[1]

JR_MPC HOLIDAY WORKSHEET -1 DATE:10-10-2018

MATHS

1. If 2 3 2 2

x x x sin x 1 x xcos .cos .cos .... , then tan tan ....2 2 2 x 2 2 2 2

A) 1 tanxx

B) 1tan xx

C) 1 cot xx

D) 1cot xx

2. If v u dv6, thenu v du

A)

17u vu 17v

B)

u 17v17u v

C)

17u vu 17v

D)

u 17v17u v

3. If 1 1 dyx and y , then

dx

A) xy

B) yx

C) xy

D) yx

4. If

2cosx 1 0

f x x 2cosx 1 then f '2 2

0 1 2cosx

A) 2 B) 2

C) 1 D) 4

5. If

313 d 4xx 3, then Cos x

2 dx 27

A) 2

39 x

B)

2

19 x

C)

2

39 x

D) 2

19 x

6. Derivatives of 1

21 1Sec w.r.to 1 3x at x is

2x 1 3

A) 0 B) 12

C) 13

D) 16

7. If

2 21

2 2x y dyCos loga, thenx y dx

A) xy

B) yx

C) yx

D) xy

8.

2 1d 1 xsin Cotdx 1 x

[2]

A) 12

B) 0 C) 12

D) –1

9. If 2 2f ' x g x and g' x f x forall x and f 3 5 f ' 3 , then f 119 g 119 A) 5 B) 25 C) 50 D) 625

10.

h 0

sin x h sin xlimh

A) cos x B) 12sin x

C) 12cos x

D) cos x2 x

11. If

2

x 2

2x 4f xf 2 2, f ' 2 1. then lim

x 2

A) –4 B) –2 C) 2 D) 4 12. If f x x 1 x 3 , thenf ' 2 A) –2 B) –1 C) 0 D) 2

13. If

1 1x 1 x 1 dyy Sin Sec then

dxx 1 x 1

A) 0 B)

22

x 1 C)

2

2

x 1 D)

1

x 1

14. If

2

x 0

f x 3g x x 3x 1 f x , f 0 3 and lim 2, then g' 0

x

A) 3 B) 12 C) 6 D) 11 15. 2f ' x 1 x 1 and g is the inverse of f then g' f 2 A) 0 B) 2 C) 4 D) 5

16. If dyy cos x y , thendx

A)

sin x2y 1

B)

sin x2y 1

C)

sinx2y 1

D)

sinx2y 1

17. If

66 6 3 3

6

dy 1 y1 x 1 y a x y and f x,y then f x,ydx 1 x

A) yx

B) xy

C) 2

2

yx

D) 2

2xy

18. If

4 f ' 4x

f x f 4x , thenf ' x

A) f x

f 4x B)

f 4xf x

C) f 4x f x D) 0

19. If

21 1 x 1y Tan then y' 0

x

[3]

A)12

B) 0 C) 12

D) 1

20. If

3 21 1

2 2 x a

f x f a3x x 1 x 1f x Tan , g x Cos and 0 a , then lim1 3x 1 x 2 g x g a

A) 23

B) 32

C) 23

D) 32

21. Differential coefficient of

1

2

xTan1 1 x

with respect to 1Sin x is

A) 12

B) 1 C) 2 D) 32

22. Let 2

f x 2y f x f y for allx,y and f 0 1 . If f is derivable at x=0 then f ' x

A) f x B) f ' 0 f x C)

f xf ' 0

D) f ' 0 f x

23. Let f and g be two differentiable functions satisfying g' 3 7, g 3 21 and 1g f . Then f ' 21

A) 13

B) 121

C) 147 D) 17

PHYSICS 1. The minimum number of vectors having different planes which can be added to give zero resultant

is____________ 2. Write a vector which is perpendicular to ˆ ˆ ˆi j k is____________

3. The area of parallelogram whose adjacent sides is given by vectors ˆ ˆ ˆA i 2j 3k

and ˆ ˆB 4i 5 j

is____________ 4. If ˆ ˆ ˆ ˆa 3i 4 j and b 7i 24 j

, then write a vector having the same magnitude as that of b

and parallel

to a

is____________ 5. The resultant of two vectors A

and B

is perpendicular to the

vector A

and its magnitude is equal to half of the magnitude of vector B

. The angle between A

and B

is____________

90

R

A

B

6. A force of ˆ ˆ ˆ(2i 3 j k) N and another force of ˆ ˆ ˆ(i j k) N are acting on a body. The magnitude of total force acting on the body is____________

7. Two forces, each equal to F, act as shown in figure. their resultant is_______

60

F

F

8. In the adjoining vector diagram, what is the angle between A and B

?

____________

A

CB

[4]

9. What is the angle made by ˆ ˆ3i 4 j with x–axis? ____________

10. If the vectors ˆ ˆ ˆ4i j 3k and ˆ ˆ ˆ2mi 6mj k are perpendicular to each other, then the value of m is____________

11. The magnitude of the vector product of two vectors is 3 times their scalar product. The angle between the two vectors is____________

12. The angle between A B

and A B

is ____________ 13. The projection of a vector ˆ ˆ ˆr 3i j 2k

on the x–y plane has magnitude____________

14. If A B A B

, then the angle between A and B

is____________

15. If vectors ˆ ˆ ˆA i 2 j 4k

and ˆB 5i

represent the two sides of triangle, then the third side of the

triangle can have length equal to____________ 16. Given 1 2 1 2A 2, A 3 and A A 3

. Find the value of 1 2 1 2(A 2A ) (3A 4A )

____________

17. If A B C

, and the magnitudes of A, B, C

are 5, 4 and 3 units, then angle between A and C

is____________

18. What is the angle between ˆ ˆ ˆi j k and i ?____________ 19. In going from one city to another, a car travels 75 km north, 60 km north–west and 20 km east. The

magnitude of displacement between the two cities is (take 1 0.72 )____________

20. The initial and final position vectors for a particle are respectively (2.0 m) +(8.0 m) and The displacement of the particle is________

CHEMISTRY

CHEMICAL AND IONIC EQUILIBRIUM 1. If is the fraction of HI dissociated at equilibrium, starting with one mole of HI, the total number of

moles of H2, I2 and HI at equilibrium is (A) 2 (B) 2 (C) 1 + 2 (D) 1 2. 0.5 mole each of H2 and I2 are reacted in an evacuated vessel at 445C, to establish the equilibrium H2

+ I2 2HI. The equilibrium constant of the reaction is 64. Then the amount of H2 remaining

unreacted at equilibrium is (A) 0.1 (B) 0.40 (C) 0.30 (D) 0.24 3. The equilibrium constant of the reaction

2 2H g I g 2HI g is K1, that for 2 21 1HI g H g I g2 2

is K2 and that for

2 2nH g & nI g 2nHI g is K3. Then the wrong statement is :

(A) 12

2 1K K

(B) n3 1K K (C) 1 2

2

1KK

(D) 2n3 2K K

4. A 1000 mL vessel contains 2 M each of P, Q, R and S at equilibrium. If 1 M each of P and Q are taken out, the value of equilibrium constant for P + Q R + S at the same temperature would be

(A) 2 (B) 1 (C) 12

(D) 14

[5]

5. Two moles of PCl5 were heated to 227C in a closed two litre vessel, and the extent of dissociation at equilibrium was found to be 40%. The equilibrium constant Kp of the reaction is

(A) 0.267 atm (B) 1.315 atm (C) 10.95 atm (D) 0.3214 atm 6. In the dissociation of AB2 as 2AB g AB g B g , the equilibrium concentration of AB2 is 400 mm

and equilibrium constant is 100 mm. The initial concentration of AB2 was (A) 600 mm (B) 200 mm (C) 400 mm (D) 800 mm 7. Reactants A and B are mixed in the molar ratio 1 : 1.5 to establish the equilibrium A 2B 2C D .

At equilibrium the concentrations of A and B are found to be equal. The equilibrium constant KC for the reaction is

(A) 0.25 (B) 4 (C) 1 (D) 2 8. Calculate pH of 10–8 M aqueous solution HCl is (A) 8 (B) 6 (C) 7.02 (D) 6.96 9. When water is heated to 65C, the neutral pH changes to 6.7. The ionic product of water at this

temperature is (A) 1 x 10–14 (B) 4 x 10–14 (C) 5 x 10–13 (D) 2.8 x 10–13 10. Equal volumes of two solutions of pH 5 and 3 are mixed and diluted 10 times. The pH of the resultant

solution is (A) 4 (B) 0.4 (C) 4.3 (D) 3.3 11. 100 ml of one normal HCl is mixed with 100 ml of NaOH solution containing 32g of NaOH per litre. The

pH value of the resultant solution is (A) 1 (B) 12 (C) 0.6990 (D) 1.301 12. For a reaction to proceed in the backward direction, conditions for reaction quotient is (A) QC > KC (B) QC < KC (C) QC = KC (D) QC = 0 13. The yield of product in the reaction 2A g 2B g C g QkJ will be higher at

(A) low temperature and high pressure (B) high temperature and high pressure (C) low temperature and low pressure (D) high temperature and low pressure 14. pH of a solution = 11. Calculate the no. of hydrogen ions present per ml of the solution. (A) 6.02 x 109 (B) 6.02 x 1011 (C) 6.02 x 1020 (D) 6.02 x 1015 15. The weakest conjugate base among the following is (A) ClO (B) 2ClO (C) 3ClO (D) 4ClO 16. Calculate the pH of a solution of H2SO4 with density of 1.02g cm–3 and containing 3.24 wt percent of

acid at 20C. Assume complete dissociation. (log 0.67 = –0.17) (A) 0.171 (B) 0.271 (C) 0.217 (D) 0.127 17. A solution containing H+ ions is diluted 1000 times. Then the pH of the solution (A) increase by 3 (B) increases 3 times (C) decreases 3 times (D) decreases to 3 18. Which of the following has lowest pH value ?

