cycle 2 quize 3.pdf

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LOCUS 1

LOCUS:65-A, Ompro Tower, Kalu Sarai, New Delhi-110016, Ph.: 011-46080145-6, Websit:www.locuseducation.org

CYCLE-2, QUIZ-3, CHEMISTRY

1. Which of the following molecules has a Trigonal-Pyramidal shape:

(a) 3 PCl (b) 3SO

(c) 23CO − (d) 4 XeF

2. Which of the following is paramagnetic

(a) CN − (b)2O−

(c) CO (d)2 NO+

3. The electronic configuration of and element is 2 2 6 2 6 5 11 2 2 3 3 3 4 . s s p s p d s This represents its

(a) Excited State (b) Cationic Form

(c) Anionic Form (d) Ground State.

4. The net Enthalpy change of a reaction is defined as the amount of energy required to break all the

bonds on the reactant molecules minus the amount of energy required to break all the bonds in the

product molecules

ASSERTION (A): For the reaction3 2( ) ( ) ( )CaCO s CaO s CO g

∆ → + the enthalpy change for the

reaction can’t be ascertained using this definition.

REASON (R) : The definition of Enthalpy given above is only an approximate relationship and

is valid when all substances (R EACTANTS AND PRODUCTS) in the reaction are in

gaseous state.

(a) Both A & R are true & R is the correct explanation of A

(b) Both A & R are true but R is not the correct explanation of A

(c) A is true but R is false

(d) R is true but A is false5. The general expression for the half life, 1 2 ,t for an nth order reaction is:

(a)

1

( 1)

( 1)(2 1)n

nin

n

C

−

−− −

(b)

1( 1)(2 1)n

nin

n

C

−− −

(c)1( 1)(2 1)n

nin

n

KC

−− − (d)1

( 1)

( 1)(2 1)n

nin

n

KC

−

−− −

.

6. At constant volume for a fixed number of moles of a gas, the pressure of the gas increases with rise of the

temperature due to:

(a) Increase in molecular attraction

(b) Increase in rate of collisions amongst molecules(c) Increase in average molecular speed

(d) Decrease in mean free path.

7. The state of hybridisation, number of bond-pairs and number of lone pairs for a Xenon Fluoride

compound having square planar structure are:

(a) 2 2 ,5,1 sp d (b) 3 2 ,4,2 sp d

(c) 2 3,4,2 sp d (d) 3 2 ,5,1 sp d .

8. The average bond enthalpy of methane is 416 kJ/mol, what does this signify with respect to the

C – H bonds in methane

(a) All the C – H bonds in methane have a bond enthalpy of 416 kJ/mol(b) Majority of C – H bonds in methane have a bond enthalpy of 416 kJ/mol

(c) The bond enthalpies of C – H bonds in methane lie in the neighbourhood of 416 kJ/mol

(400-430) kJ/mol.

(d) The bond enthalpies of C – H bonds in methane vary significantly from each other but their

average is 416 kJ/mol.



LOCUS 2


9. What is the standard enthalpy of formation of 2 ( ) H O l given

2 2 22 ( ) ( ) 2 ( ) H g O g H O l + → ; 0 1571 6 kJmol f H −∆ = − ⋅

(a) 1571 6 kJ mol−⋅ (b) 1571 6 kJ mol−− ⋅

(c)1

285 8 kJ mol−

− ⋅ (d) can’t be assertained from the given data.

10. Which of these correctly represents the reaction: 1 2k k A B C → →

(a)

T max

B max

conc.

Time

(b)

T max

B max

conc.

Time

C

B

(c)

T max

B max

conc.

Time

(d)

T max

B max

conc.

Time

B

C

.

11. Statement A : For a process to be elementary, order must be equal to molecularity.

Statement B: Molecularity is always an integer greater than zero.

Choose the correct option:

(a) both A & B are correct (b) only A is correct

(c) only B is correct (d) both are false.

12. The correct order of increasing C – O bond length in CO, 23CO − & 2CO is

(a) 23 2CO CO CO−< < (b) 2

2 3CO CO CO −< <

(c) 23 2CO CO CO− < < (d) 2

3 2CO CO CO− < < .

13. Which of the following do not conduct electricity in the fused state

(a) 2 MgCl (b) 2SnCl (c) 2 BaCl (d) 2 BeCl .

14. Assertion(A): The experimental value of enthalpy change for a reaction is obtained using a Bomb

Calorimeter

Reason (R) : Bomb Calorimeter is a vessel of constant volume allowing no mass transfer between

system & surroundings

(a) Both A & R are correct & R is the correct explanation of A

(b) Both A & R are correct but R is not the correct explanation of A

(c) A is correct but R is wrong

(d) R is correct but A is wrong.



LOCUS 3


15. Arrange the following in decreasing order of bond strengths:

1. Nuclear Forces over long range 2. Van Der Waals Forces

3. Covalent Bond 4. Ionic Bond.

(a) 4 5 3 2 1> > > > (b) 1 4 5 3 2> > > >

(c) 1 5 4 3 2> > > > (d) 4 5 3 1 2> > > > .

