

E

8. One quantum number value should not exceed others.

9. Energy order Cs K Cu Pt . 10. It can be decided on the basic of S.R.P

2 0

3 0

2 1.99

3 1.66

Be e Be E V

Al e Al E V

0

7 62 6 6 1.56B H e B H E V

0

22 2 1.360

g gCl e Cl E V

11. Generally interstitial hydrides are formed by transitional elements 6, 7, 8, 9 groups do not form interstitial hydrides. That is

called hydride gap. 12. 0 1 2 3 4s p d f g

0 1 2 3 4l l l l l .

(angular nodes). It is based on l value.

13. Beta rays e/m is high because mass is very low. Beta rays are fast moving electrons

their e/m value is taken as an equivalent to

electron 19

8

28

1.6 101.76 10 /

9.11 10c gm .

14. Highest e/m ratio for beta rays.

15. 3I and 4I largely differ hence the

covalency of M is 3

Z=16 indicates minimum covalency of it is 2.



3 2

2 3M S M S .

16. 3rd period has no 5th group.

17. BeO, ZnO and 2 3Al O react with both acids

and bases, hence amphoteric.

18. Along a period size decreases. 19.

4 3 3 26 4 10 7 3 10 13 3 10 12 2 10C N Al Ma2 3

2 3 4

16 2 18 15 3 18 18 17 1 18

11 1 10 12 2 10 13 3 10 14 4 10

S P Ar Cl

Na Mg Al Si

20. Species with nearly same polarizing power

are diagonally related.

2 2 2 3 4& , & &Li Mg Be Al B Si

exhibit

Diagonal relation ship due to nearly same polarizing paver.

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