(A) 0.1 M HCl (B) 0.1 M H2SO4 (C) 0.1 N CH3COOH (D) N NaOH10

19. The ratio of Kp to KC for the equilibrium reaction 4 3NH Cl s NH g HCl g at 300 K is

(A) 24.63 I atm mol–1 (B) 0.0406 I–1 atm–1 mol (C) 606.6 I2 atm2 mol–2 (D) 1.6 x 10–3 I–2 atm–2 mol2 20. At 90°C, pure water has [H+] = 10–6 moles/Lit. What is the value of Kw at this temperature? (A) 10–6 (B) 10–12 (C) 10–14 (D) 10–9

[1]

JR_MPC HOLIDAY WORKSHEET -2 DATE:11-10-2018

MATHS 1. If f is a differentiable function and 2f sin x f cos x x x R then f ' x

A) sin x cosx B) sin x cosx C) 21 x D) 2

11 x

2. If

2 2 4 4 2 32

1 1 dyx y t and x y t , then x yt t dx

A) –1 B) 1 C) xy

D) yx

3. Let

1 1 sin x 1 sinxy Tan , then

1 sinx 1 sin x

Statement-I: dy 1 if x 0, / 2dx 2

Statement-II: dy 1 if x 0, / 2 ,dx 2

then which of the following is correct?

A) I is correct II is incorrect B) I is incorrect and II is correct C) Both I and II are correct D) Both I and II are incorrect

4. If

21 1

2

elog3 2log xxy Tan Tan , then

logex 1 6log x

Statement-I: 1 1y Tan 1 Tan 3

Statement-II: dy 0dx

Which of the following is correct? A) I is correct, II is wrong B) I is wrong, II is correct C) Both I and II are correct D) Both I and II are wrong

5. If

1 3cosx 4sin x dyy Cos , then5 dx

A) 2

11 x

B)

2

11 x

C) 0 D) 1

6. If

f x f yx yf for all x, y R and f ' 0 1, f 0 1, then f 22 2

A) 12

B) 1 C) –1 D) 12

7. If f x x 7 and g x fofof x , then for x 21, g' x

[2]

A) 1 B) 0 C) –1 D) 12

8. If

h 0 h 0

f x y f x f y and f x 1 xg x H x where limg x 2 and limH x 3, then f ' x

A) 6f x B) 3f x C) 2f x D) 5f x

9. If

2f x sin 2x 2 x for 0 x 1, then f '2

A) 2

B) C) 0 D) 2

10. If 1 1 1

2 2 21 1 1y Tan Tan Tan , then y ' 0

1 x x x 3x 3 x 5x 7

A) 310

B) 510

C) 710

D) 910

11. If 1 2 5 1 dyy Sin x 1 x x 1 x where 0 x , then

2 dx

A)

1 1 11 x 1 x 2 x

B)

1 1 11 x 1 x 2 x

C)

1 1 11 x 1 x 2 x

D)

1 1 11 x 1 x 2 x

12. If 1 3cosx 4sin x dyy Tan , then

4cosx 3sinx dx

A) 1 B) 12

C) 0 D) –1

13. If sinx dyy x , thendx

A) sin x sin xx cosxlog x

x B)

sin x sin xx cosxlog xx

C) sin x sinxx cosx log x

x D)

sin x sinxx cosxlog xx

14. If 2 2 dy2x 3xy y x 2y 8 0, thendx

A)

3y 4x 12y 3x 2

B)

3y 4x 12y 3x 2

C)

3y 4x 12y 3x 2

D)

3y 4x 12y 3x 2

15. Let f : R R be a differentiable function and f(1)=4. Then the value of

f x

x 14

2tdtlimx 1

A) 8f ' 1 B) 4f ' 1 C) 2f ' 1 D) f ' 1 16. The left hand derivative of f x x sin x at x k an integer is

A) k1 k 1 B)

k 11 k 1 C)

k1 k D)

k 11 k

[3]

17. Let f : R R be a function defined by 3f x max x, x . Then the set of all points where f(x) is not differentiable is

A) 1, 1 B) 1,0 C) 0,1 D) 1,0, 1

18. If

m nm n dyx y x y , thendx

is

A) xy B) x/y C) y/x D) x yxy

19. If f is a real-valued differentiable function satisfying

2f x f y x y , x, y R and f 0 0, then f 1 equals A) 0 B) –1 C) 1 D) 2

20. If

y ...toy e dyx e , x 0, thendx

is

A) 1 xx

B) 1x

C) 1 xx

D) x

1 x

21. If t = sin x and z = cos x, then derivative of 1 tTan1 z

w.r.t 1 zTan1 t

is

A) -1 B) 0 C) 1 D) 2

22. If 1 1 sin x 1 sin x0 x , y Cot ,2 1 sin x 1 sin x

then dy

dx =

A) -1 B) 1 C) 12

D) 12

23. If x > 0 and y x yx e then dydx

=

A) 2

11 log x

B) 2

log x1 log x

C) 2

log x1 log x

D) 2log x1 log x

PHYSICS

1. The position x of a particle varies with time(t) as x = at2 – bt3. The acceleration at time t of the particle

will be equal to zero, where t is equal to____________

2. A particle moving in a straight line covers half the distance with speed of 3 m/s. The other half of the

distance is covered in two equal time intervals with speed of 4.5 m/s and 7.5 m/s respectively. The

average speed of the particle during this motion is____________

3. Two balls of different masses ma and mb are dropped from two different heights, viz, a and b. The ratio

of times taken by the two to drop through these distance is____________

4. A body starting from rest moving with uniform acceleration has a displacement of 16 m in first 4

seconds and 9 m in first 3 seconds. The acceleration of the body is____________

[4]

5. The velocity–time relation of an electron starting from rest is given by v = kt where k = 2 m/s2. The

distance traversed in first 3 s is____________

6. A ball is thrown upwards with speed v from the top of a tower and it reaches the ground with speed

3v. What is the height of the tower ? ____________

7. The variation of velocity of a particle moving

along a straight line is shown in figure. the

distance travelled by the particle in 12 s

is____________

V (m/s)

2

5

2 4 6 8 10 12

t (sec.) 0 14

2

-2.5

-5

8. The velocity–time graph of a body is given below. The

maximum acceleration in ms–2 is____________

v/ms–1

t/s

60

20

20 30 40 70

9. An object is thrown vertically up. Then draw velocity–time graph for the motion of the particle

____________

10. The range R of projectile is same when its maximum heights are h1 and h2. What is the relation

between R, h1 and h2 ?____________

11. A ball rolls off the top of a staircase with a horizontal velocity u m/s. If the steps are h metre high and b

metre wide, the ball will hit the edge of the nth step, if____________

12. A number of bullets are fired in all possible directions with the same initial velocity u. The maximum

area of ground covered by bullets is____________

13. A body is projected horizontally from the top of a tower with initial velocity 18 ms–1. It hits the ground

at angle 45. What is the vertical component of velocity when it strikes the ground ? ____________

14. A hose lying on the ground shoots a stream of water upward at an angle of 60 to the horizontal with

the velocity of 16 ms–1. The height at which the water strikes the wall 8 m away is____________

15. There are two values of time for which a projectile is to the same height. The sum of these two times is

equal to (T = time of flight of the projectile) ____________

16. A boat is moving with a velocity ˆ ˆ3i 4 j with respect to the ground. The water in the river is flowing

with a velocity – ˆ ˆ3i 4 j with respect to the ground. The velocity of the boat relative to the water

is____________

[5]

17. Rain is falling vertically downwards with a velocity of 3 kmph. A man walks in the rain with a velocity of

4 kmph. The rain drops will appear to be falling on the man with a velocity of ____________

18. A boat which has a speed of 5 kmph in still water crosses a river of width 1 km along the shortest path

in 15 minutes. The velocity of the river water is____________

19. A man is 45 m behind the bus, when the bus starts accelerating from rest with acceleration

With what minimum velocity should the man start running to catch the bus?_____________

____________

20. A body is falling freely under gravity. The distances covered by the body in first, second and third minute of its motion are in the ratio_____________

CHEMISTRY

CHEMICAL AND IONIC EQUILIBRIUM 1. Choose correct statements (I) NH3 is a lewis base (II) HCl (aq) is an Arhenius acid (A) only (I) (B) only (II) (C) both (I) & (II) (D) none 2. Determine the pH of a solution made by mixing 50 ml of 0.01 M Ba(OH)2 with 50 ml water. (A) 2 (B) 12 (C) 3 (D) 10 3. 10–2 mole of NaOH was added to 10 litre of water at 250C. The pH will change by (A) 4 (B) 3 (C) 11 (D) 7 4. For a chemical reaction at the state of equilibrium, which of the following statements is incorrect? (A) none of the variables, temperature, pressure or volume appear to change (B) reaction system has maximum stability with minimum energy content. (C) addition of catalyst disturbs the point of equilibrium (D) addition of inert gas at equilibrium for constant pressure system will move the equilibrium in the

direction where more number of moles of gases are present. 5. The equilibrium pressure in the reaction system: 2NF3(g) N2(g) + 3F2(g) is increased ten times,

the equilibrium constant in terms of mole fractions (Kx) would: (A) increase ten times (B) decrease ten times (C) increase hundred times (D) decrease hundred times

6. AB3(g) is dissociates as AB3(g) AB2(g) + 12

B2(g). When the initial pressure of AB3 is 800 torr and

the total pressure developed at equilibrium is 900 torr. What fraction of AB3(g) is dissociated? (A) 10% (B) 20% (C) 25% (D) none of these 7. Which among the following is not a conjugate acid–base pair ? (A) NH3 and 2NH (B) NH3 and 4NH (C) 3CH and CH4 (D) 3CH and 3CH 8. Which among the following is wrong ?