16. In Thermodynamics, a process is called reversible when:

(a) Surroundings & system change into each other

(b) There is no boundary between system & surroundings

(c) The surroundings are always in equilibrium with the system

(d) The system changes into the surroundings spontaneously

17. For first order reaction:

(a) The degree of dissociation is equal to (1 ) Kt e−−

(b) A plot of reciprocal concentration of the reactant vs time gives a straight line

(c) The time taken for the completion of 75% reaction is thrice the 1 2t of the reaction(d) The pre-exponential factor in the Arrhenius equation has the dimension of time 1.T −

18. The correct hybridisation states of nitrogen in 2 3, NO NO+ − &

4 NH + is

(a) 3 2 3, , sp sp sp (b) 2 3, , sp sp sp

(c) 3 3, , sp sp sp (d) 3 2, , sp sp sp .

19. The correct arrangement of these compounds in increasing order of ionic character is

2 3 2, , , NaCl CaCl AlCl SnCl

(a) 3 2 2 AlCl SnCl CaCl NaCl < < < (b) 2 2 3 NaCl CaCl SnCl AlCl < < <

(c) 3 2 2 AlCl CaCl SnCl NaCl < < < (d) 2 2 3 NaCl SnCl CaCl AlCl < < < .

20. Choose the correct option : p nn n n∆ = ∑ − ∑

(a) ( ) nc p K K RT ∆= (b) ( ) n

p x T K K P ∆=

(c)

n

c x

RT K K

PT

−∆ =

(d)

n

x c

n K K

V

−∆∑ =

.

21. According to the Kinetic Molecular Model of a gas the pressure of a gas is given by 21

3

NA p mU

V

− =

where A N is the avagdro constant ;

V is the volume of container ;

M is the mass of a gas molecule &

U is the mean square speed of a gas molecule.

Using this model predict what will be Average Translational Kinetic Energy of gas molecule

(a)3

2 KT (b)

3

2 RT

(c)1

2 KT (d) None of these.



LOCUS 4


22. Which of the following graphs represent an exothermic reaction?

(a)t

lnKp

1

T

(b)t

lnKp

1

T

(c)t

lnKp

1

T

(d)t

lnKp

1

T

.

23. Consider the reaction :2 2 22 ( ) ( ) 2 ( .) H g O g H O liq+ →

Assertion (A): You can store the two gaseous reactants in the same container indefinitely without

any observable change occurring.

Reasons (R): The reaction is highly favaured thermodynamically but inhibited kinetically

(a) Both A & R are correct & R is the correct explanation of A

(b) Both A & R are correct but R is not the correct explanation of A

(c) A is correct but R is wrong

(d) R is correct but A is wrong.

24. The correct explanation for ice being less dense than water is :

(a) In water there is H-bonding in ice there is none

(b) The H-bonding in water is stronger than that in ice

(c) Due to H-bonding ice assumes a cage like structure

(d) None of these.

25. Arrange the given molecules in order of increasing strength dipole moment

2 3 3, , H O NH NF &2CO

(a) 2 3 2 3CO NF H O NH < < < (b) 2 3 3 2CO NF NH H O< < <

(c) 2 2 3 3 H O CO NF NH < < < (d0 3 2 2 3 NF H O CO NH < < < .

26. Calculate the order of reaction A + B → Product, with respect to A & B from the following data:

5[ ] [ ] Rate 10

mole/L mole/L (mole/L/s)

(i) 0.01 0.010 5

(ii) 0.01 0.015 5

(iii) 0.02 0.010 14.1

A B −×

(a) 1, 2 (b) 1.5, 2(c) 2, 0 (d) 1.5, 0.

27. For a soluble salt , p q A B the relationship of its solubility product ( Ls) with its solubility (s) is :

(a) . p q q p s L s p q

+= (b) p q p q s L s p q

+=

(c) pq p q s L s p q= (d) ( )( ) pq p q

s L s pq += .

28. Arrange these metal oxides in increasing order of their acid character:

2 3 2 4 10, , & Al O MgO SiO P O

(a) 2 3 2 4 10 MgO Al O SiO P O< < < (b) 2 2 3 4 10 MgO SiO Al O P O< < <(c) 4 10 2 3 2 P O Al O SiO MgO< < < (d) 4 10 2 2 3 P O SiO Al O MgO< < < .



LOCUS 5


29. The pH of an aqueous solution of ammonia is 11.5. Find the molarity of the solution5

4( ) 1.8 10b K NH OH −= ×(a) 5.7 M (b) 11.4 M

(c) 1.54 M (d) 0.57 M.

30. The pH of

8

37 10 M CH COOH

−

× is

14

( 1 10 ) Kw

−

= ×(a) 3.2 (b) 6.85

(c) 4.2 (d) 7.9.