(A) aKc

(B) 3 aH O K c (C) 3

w 22

H O OHK

H O

(D) 2bK c

[6]

9. The pH of a 0.1 M monobasic acid is 2.0. The percentage degree of dissociation is (A) 10 (B) 1 (C) 50 (D) 25 10. For the hydrolysis of NH4Cl, the correct expression is

(A) wh

a b

KK

K K

(B) w

a b

Kh

K K

(C) a b

1pH 7 pK pK2

(D) both A and C

11. Equal volumes of two solutions of pOH 12 and 11 are mixed. pH of the resulting solution is (given log 55 = 1.7403)

(A) 3.5 (B) 3.26 (C) 2.26 (D) 2 12. A precipitate of CaF2 10

spK 1.7 10 units is obtained when equal volume of which of the following

are mixed ? (A) 10–4 M Ca2+ & 10–4 MF– (B) 10–2 M Ca2+ & 10–3 MF– (C) 10–5 M Ca2+ & 10–3 MF– (D) 10–3 M Ca2+ & 10–5 MF– 13. The decreasing order of pH value of the following salts in aqueous solution is (A) NH4Cl > NaCl > NaCN (B) NaCN > NaCl > NH4Cl (C) NaCl > NaCN > NH4Cl (D) NaCl > NH4Cl > NaCN 14. The solubility product of Ag2CrO4 is 32 x 10–12 mol3. The solubility of Ag2CrO4 is (A) 5 x 10–13 (B) 2x 10–4 (C) 1.25 x 10–4 (D) 2 x 10–12 15. Which among the following is a wrong statement ? (A) Larger the value of Ka, stronger is an acid (B) Kw increase with temperature (C) Lower the pKb, stronger the base (D) pH of water decreases while pOH increases with increase in temperature 16. The solubility product of AgCl is 1.8 x 10–10 at 27C. CaCl2 solution of which of the following

concentration cannot precipate AgCl from a solution of 10–2 molar AgNO3 ? (A) 1.08 x 10–8 (B) 1.7 x 10–8 (C) 9 x 10–9 (D) 1.8 x 10–4 17. A solution of KBr (0.1 M) was slowly added to 0.005 M. AgNO3 solution to precipitate AgBr

13spK 5 10 until Br

becomes 0.01 M. Calculate the concentration of Ag+ ion.

(A) 5 x 10–15 M (B) 5 x 10–12 M (C) 1 x 10–4 M (D) 5 x 10–11 M 18. Ksp for a certain sparingly soluble salt is 1.1 x 10–11. If the solubility is = 1.4 x 10–4 M and the salt has the

formula nMX (x : univalent), determine n.

(A) 1 (B) 2 (C) 3 (D) 4 19. The solubility ‘s’ and solubility product Ksp for PbI2 are related as

(A)

13

sp

4SK

(B) 12spK

S4

(C) 3

spKS

4

(D) 13spK

S4

20. An aqueous solution is twice as acidic as pure water at 298 K. pH of the solution is (A) 6.7 (B) 7 (C) 14 (D) 7.3

_______________________________________________________________________________________ 1

JR_MPC HOLIDAY WORKSHEET -3 DATE:12-10-2018

MATHS CONTINUITY AND DIFFERENTIABILITY

Integer answers type questions:

1. If 2 2

2 2x xF x f g

where f ’’(x) = –f(x) and 1g x f x and given that

F(5) = 5, then F(10) is equal to

2. The function given by

1cos 11

1 1

x xxf xx

the value of for which the

function f(x) is continuous at 1x from the right, must be ____________

3. Over the interval 1 1,2013 2007

the function cos1sin

x

x

is discontinuous at K points

then K must be equal to __________ 4. The number of two digits numbers ‘a’ whose sum of digits is 9 such that

32 sin 2 cos 2xf x x a x

a

is continuous in 4,6 is.

Here . denotes the greatest integer function

5. If

1+ x, 0 x 2f x =

3 - x, 2 < x 3 then the number of points of discontinuity of the function

(fof) (x) in [0, 3] is 6. The number of points at which 1 , 1 3f x x x x is not differentiable is

where [ . ] denotes G.I.F 7. Number of points of discontinuity of the function 2( ) 1 ; where [.] denotes . . . [1,3]f x x G I F x is

8. If the function 5 3 2 /74 3 2 xf x x x x e and 1g x f x then the value of

' 1g is. 9. Let :f R R and :g R R be twice differentiable functions satisfying '' '' ,2 ' 1 ' 1 4f x g x f g and 3 2 2 9f g then the value of

15 4 4f g is equal to

10. Let f x be a real function not identically zero such that

2 12 1 nnf x y f x f y

n N and x, y are any real numbers and ' 0 0f , then the value of 5f is.

_______________________________________________________________________________________ 2

11. Let f x be a function such that 1 1 3.f x f x f x x R . If 5 10f .

Then the value of 'g x where 99

05 12

rg x f r

is.

12. 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

' 26

f is.

13. If , 1 1, 0 then the number of points where the function

2 1f x x x is not differentiable is.

14. Number of point (s) of discontinuity of the function 1xf x x , x 0

where [ . ]

represents G.I.F PHYSICS

1. When a body is stationary____________ 2. When a body is in translatory equilibrium____________ 3. A bullet moving with a velocity of 100 m/s can just penetrate two planks of equal thickness. The

number of such planks penetrated by the same bullet, when the velocity is doubled, will be____________

4. A block of metal weighing 2 kg is resting on a frictionless plane. It is struck by a jet releasing water at a rate of 1 kg/s and speed of 5 m/s. The initial acceleration of the block will be____________

5. Two persons are holding a rope of negligible weight tightly at its ends so that it is horizontal. A 15 kg weight is attached to the rope at the mid point which now no longer remains horizontal. The minimum tension required to completely straighten the rope is____________

6. A body of mass 10 kg is hanging from another body of mass 15 kg. The combination is pulled up by a string with an acceleration of 1.2 ms–2. Find the tension (in N) at A and B as shown in figure. (take g = 9.8 m/s2)

____________

15 kg

B

A

10 kg 7. The blocks are connected as shown in figure on

a horizontal frictionless table. if m1 = 1 kg, m2 = 8 kg, m3 = 27 kg and T3 = 64 N, T2 will be_____________

___________

T1 T2 T3 m1 m2 m3

8. A force F is applied on block a as shown in figure. the contact force between the blocks A and B and between the blocks B and C respectively are (assume frictionless surface) ____________

m 2m 4m

A B C

F

9. Three equal weights A, B, 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____________

A B

C

_______________________________________________________________________________________ 3

10. A block of mass M is pulled along a horizontal frictionless surface by a rope of mass m. Force P is applied at one end of the rope. The force which the rope exerts on the block is____________

11. Two bodies of mass 4 kg and 6 kg are attached to the ends of a string passing over a pulley. The 4 kg mass is attached to the table top by another string. The tension in this string T1 is equal to (take g = 10 m/s2)

____________

4kg

6kg

12. Two masses 40 kg and 30 kg are connected by a weightless string

passing over a frictionless pulley as shown in the following figure. the tension in the string will be____________

30 30

T T

40kg 30kg m1 m2

13. A body of mass M is acted upon by a force F and the acceleration produced is a. If three forces each

equal to F and inclined to each other at 120 act on the same body, the acceleration produced will be____________

14. A packet of weight W is dropped with the help of a parachute and on striking the ground comes to rest with retardation equal to twice the acceleration due to gravity. What is the force exerted on the ground? ____________

15. An object is resting at the bottom of two strings which are inclined at an angle of 120 with each other. Each string can withstand a tension of 20 N. The maximum weight of the object that can be sustained without breaking the string is____________

16. In the following figure, the pulley P1 is fixed and the pulley P2 is movable. If W1 = W2 = 100 N, what is the angel AP2P1?

____________

A P2 P1

W2 W1

17. A body of mass 10 kg moves at a constant speed of 10 m/s. A constant force then acts for 4 second

on the body and gives it a speed of 2 m/s in opposite direction. The force acting on the body is____________

18. A man sits on a chair supported by a rope passing over a frictionless fixed pulley. The man who weighs 1000 N exerts a force of 450 N on the chair downwards while pulling the rope on the other side. If the chair weighs 250 N, then the acceleration of the chair is____________

19. Two blocks of masses 6 kg and 4 kg connected by a rope of mass 2 kg are resting on a frictionless floor as shown in the figure. If a constant force of 60 N is applied to 6 kg block, the acceleration of the system is____________

A F=60N 4kg 6kg C

2kg

B

20. Objects A and B each of mass m are connected by light inextensible cord. They are constrained to move on a frictionless ring in a vertical plane as shown in figure. The objects are released from rest at the positions shown. The tension in the cord just after release will be ____________

_______________________________________________________________________________________ 4

CHEMISTRY

CHEMICAL AND IONIC EQUILIBRIUM 1. In which of the following media would Ag2CrO4(s) have the least solubility ? Ksp = 1.9 x 10–12. (A) water (B) 0.1 M AgNO3 (C) 0.1 M NaNO3 (D) 0.1 M NaCl 2. 50 mL of weak mono protic organic acid (Ka = 1.75 x 10–5) of molarity 0.02 is titrated against 0.2 M

NaOH. Calculate the pH after the addition of 3 mL of the alkali. [log 1.75 = 0.25 log 1.5 = 0.18] (A) 3.5 (B) 3.93 (C) 2.5 (D) 4.93 3. The solubility product of CaF2 in water at 18C is 3.2 x 10–11. Calculate solubility in g/L. (A) 2 x 10–4 (B) 0.0156 (C) 0.0078 (D) .02 4. The hydrolytic constant of urea hydrochloride is 0.01 at 25C. 14

wK 10 . Calculate Kb for urea (A) 10–12 (B) 10–16 (C) 10–9 (D) 10–5 5. Ka for benzoic acid is 3 x 10–6. Find the number of H+ ions in 100 mL of 0.12 M benzoic acid. (A) 3.6 x 10–19 (B) 1.8 x 10–19 (C) 6 x 10–4 (D) 6 x 10–3 6. Given Ka for HA (weak acid) = 2 x 10–5 and Kb for BOH(weak base) = 4 x 10–10 (Kw = 10–14) at 298

K. Calculate Kh of the salt AB ? (A) 2.5 (B) 7 (C) 1.25 (D) 2 7. Ammonium chloride is added to ammonium hydroxide. Then (A) concentration of OH– increases (B) concentration of H+ decreases (C) concentration of OH– decreases (D) concentration of 4NH and OH– decreases 8. The Ka value of HCN is 5 x 10–10. A solution is prepared by mixing HCN and KCN in the molar

ratio 1 : 5. The pH of the solution is (log 5 = 0.7) (A) 10 (B) 8.601 (C) 11.398 (D) 4 9. The pH of a solution obtained by mixing 0.1 M CH3COOH and 0.01 M CH3COONa is (pKa for

CH3COOH = 4.74) (A) 5.74 (B) 2.74 (C) 3.74 (D) 4.74 10. Calculate the change in pH when a 0.1M solution of acetic acid (Ka 10–5) in water at 25C is

diluted to a final concentration of 0.001 M. (A) 0.5 (B) 0.4 (C) 0.7 (D) 0.6 11. Given Ka = 1.785 x 10–5 for acetic acid at 298 K. Calculate the pH of the solution obtained by mixing

equal volumes of 0.2 M HCl and 0.6 M sodium acetate (log 2 = 0.3010; log 1.785 = 0.252) (A) 4.0 (B) 4.4 (C) 5.05 (D) 6.18 12. The amount of NH4OH and NH4Cl required to prepare a buffer solution of pH = 9, when the total

concentration of buffering reagents is 0.6 mol I–1 (pKb for NH4OH is 4.7). (A) NH4OH = 0.2 mol I–1 NH4Cl = 0.4 mol–1 (B) NH4OH = 0.4 mol I–1 NH4Cl = 0.2 mol I–1

(C) NH4OH = 0.3 mol I–1 NH4Cl = 0.3 mol I–1 (D) NH4OH = 0.1 mol I–1 NH4Cl = 0.5 mol I–1

13. The pH of a buffer solution containing equal concentration of X– and HX at 25C is (Kb for X– is 10–

8) (A) 4 (B) 8 (C) 6 (D) 7 14. The PH of 10–7 M HCl solution is (A) 7 (B) 8 (C) 5 (D) 6.7 15. Which of the following salts do not undergo hydrolysis ? (A) K2CO3 (B) KCN (C) CH3COONH4 (D) K2SO4 16. An acidic buffer among the following is (A) CH3COOH + CH3COONH4 (B) CH3COOH + NaCl (C) CH3COOH + CH3COOK (D) NH4OH + NH4Cl

Kc and Kp and their relation: 17. Which of the following statements are incorrect about equilibrium state. I) The properties such as pressure, concentration, etc remain unchanged with time.

_______________________________________________________________________________________ 5

II) Addition of a catalyst to the reaction alter the position of the equilibrium III) Change in pressure or concentration of the reactants does not alter the position of

equilibrium. IV) The equilibrium state can be attained from the side of reactants only 1) I, IV 2) I, II, III 3) II, III, IV 4) I, II 18. The active mass of 4gm of hydrogen in 2L vessel is 1) 2 M 2) 1 M 3) 4 M 4) 0.5 M 19. The active mass of 10 gm of CaCO3 in 2L vessel is 1) 0 2) 1 3) 0.05 M 4) 10 M

20. For the reaction, )g(H23)g(N

21

22 )g(NH3 the Kc expression is

1) Kc= 3

23

22

12

NHHN 2) Kc =

2

32

21

2

3

HN

NH

3) Kc = [ N2]1/2 [H2]3/2 4) Kc =

21

22

32

3

HN

NH

_______________________________________________________________________________________ 1

JR_MPC HOLIDAY WORKSHEET -4 DATE:13-10-2018

MATHS FUNCTIONS

Single answer type questions: 1. Let f x be a function such that ,f x x x where x is the greatest integer

less than or equal to x. Then the number of solutions of the equation

1 1f x fx

is (are)

A) 0 B) 1 C) 2 D) infinite 2. Let W be the set of whole numbers and :f W W be defined by

10log10 10 0

10 100 0

xx xx f if xf x

if x

where y denotes the largest integer y . Then 7752f

(A) 7527 (B) 5727 (C) 7257 (D) 2577

3. The domain of the function 4 210 21f x x x is

(A) [5, ) (B) 21, 21

(C) , 21 21,5 05 (D) ( , 5]

4. sin sin ,02

f x x x x , where represents the greatest integer function,

can also be represented as

(A) 0 , 0 1

1 sin1 , 12

x

x

(B)

1 , 042

1 1 31 ,2 2 4 22

x

x

(C) 0 , 0 1

sin1 , 12

x

x

(D)

0 , 04

1 , 14

sin1 , 12

x

x

x

5. If :f N N is defined by 1 nf n n , then (A) f is one-one but not onto (B) f is both one-one and onto (C) f is neither one-one nor onto (D) f is onto but not one-one

_______________________________________________________________________________________ 2

6. Let : 3f R R be a function such that for some 0p ,

53

f xf x p

f x

for all x R . Then, period of f is (A) 2 p (B) 3 p (C) 4 p (D) 5 p 7. If 2 2

2 3 3 7log 6 23 21 4 log 4 12 9x xx x x x , then the value of 4x is

A) 0 B) 1 C) 2 D) 14

8. The domain of the function

12 42 2 139 27 219 3

x xxf x

A) 3,3 B) 3, C) 5 ,2

D) 0,1

9. Period of the function 12 3 4 ....

2n n x

f x x x x x nx

, where, n N

and denotes the greatest integer function, is

A) 1 B) n C) 1n

D) 2n

10. If f and g are two functions defined on N, such that 2 12 2

n if n is evenf n

n if nis odd

and

1g n f n f n . Then range of g is A) { /m N m = multiple of 4} B) { set of even natural numbers} C) { / 4 3,m N m k k is a natural number} D) { /m N m multiple of 3 or multiple of 4}

11. Let 1

x,0 x 1f x 1, x 1

0, otherwise

and 2 1f x f x for all x

3 2f x f x for all x

4 3f x f x for all x

Which of the following is necessarily true? (A) 4 1f x f x for all x (B) 1 3f x f x for all x (C) 2 4f x f x for all x (D) 1 3f x f x 0 for all x

12. Let 117

1

12[ ] 1r

Sr

where [.] denotes the greatest integer function. The value of S is

(A) 697

(B) 20621

(C) 767

(D) 22721

PHYSIC 1. Work done in time t on a body of mass m which is accelerated from rest to a speed v in time t1 as a

function of time t is given by____________ 2. The displacement x in m of a particle of mass m kg moving in one dimension under the action of a

force is related to the time t in seconds by the equation t x 3 , the work done by the force (in J) in first six seconds is____________

_______________________________________________________________________________________ 3

3. The work done in moving a body of mass 4 kg with uniform velocity of 5 ms–1 for 10 seconds on a surface of = 0.4 is (take g = 9.8 m/s2) ____________

4. A body is acted upon by a force which is proportional to the distance covered. If distance covered be denoted by x, then work done by the force will be proportional to____________

5. A force 2ˆ ˆ ˆF 2xi 2 j 3z k

N is acting on a particle. Find the work done by this force in displacing the body from (1, 2, 3)m to (3, 6, 1)m. ____________

6. Work–energy theorem is valid in the presence of____________ 7. An engine pumps up 100 kg of water through a height of 10 m in 5 s. Given that the efficiency of the

engine is 60%, what is the power of the engine? Take g = 10 ms–2. ____________ 8. The distance covered by a body to come to rest when it is moving with a speed of 4 ms–1 is s when a

retarding force F is applied. If the KE is doubled, the distance covered by it to come to rest for the same retarding force F is____________

9. Find the speed v reached by a car of mass m, driven with constant power P, is ____________ 10. An object of mass m is allowed to fall from rest along a rough inclined plane. The speed of the object

on reaching the bottom of the plane is proportional to____________ 11. Given that the position of the body in m is a function of time as follows x = 2t4 + 5t + 4. The mass of

the body is 2 kg. What is the increase in its kinetic energy one second after the start of motion? ____________

12. The kinetic energy K of a particle moving along a circle of radius R depends upon the distance s as K = as2. The force acting on the particle is____________

13. Figure shows a smooth curved track terminating in a smooth horizontal part. A spring of spring constant 400 N/m is attached at one end to the wedge fixed rigidly with the horizontal part. A 40 gm mass is released from rest at a height of 5 m on the curved track. Find the maximum compression of the spring ____________

5m

14. A particle of mass 0.1 kg is subjected to a force which varies with displacement as shown in figure. It starts its journey from rest at x = 0, its velocity at x = 12 m is____________

10

0 4 8 12 x

F

15. A toy spring gun is used to fire a ball as a projectile. The mass of the ball is 50 gm and the gun is

fired at an angle of 45. When the spring is compressed by 10 cm the range of the projectile is found to be 1.50 m. Then the spring constant of the spring is (take g = 9.8 ms–2) ____________

16. The potential energy between two atoms, in a molecule, is given by 10 5a bU(x)

x x where a and b are

positive constants and x is the distance between the atoms. The atoms are in stable equilibrium, when____________

17. A small block of mass m is kept on a rough inclined surface of inclination fixed in an elevator. The elevator goes up with a uniform velocity v and the block does not slide on the wedge. The work done by the friction force on the block in time t will be

____________

_______________________________________________________________________________________ 4

18. A block of 4 kg mass starts at rest and slides a distance d

down a frictionless incline (angle 30) where it runs into a spring of negligible mass. The block slides an additional 25 cm before it is brought to rest momentarily by compressing the spring. The force constant of spring is 400 N/m. The value of d is then (take g = 10 ms–2) ____________

30

d

k

m

19. A body constrained to move in the y-direction is subjected to force N. The work done by this force in moving the body through a distance of 10 m along y-axis is____________

20. A uniform chain of length 2 m is kept on a table such that a length of 60 cm hangs freely from the edge of the table. The total mass of the chain is 4 kg. What is the work done in pulling the entire chain on the table? ____________

CHEMISTRY

CHEMICAL AND IONIC EQUILIBRIUM 1. For the reaction, CaCO3(s) CaO (s) + CO2 (g) the Kc expression is

1) Kc = 3

2

CaCOCOCaO 2) Kc = [CaCO3] 3) Kc = [CO2] 4) Kc =

3

2

CaCOCO

2. For the reaction, NH3 (g) + H2O (l) (excess) NH4+ (aq) + OH- (aq) the Kc expression is

1) Kc = OHNH

OHNH

23

-4

2) Kc =

3

-4

NHOHNH

3) Kc = [NH3] 4) Kc = 4NH [OH-]

3. For the following reaction, the Kc expression is CH3COOH (l) + C2H5OH(l) CH3COOC2H5(l) + H2O

1) Kc = OH]H[C COOH][CH

O]H[HCOOCCH

523

2523 2) Kc = OH]H[C COOH][CH

HCOOCCH

523

523

3) Kc = [CH3COOC2H5] [H2O] 4) Kc = ]HCOOC[CH

COOH]CH[

523

3

4. For the reaction, CaCO3 (s) CaO (s) + CO2 (g) the Kp expression is

1) Kp = [CO2] 2) Kp = Pco2 3) Kp = 3

2

CaCO

COCaO

PP.P

4) Kp = Kc [CO2]

5. Match the following List – I List – II (Equation) (Relation between Kc and Kp) 1) N2 (g) + 3 H2 (g) 2 NH3 (g) 1) Kp = Kc 2) 2 SO2 (g) + O2 (g) 2 SO3 (g) 2) Kp < Kc 3) H2 (g) + I2 (g) 2 HI (g) 3) Kp > Kc 4) PCl5 (g) PCl3 (g) + Cl2 (g) 4) Kp Kc

_______________________________________________________________________________________ 5

A B C D A B C D 1) 1 2 3 4 2) 2 2 1 3 3) 2 2 3 1 4) 1 3 1 3 6. Match the following List – I List – II A) A (g) + 3 B (g) 2 C (g) 1) Kc > Kp B) 2 A (g) + B (g) 2 C (g) 2) Kc < Kp C) A(g) + B (g) C (g) 3) Kc = Kp D) A(g) B (g) + C (g) 4) Kc Kp A B C D A B C D 1) 1 1 1 2 2) 1 2 3 4 3) 4 1 3 4 4) 2 1 1 2

7. The relation between Kc and Kp for the reaction )(NH )(H 23 (g) N

21

322 gg is

1) (RT)KK c

p 2) (RT)K

K pc 3) Kp = Kc (RT) 4) Kp = Kc

8. The relation between Kc and Kp for the reaction PCl5 (g) PCl3 (g) + Cl2 (g) is 1) Kp = Kc (RT)1 2) Kc = Kp (RT) 3) Kp = Kc (RT) 4) Kc = Kp 9. The relation between Kc and Kp for the reaction NH4HS(s) NH3 (g) + H2S (g) is 1) Kp = Kc(RT)1 2) Kp = Kc(RT)2 3) Kp = Kc (RT)-2 4) Kp = Kc Equilibrium-problems: 10. The molar concentration of A, B and C at equilibrium for the reaction A + 2B 4C are 1M,

2M and 4M respectively. The value of Kc is 1) 8 2) 16 3) 64 4) 1

11. The molar concentration of A, B and C at equilibrium for the reaction ABB21A

21

22 are

1M, 2M and 3M respectively. The value of Kc is

1) 2/3 2) 3/2 3) 3 4) 23 12. The molar concentration of N2, H2 and NH3 at equilibrium for the reaction

322 NHH23N

31

are 2M, 1M and 2M respectively. The value of Kc is

1) 3/22 2) 2/32 3) 2 4) 1 13. When 1 mole of H2 is heated with 1 mole of I2, it was found that 3/4 mole of HI is formed at

equilibrium for the reaction H2 + I2 2HI. The value of Kc is 1) 1.44 2) 9 3) 5/8 4) 3/8 14. In the reaction A + B 2C + D. The initial concentration of reactants is 1M each. The

equilibrium concentration of D is 0.3M. The value of Kc is 1) 20 2) 0.6 3) 0.22 4) 36/49 15. The Kc value of a reversible reaction is 100, the rate constant for forward reaction is 10-1.

The rate constant for backward reaction is 1) 103 2) 10-3 3) 10-1 4) 102

______________________________________________________________________________________ 1

JR_MPC HOLIDAY WORKSHEET -5 DATE:14-10-2018

MATHS INVERSE TRIGONOMETRIC FUNCTIONS

Comprehensions type questions: Passage - I

If x,y are real numbers such that xy< 1 then 1 1 1

1x yTan x Tan y Tan

xy

1. If a,x,y are all +ve real numbers and xy = 2 1a the 1 11 1Tan Tana x a y

=

(a) 1 1Tana x y

b)

1 1Tana x y

(c)

1 1Tana x y

d)independent of x and y

2. 5 1 1 11 1 12 38 18 57

Tan Tan Tan = _______

(a)2 (b)

4 (c) (d) 3

2

(Hint: Use the result of above question)

3. Number of real solutions of the equation 1 12 4 2 0iTan x Tan Tan xx x x

(a)1 (b)2 (c)3 (d) 0 One or more than one answer type questions: 4. The value of x satisfying 1 1 1sin x sin 1 x cos x are

(A) 0 (B) 12

(C) 1 (D) 2

5. Consider the equation 1 2 1 2 32sin 12

x x cos x x

A) number of solutions is two B) sum of solutions is -1 C) number of solutions is 3 D) Sum of solutions is zero Matching answer type questions: 6. Match the values of column-1 with the values of column-2 Column – 1 Column- 2

(a) 1 1 14 5 165 13 65

Sin Sin Sin p) 34

(b) 1 1 13 3 84 5 19

Tan Tan Tan q) 4

(c) 1 1 112 4 6313 5 16

Sin Cos Tan r)

(d) 1 11 127 3

Tan Tan s) 2

t ) 0

______________________________________________________________________________________ 2

7. Column-I Column-II

A) 1 3sin 24

Tan

P)1415

B) 1 1cos 27

Tan

Q) 35

C) 1 1sin 43

Tan

R) 213

D) 1 11 2cos 24 9

Tan Tan

S) 1

T) 2425

PHYISCS 1. If the body is moving in a circle of radius r with a constant speed v , its angular velocity is

____________ 2. Two racing cars of masses 1m and 2m are moving in circles of radii 1r and 2r respectively. Their

speeds are such that each makes a complete circle in the same duration of time t . The ratio of the angular speed of the first to the second car is ____________

3. A cyclist turns around a curve at 15 miles/hour. If he turns at double the speed, the tendency to overturn is____________

4. A body of mass m is moving in a circle of radius r with a constant speed v . The force on the body is

rmv 2

and is directed towards the centre. What is the work done by this force in moving the body over

half the circumference of the circle____________ 5. If a particle moves in a circle describing equal angles in equal times, its velocity vector

____________ 6. A stone of mass m is tied to a string of length l and rotated in a circle with a constant speed v . If the

string is released, the stone flies ____________ 7. A body is moving in a circular path with a constant speed. It has ____________ 8. A motor cyclist going round in a circular track at constant speed has____________ 9. A particle P is moving in a circle of radius ''a with a uniform speed v . C is the centre of the circle

and AB is a diameter. When passing through B the angular velocity of P about A and C are in the ratio ____________

10. A car moving on a horizontal road may be thrown out of the road in taking a turn____________ 11. In a circus stuntman rides a motorbike in a circular track of radius R in the vertical plane. The

minimum speed at highest point of track will be____________ 12. A block of mass m at the end of a string is whirled round in a vertical circle of radius R . The critical

speed of the block at the top of its swing below which the string would slacken before the block reaches the top is____________

______________________________________________________________________________________ 3

13. A sphere is suspended by a thread of length l . What minimum horizontal velocity has to be imparted the ball for it to reach the height of the suspension ____________

14. A bottle of sodawater is grasped by the neck and swing briskly in a vertical circle. Near which portion of the bottle do the bubbles collect____________

15. A bucket tied at the end of a 1.6 m long string is whirled in a vertical circle with constant speed. What should be the minimum speed so that the water from the bucket does not spill, when the bucket is at the highest position (Take 2sec/10mg ) ____________

16. A wheel is subjected to uniform angular acceleration about its axis. Initially its angular velocity is zero. In the first 2 sec, it rotates through an angle 1 . In the next 2 sec, it rotates through an additional angle 2 . The ratio of 12 / is ____________

17. A 1 kg stone at the end of 1 m long string is whirled in a vertical circle at constant speed of 4 m/sec. The tension in the string is 6 N, when the stone is at( position) (g = 10 m/sec2)____________

18. A cane filled with water is revolved in a vertical circle of radius 4 meter and the water just does not fall down. The time period of revolution will be ____________

19. A 2 kg stone at the end of a string 1 m long is whirled in a vertical circle at a constant speed. The speed of the stone is 4 m/sec. The tension in the string will be 52 N, when the stone is ____________

20. A body slides down a frictionless track which ends in a circular loop of diameter D, then the minimum height h of the body in term of D so that it may just complete the loop, is____________

CHEMISTRY CHEMICAL AND IONIC EQUILIBRIUM

1. For the reaction S (s) + O2 (g) SO2 (g), the partial pressures of SO2 and O2 are 105Nm-2 and 2 x 105Nm-2 respectively at equilibrium. The value of Kp is

1) 0.2 2) 5 3) 0.5 4) Zero 2. For the reaction NH4HS (s) NH3 (g) + H2S (g), the total pressure at equilibrium is

5 x 106 Nm-2. The value of Kp is 1) 6.25 x 105 2) 6.25 x 1012 3) 62.5 x 107 4) 625 3. For the reaction A2B (s) 2 A (g) + B (g), the total pressure at equilibrium is 6atm. The

value of Kp is 1) 32 atm2 2) 16 atm3 3) 32 atm3 4) 6 atm 4. For the reaction 2 SO2 (g) + O2 (g) 2 SO3 (g), the value of Kp is 5 atm-1. What is the

equilibrium pressure of O2, if the equilibrium pressure of SO2 is twice that of SO3. 1) 5 atm 2) 0.5 atm-3 3) 0.05 atm-4 4) 50 atm 5. For the reaction PCl5 (g) PCl3 (g) + Cl2 (g), the value of Kp is 10-2 atm, the pressure at

equilibrium is 1 atm, what is the degree of dissociation of PCl5 1) 1 2) 0.1 3) 0.01 4) 10 6. At 300K and 1 atm pressure 40% of N2O4 is dissociated into NO2. The value of Kp is

1) 1621 2)

2116 3)

74 4)

499

7. The reaction A + 2B 2 C + D was studied using an initial concentration of B which was 1.5 times of A. But at the equilibrium the concentration of A and B were found to be equal. The value of Kc is

1) 2 2) 4 3) 1/4 4) 8

______________________________________________________________________________________ 4

8. 1 mol HI was heated to 4400C in a closed vessel till equilibrium was established as 2HI H2 + I2. At this temperature 25% of HI was dissociated. The value of Kc is

1) 4 2) 1/4 3) 16 4) 1/9 9. PCl5 was heated in a 2L vessel till equilibrium was attained, At this temperature 20% of

PCl5 was dissociated as PCl5 PCl3 + Cl2. The value of Kc is

1) 201 2)

401 3) 20 4) 4

10. The Kc value for the reaction, CH3COOH (l) + C2H5OH (l) CH3COOC2H5(l) + H2O (l) is 16. The initial concentration of

CH3COOH and C2H5OH is 4M. The concentration of ester at equilibrium will be

1) 165 2)

516 3)

85 4)

41

11. In the reversible reaction 2 NH3 N2 + 3H2, when 2 mol of NH3 is taken initially in a 2L flask, 0.5 mol of N2 are formed at equilibrium, the value of Kc is

1) 4/3 2) 3/4 3) 27/64 4) 3 12. One mole of A and two mole of B are allowed to react in a 2L flask. At equilibrium 0.5 mole

of D is formed the value of Kc for A + 2B C + 2 D is

1) 27 2) 274 3)

91 4)

271

13. The partial pressures of NH3, N2 and H2 are 3NHP = 3 atm;

2HP = 2 atm, 2NP = 1 atm. The

value of Kp for 322 NH2H23N

21

is

1) 23 2)

83

3) 8

9 4)

23

14. The Kc value for the reaction H2 + I2 2 HI is 81 at a certain temperature. At equilibrium the concentration of H2 and I2 are 2M each. The equilibrium concentration of HI is

1) 9 2) 81 3) 18 4) 2 15. At 4270C for the reaction H2 + I2 2 HI the value of Kc is 49. What weight of HI is formed at

equilibrium if one mole of H2 and one mole of I2 are placed in a one litre flask (MW of HI is 128)

1) 128 gm 2) 199.11 gm 3) 12.8 gm 4) 45 gm

_______________________________________________________________________________________ 1

JR_MPC HOLIDAY WORKSHEET -6 DATE:15-10-2018

MATHS LIMITS

Single answer type questions:

1. If 3

n

mx e

(ln x 3)limln((cos (ln x 3)))

= –1 (n, mN) then n/m is equal to

(A) 3 (B) 4 (C) 9 (D) 1

2. Let , be the roots of the equation 2 0ax bx c . If 2

2lim 1,x m

ax bx cax bx c

then

A) 1,a

ma

B) 0,a m C) 1,a

ma

D) 0,a m

3. Let :f R R be a function satisfying the relation .f x f y f xy x for all

,x y R . Then

1/3

1/20

1lim

1x

f x

f x

(A) 1 (B) 12

(C) 23

(D) 32

4. The value of 0

limx

f x

where 4

cos sin cosx xf x

x

, is

(A) 2 (B) 1/ 6 (C) 2 / 3 (D) 1/ 3

5. Let 1 1x and 14 33 2

nn

n

xxx

for 1n . If lim nn

x

exists finitely, then the limit is equal to

(A) 2 (B) 1 (C) 2 (D) 2 1

6. Let 3 2 4 1 2f x x x x x . Then limx

f x

is equal to

(A) 1

2 2 (B)

14 2

(C) 3

4 2 (D) does not exist

7. If na and nb are positive integers and 2 2 2n

n na b , then lim n

nn

ab

A) 2 B) 2 C) 2e D) 2e

8. If

20

tan sinlim 0x

a n nx x n xx

, where ~ 0n R , then a is equal to

A) 0 B) 1

nn

C) n D) 1nn

9. For each positive integer n, let

3 4 5 2.....1.2.4 2.3.5 3.4.6 1 3n

nsn n n

. Then lim nn

s

equals

A) 296

B) 2936

C) 0 D) 2918

_______________________________________________________________________________________ 2

10. tan sin

0lim

tan sin

x x

x

a ax x

is equal to 0a

A) loge a B) 1 C) 0 D)

11.

3 3

4

2

1 sin 8 coslim

2x

x x x

x

A) 2

16

B) 23

16 C)

2

16 D)

2316

12. nLt

3

33

88

n

r

rr

a) 27

b) 37

c) 47

d) 57

13. If 5 30

sin sin sin 112x

x xLt

ax bx c

, then

a) 2, 0, 1a b c b) 0, 2,a b c R c) 2, , 0a b R c d) , 2, 0a R b c

14. If 20

ax x

x

e e xLt bx

(finite), then

a) 2, 0a b b) 30,2

a b c) 32,2

a b d) 0, 2a b

15. 1 1

30

sin tanlimx

x xx

is equal to

(A) 16

(B) 12

(C) 2 (D) 12

16. Let f : R R be a positive decreasing function with

3

x

x xf6

lim 1f x

then

x

f sin xlim

f x

(A) 2 (B)

36 (C) 1

6 (D) 1

PHYISCS 1. A bullet of mass m is fired from a rifle of mass M. If

v be the velocity of bullet, velocity acquired by the rifle is____________

2. In case of rifle shooting the kick will be minimum when____________ 3. A bullet weighing 50 gm leaves the gun with a velocity of 30 m/s. If the recoil speed imparted to the

gun is 1 m/s, the mass of the gun is____________ 4. A cannon ball is fired with a velocity 200 m/s at an angle of 60o with the horizontal. At the highest

point of its flight it explodes into 3 equal fragments, one going vertically upwards with a velocity of 100 m/s, the second the falling vertically downwards with a velocity 100 m/s. The third fragment will be moving with a velocity____________

_______________________________________________________________________________________ 3

5. A shell is fired from a cannon with velocity V m/s at an angle with the horizontal direction. At the highest point in its path it explodes into two pieces of equal mass. One of the pieces retraces its path; to the cannon and the speed in m/s of the other piece immediately after the explosion is_____________

6. Two balls A and B of mass 0.10 kg and 0.25 kg respectively are connected by a stretched spring of negligible mass and placed on a smooth table. When the balls are released simultaneously the initial acceleration of ball B is 10 cm/s2 westward. The magnitude and direction of acceleration of the ball A are____________

7. A bullet of mass 0.01 kg and traveling at a speed of 500 m/sec strikes a block of 2 kg which suspended by a string of length 5 m. The centre of gravity of the block is found to rise a vertical distance of 0.1 m. What is the speed of the bullet after it emerges from the block? ____________

8. Two pendulum each of length l are initially situated as shown in figure. The first pendulum is released and strikes the second. Assume that the collision is completely inelastic and neglect the mass of the string and any frictional effects. How high does the centre of mass rise after the collision?

____________

d

m1

m2

l l

9. A body x with a momentum p collides with another identical stationary body y one dimensionally. During the collision y gives an impulse J to body x. Then coefficient of restitution is____________

10. A bullet of mass m is fired with a velocity v on to a block of wood of mass M and initially at rest. The final velocity of the system will be____________

11. A moving mass of 8 kg collides elastically with a stationary mass of 2 kg. If E be the initial kinetic energy of the moving mass the kinetic energy left with it after the collision will be____________

12. A ball collides elastically with another ball of the same mass. The collision is oblique and initially one of the balls was at rest. After the collision, the two balls move with same speeds. What will be the angle between the velocity of the balls after the collision? ____________

13. A cannon of mass 1000 kg located at the base of an inclined plane fires a shell of mass 100 kg in horizontal direction with a velocity 180 kmph. The angle of inclination of inclined plane with the horizontal is 45o. The coefficient of friction between the cannon and inclined plane is 0.5. The height in meter to which the cannon ascends the inclined plane as a result of recoil is (g = 10 m/s2) ____________

14. An object of mass 2 kg is moving with a velocity of 3 m s-1 and collides head on with an object B of mass 1 kg moving in the opposite direction with a velocity of 4 m s-1. After collision both the objects coalesce so that they move with a common velocity v equal to____________

15. The centre of mass of a system of particles does not depend on____________ 16. Four identical spheres each of radius 10 cm and mass 1 kg are placed on a horizontal surface

touching one another so that their centers are located at the corners of square of side 20 cm. What is the distance of their centre of mass from centre of either sphere? ____________

17. Three particles of masses 1 kg, 2 kg and 3 kg are situated at the corners of an equilateral triangle of side b. The coordinates of the centre of mass are____________

18. A circular ring of mass 6 kg and radius a is placed such that its centre lies at the origin. Two particles of masses 2 kg each are placed at the intersecting points of the circle with +ve x-axis and +ve y-axis. Then the angle made by the position vector of centre of mass of entire system with x-axis is____________

_______________________________________________________________________________________ 4

19. If the linear density of the rod of length L varies as = A + Bx, then its centre of mass is given by____________

20. Centre of mass of three particles of masses 1 kg, 2 kg and 3 kg lies at the point (1, 2, 3) and centre of mass of another system of particles 3 kg and 2 kg lies at the point (-1, 3, -2). Where should we put a particle of mass 5 kg so that the centre of mass of entire system lies at the centre of mass of 1st system? ____________

21. 3 particles of masses 2 kg each are placed such that one lies on –ve x-axis, 2nd one lies on –ve y-axis and the third one lies on +ve z-axis at distances of 2m, 3m and 1m respectively from the origin. Then the square of the distance of centre of mass of the system from the origin is____________

22. Mass is distributed uniformly over a thin square plate. If two end points of a diagonal are (-2, 0) and (2, 2), what are the coordinates of centre of mass of plate? ____________

23. Three identical spheres each of radius 10 cm and mass 1 kg are placed touching one another on a horizontal surface. Where is their centre of mass located? ____________

CHEMISTRY

CHEMICAL AND IONIC EQUILIBRIUM 1. In the reversible reaction, NH4HS (s) NH3 (g) + H2S (g) at equilibrium the value of Kp is

2.5 x 104 Nm-2. What is the partial pressure of NH3 at equilibrium. 1) 5 x 104Nm-2 2) 2x104Nm-2 3) 1.58 x 102Nm-2 4) 5 x 103Nm-2 2. A2B dissociates as A2B (g) 2 A (g) + B (g) the initial pressure of A2B is 600 mm of Hg. At

the equilibrium the pressure is 800mm of Hg. The value of Kp is. Assume that the volume of the system remains same.

1) 200 2) 2000 3) 100 4) 20 3. A mixture of 2 moles of N2 and 6 moles of H2 is heated in a 2L vessel. At equilibrium 0.2

moles of N2 was formed. The equilibrium concentration of H2 was for N2 + 3 H2 2NH3 1) 0.6 M 2) 0.3 M 3) 116 M 4) 3 M 4. In the reaction, A(g) B (g) + 3 C (g). The initial pressure of A is 100 mm of Hg. If the

degree of dissociation of A is 20%, the equilibrium pressure is 1) 160 2) 100 3) 14 4) 40 5. The pressure required to obtain 75% dissociation of PCl5 is ____ times of Kp. PCl5

dissociates as PCl5 PCl3 + Cl2

1) pK97 2) pK

79 3) pK

76 4) 3Kp

6. 2 moles of PCl3 and 4 moles of Cl2 were placed in a 3L vessel and heated to 400 K. At equilibrium 1.5 moles of PCl3 remains. The value of Kc for the reaction PCl3 + Cl2 PCl5

1) 200 2) 20/32 3) 10/35 4) 0.2 7. N2O4 dissociates as N2O4 2NO2. The degree of dissociation of N2O4 is 0.2 when the

reaction is conducted in a 2L vessel. The value of Kc is 1) 10 2) 0.1 3) 100 4) 20 8. When CO2 dissolves in water the following equilibrium is established CO2 + 2 H2O H3O+ + HC

3O for which the equilibrium constant is 10-7 and PH = 5 The ratio of [

3HCO ] to [CO2] would be

1) 2 x 10-7 2) 2 x 10-8 3) 10-2 4) 2 x 10-5

_______________________________________________________________________________________ 5

9. N2 + 3 H2 2NH3 K1 = 49, 322 NHH23N

21

K2 = ?

1) 49 2) 1/49 3) 1/7 4) 7 10. N2 + O2 2NO K1 = 10, 2 NO N2 + O2 ; K2 = ? 1) 10 2) 100 3) 0.1 4) 0.01

11. 2 SO2 + O2 2 SO3 K1 = 100, SO3 SO2 + 21 O2 ; K2 = ?

1) 100 2) 10 3) 0.1 4) 0.01 12. A + B C; K1 = 4, 2 A + D C, K2 = 6 Then C + D 2 B K3 = ?

1) 38 2)

161 3)

43 4)

83

13. H2 + I2 2 HI Kc = 49, 21 H2 +

21 I2 HI , Kp = ?

1) 7 2) 1/7 3) 49 4) 21

14. 2 SO2 + O2 2SO3 Kc = 100, SO3 SO2 + 21 O2 KP = ?

1) 0.1 2) 10 3) 10RT 4)

RT10

15. When ethyl alcohol and acetic acid are mixed in equivalent proportion, equilibrium is established when 2/3 rd of the acid and alcohol are consumed. How much ester will be present in the mixture, when 2 mole of acetic acid were to react with 2 mole of ethyl alcohol.

1) 4/3 2) 1/3 3) 2/3 4) 8/3

_______________________________________________________________________________________ 1

JR_MPC HOLIDAY WORKSHEET -7 DATE:16-10-2018

MATHS LIMITS

Matching answer type questions: 1.

COLUMN-I COLUMN-II

(A) sgn 1f x x x (p) 1

limx

f x

doesn’t exist

(B)

2sin sin tan / 2

log cos3

xf x

x

(q) 0

limx

f x

doesn’t exist

(C)

3 31 1

1 1

1 tan 3 1 sin 31 sin 2 1 tan 2

x xf xx x

(r) 0

lim 1/ 9x

f x

(D)

1/

1/

11

x

x

ef xe

(s) 0

lim 1x

f x

2. COLUMN-I COLUMN-II

(A) 3

23

27 log 2lim

9x

x xx

(p) 12

(B) 1

0

1limx

xx x e

x

ex

(q) 8

(C) If

30

cos sinlim 1x

x a x b xx

then a and b

are respectively

(r) 9

(D) If f x is a thrice differentiable function such that

30

4 3 3 3 2lim 12x

f x f x f x f xx

, then ''' 0f is equal to

(s) 1e

3. Let 2

2

1lim1

n

nn

xf xx

Column-1 Column-2 (A) 1f on (P) 1, (B) 1f on (Q) 2, (C) 0f on (R) 2, (D) sgn 1f x x on (S) 1 1,2 2

_______________________________________________________________________________________ 2

One or more than one answer type questions:

1. If , ,02

such that sinsin sin 0

sin

and

sinsin sin 1sin

and

2

21 2sin

lim2sin

n

nn

then

(A) 52 36

(B) 56

(C) 3

(D)

3

2. If 7 7

x a

x alim 7,x a

then the value of a is

(A) 1 (B)–1 (C) 7 (D) –7 PHYSICS

1. Two bodies A and B are attracted towards each other due to gravitation. Given that A is much heavier than B, which of the following correctly describes the relative motion of the centre of mass of the bodies? ____________

2. Two particles of masses m1 and m2 separated by a distance d are at rest initially. If they move towards each other under mutual interaction (say electric, gravitational or elasti(C), where will they meet? ____________

3. Two particles of masses 4kg, 8kg are separated by a distance of 12 m. If they are moving towards each other under the influence will meet each other at a distance of____________

4. Two bodies of masses 5 kg and 2 kg are placed on a frictionless surface and connected by a spring. An external kick gives a velocity of 14 m/sec to the heavier block in the direction of lighter one. The velocity gained by the centre of mass is____________

5. In the Q. No.4, velocities of two blocks in the centre of mass frame just after the kick are respectively given by____________

6. A 500 kg boat is 9 m long and is floating without motion on still water. A man of mass 100 kg is at one end and if he runs to the other end of the boat and stops, the displacement of the boat is____________

7. A dog weighing 5 kg is standing on a flat boat so that it is 10 m from the shore. The dog walks 4 m on the boat towards the shore and then halts. The boat weighs 20 kg and one can assume that there is no friction between it and the water. How far is the dog from the shore at the end of this time? ____________

8. A man of mass m climbs a rope of length L suspended below a balloon of mass M. The balloon is stationary with respect to ground. If the man begins to climb up the rope at a speed vrel. (relative to rope) in what direction and with what speed (relative to groun(D) will the balloon move? ____________

9. Two bodies A and B have masses M and m respectively where M >m and they are at a distance d apart. Equal force is applied to each of them so that they approach each other. The position where they hit each other is____________

10. Two particles of masses m1 and m2 (m1>m2) attract each other with a force inversely proportional to the square of the distance between them. The particles are initially held at rest and then released. Which one is correct? ____________

11. A shell is fired from a gun with a muzzle velocity u m/sec at an angle with the horizontal. At the top of the trajectory the shell explodes into two fragments P and Q of equal mass. If the speed of the

_______________________________________________________________________________________ 3

fragment P immediately after explosion becomes zero, where does the centre of mass of the fragments hit the ground? ____________

12. A block Q of mass M is placed on a horizontal frictionless surface AB and a body P of mass m is released on its frictionless slope. As P slides by a length L on this slope of inclination , the block Q would slide by a distance

____________

P

C

A B

M Q

13. A ring and a disc have same mass and radius. The ratio of their moment of inertia about an axis passing through their centers and perpendicular to their plane is ____________

14. The radius of gyration of a sphere of radius R about a tangent is____________ 15. A thin wire of length L and uniform linear mass density is bent

into a circular loop with centre at O as shown. The moment of inertia of the loop about an axis XY is____________

X Y

O

16. A semicircular ring of mass M and radius R is rotating about its diameter AB. The moment of inertia of the semicircular ring about AB will be____________

R

M

B A

(Q.17 – Q.20) A uniform disc of mass M and radius R is mounted on an axle supported in frictionless bearings. a light cord is wrapped around the rim of the disc and steady downward pull T is exerted on the cord. 17. The angular acceleration of the disc is____________ 18. The tangential acceleration of a point on the rim is____________ 19. If we hang a body of mass m from the cord, the tangential____________ 20. The tension in the cord in the above problem is____________ 21. A thin circular ring of mass M and radius R is rotating about its axis with a constant angular velocity

. Two objects, each of mass m are attached gently to the ring. The ring now rotates with an angular velocity____________

22. A mass is whirled in a circular path with a constant angular velocity and its angular momentum is L. If the string is now halved keeping the angular velocity same, the angular momentum is____________

23. A constant torque acting on a uniform circular wheel changes its angular momentum from A0 to 4A0

in 4 s. The magnitude of this torque is equal to____________ 24. The kinetic energy of rotation (K) and the angular momentum (L) of a rigid body rotating about a

fixed axis are graphically related as____________

K

O L

K

O L

K

O L

K

O L

(A) (B) (C) (D)

25. When a sphere rolls without slipping the ratio of its kinetic energy of translation to its total kinetic

energy is

_______________________________________________________________________________________ 4

____________ 26. A uniform rod of length is free to rotate in a vertical plane about a

fixed horizontal axis through O. The rod is allowed to rotate from rest from its unstable vertical position. Then, the angular velocity of the rod when it has turned through an angle is____________

27. A disc of radius R and mass M is rolling horizontally without slipping with speed v. It then moves up an incline as shown in the figure. The maximum height up to which it can reach is____________

28. A solid sphere and a disc of same radii are falling along an inclined plane without slip. One reaches earlier than the other due to____________

29. A homogeneous ball is placed on a plane making an angle q with the horizontal. At what values of the coefficient of friction m will the ball roll down the plane without slipping? ____________

30. A sphere of outer radius R having some cavity inside is allowed to roll down on an incline without slipping and it reaches a speed v0 at the bottom of the incline. The incline is then made smooth by

waxing and the sphere is allowed to slide without rolling and now the speed attained is 05 v4

. What

is the radius of gyration of the sphere about an axis passing through its centre? ____________ 31. A cord is wound round the circumference of wheel of radius r. the axis of the wheel is horizontal and

fixed and moment of inertia about it is I. A weight mg is attached to the end of the cord and falls from rest. After falling through a distance h, the angular velocity of the wheel will be____________

CHEMISTRY CHEMICAL AND IONIC EQUILIBRIUM

1. One mole of N2 is mixed with 3 mol of H2 in a 4L container. If 1/2 mol of N2 is converted to NH3 by the following reaction at equilibrium. The value of Kc is

N2 (g) + 3 H2 (g) 2NH3 (g) 1) 2.37 2) 23.7 3) 948 4) 0.948 2. The Kc for the reaction, A2 (g) + B2 (g) 2 AB (g) at 1000C is 49. If one litre flask

containing one mole of A2 is connected to a two litre flask containing one mol of B2, how many moles of AB will be formed at 373 K.

1) 7 2) 97 3)

117 4)

23

3. At a certain temperature, Kc is 16 for the following reaction SO2 (g) + NO2 SO3 (g) + NO(g). If we take 1 mol of each of all the four gases in a

one litre flask. What would be the equilibrium concentration of NO and NO2 1) [NO] = 1.6 [NO2] = 0.4 2) [NO] = 0.8 [NO2] = 0.4 3) [NO] = 0.4 [NO2] = 1.6 4) [NO] = 0.2 [NO2] = 0.8 4. The equilibrium constant for the reaction H2 (g) + I2 (g) 2 HI (g) is 64 at a certain

temperature. The equilibrium concentrations of H2 and HI are 2 and 6 mol L-1 respectively. What is the equilibrium concentration of I2 ( in mol L-1)

1) 0.4 2) 0.28 3) 0.8 4) 2.8

_______________________________________________________________________________________ 5

5. The equilibrium constant for the reaction H2O (g) + CO (g) H2 (g) + CO2 (g) is 81. If the velocity constant of the forward reaction is 164 L mol-1s-1. What is the velocity constant for the backward reaction ( in L mol-1s-1)

1) 13122 2) 2 3) 261 4) 243 6. One mole of A(g) is heated to 2000C in a one litre closed flask till the following equilibrium is

reached A (g) B (g). The rate of forward reaction at equilibrium is 0.02 mol L-1 min-1. What is the rate of the backward reaction at equilibrium ( in mol L-1. min-1)

1) 0.04 2) 0.01 3) 0.02 4) 1 7. Consider N2 (g) + 3 H2 (g) 2 NH3 (g). Initially, 1 mol of N2 and 3 mol of H2 are taken is a

2L flask. At equilibrium state if the number of moles of N2 is 0.6, What is the total number of moles of all gases present in the flask.

1) 0.8 2) 1.6 3) 3.2 4) 6.4 8. 4 mol of HI is taken in a 1L closed vessel and heated till equilibrium is reached. At

equilibrium the concentration of H2 is 1 mol L-1. What is the equilibrium constant for 2HI (g) H2 (g) + F2 (g) 1) 4 2) 0.5 3) 2 4) 0.25 9. 9.2 gm of N2O4 (g) is taken in a closed one litre vessel and heated till the following

equilibrium is reached N2O4 (g) 2 NO2 (g). At equilibrium 50% of N2O4 is dissociated. What is the equilibrium constant (in mol L-1)

1) 0.1 2) 0.2 3) 0.4 4) 2 10. In the reaction PCl5 (g) PCl3 (g) + Cl2 (g), the equilibrium concentrations of PCl5 and PCl3

are 0.4 and 0.2 mol L-1 respectively. If the value of Kc is 0.5, what is the concentration of Cl2 in mol L-1.

1) 2 2) 1.5 3) 1 4) 0.5 11. One mole of A(g) is heated to 3000C in a closed one litre vessel till the following equilibrium

is reached A(g) B(g). The equilibrium constant of this reaction at 3000C is 4. What is the concentration of B ( in mol L-1) at equilibrium.

1) 0.2 2) 0.6 3) 0.8 4) 0.1 12. In which of the following reactions, the concentration of reactant is equal to concentration of

product at equilibrium 1) A B K = 0.01 2) R P K = 1 3) X Y K = 10 4) L J K = 0.025 LeChatlier's principle: 13. Which of the following should be done in order to increase the ionisation of acetic acid CH3COOH (l) H+ (aq) + CH3COO- (aq) I) Increase the concentration of CH3COOH II) Remove H+ ions as soon as it is formed III) Increase the concentration of CH3COO- IV) Add little HCl solution. 1) I, III 2) I, III, IV 3) II, III 4) only II 14. Which of the following should be done in order to increase the evolution of CO2 in the

following reaction. CaCO3 (s) CaO (s) + CO2 (g) I) Increase the amount of CaCO3 II) Remove CaO as soon as it is formed III) Remove CO2 as soon as it is evolved IV) Increase the amount of CaO 1) I, II, III 2) II, I 3) III 4) III, IV