LOCUS 6


CYCLE-2, QUIZ-3, MATHEMATICS

1. The maximum value of 2 2,

(1 )(1 )

n m

n n

x y

x y+ + where x, y are positive real numbers and m, n are positive

integers is

(a)1

6(b)

1

4

(c)1

2(d) None of these.

2. 2(666......... to 10 digits) (888......... to 10 digits)=λ + then value of ‘λ ’ is

(a) 444............ to 20 digits (b) 666............ to 20 digits

(c) 444............ to 30 digits (d) 666............ to 30 digits

3. If the determinant

2 2

2 2

2 2

aba x ca

ab b x bc

ca bc c x

++

+

is

divisible by ,r x then the value of r is

(a) 1 (b) 3

(c) 4 (d) 6.

4. If A, B, C are angles of triangle ABC then

2

2

2

i A iC iB

iC i B iA

iB iA i C

e e e

e e e

e e e

− −

− − −

− − is

(a) purely imaginary (b) purely real

(c) a complex number (d) equal to zero.

5. Sum of the series3 5 7 92 1

......3 5 7 9

x x x x x1 2

− + + − + + ∞ is

(a)

3

2

(1 )(1 )ln

(1 )

x x

x x

+ +

− + (b)

3

3

(1 )(1 )ln

(1 )(1 )

x x

x x

+ −

+ −

(c)1 22

2

1ln

1

x x

x x

+ + − +

(d)2

2

1 1ln

2 1

x x

x x

− + + +

.

6. A man wants to throw a ball out of the window shown in the

figure. It has square openings of side ‘a’ units. It is given that

when ball is thrown by man it completely remains within the

frame of the window only and ball is a sphere of radius ‘r ’. the

probability of ball going out of window is

(a)

2

2

( 2 )

(4 )

a r

a r

−− (b)

2

2

16( 2 )

(2 )

a r

a r

−−

a

a

(16 squares)

4a

(c)

2

2

4( 2 )a r

aπ

−(d)

2

2

4( 2 )

(2 )

a r

a r

−−

.



LOCUS 7


7. One die has 3 faces marked 1, 2 faces marked 2, 1 face marked 3. Another die has 1 face marked 1, 2

faces marked 2 and 3 faces marked 3. The probability of the most probable number that turns up when

both dice are thrown together is

(a)7

18(b)

2

9

(c)1

12(d)

7

9.

8. Area of the triangle formed by the straight lines 2 2 2 2 2 2( 3 ) 8 ( 3 ) 0 A B x ABxy B A y− + + − = and

0 Ax By C + + = is

(a)3 ABC

AB BC CA+ +(b) ( )

2

2 2 23

C

A B C + +

(c)

2

2 2

3

3( )

C

A B+ (d) 2 2

3

( )

ABC

A B+ .

9. A point (h, 0) divides a chord of the circle2 2 2 x y r + = in ratio λ : 1. If the chord makes an angle α

with x-axis. Then value of ‘α ’ is.

(a)2 2

1 ( )cos

h r

h

λ − −

(b)2 2

1 1cos

2

h r

h

λ

λ

− + −

(c)

2 21 1

cos2

h r

h

λ

λ

− + −

(d) None of these.

10. Common chord of a fixed circle and a variable circle through two fixed points

(a) always remains same

(b) always passes through a frixed point

(c) keeps on varying but does not pass through a fixed point

(d) Nothing can be said.

11. Sum of3 2 1

2 4 2

1 2 2.......

1 1 1 1

nn

n

x x x

x x x x

−

+ + + ++ + + +

for very large values of n will be approximately equal

to (where x > 1)

(a)1

1 x−

(b)1 2

1 1 x x

+

− +

(c)11 2

1

n

x x

+

+−

(d)1 2

1 1

n

x x+

− +.

12. A is a fixed point on x-axis whose coordinates are (a, 0). AB is the diameter of the circle whose

centre is at origin. ( cos , sin ) P a aα α and ( cos , sin )Q a aβ β are two points on circle such that

2 ( 0).k k α β − = > Then the locus of point of intersection of AP and BQ is

(a) 2 2 22 tan x y ay k a− − = (b) 2 2 22 cot x y ay k a− − =

(c) 2 2 22 tan x y ay k a+ + = (d) 2 2 22 cot x y ay k a+ + = .



LOCUS 8


13. u ax by c≡ + + and .v a x b y c′ ′ ′≡ + + Then the equation of diagonal of a parallelogram whose sides are

, ,u p u q v r = = = and v s= is

(a)

1

1 0

1

u r

v s

p q

= (b)

1

1 0

1

u v

s p

r q

=

(c)

1

1 0

1

u v

r s

q p

= (d)

1

1 0

1

u v

p r

q s

= .

14. Given a matrix

a b c

A b c a

c a b

=

, where a, b, c are positive real numbers such that abc = 1 and AT A = I

Then value of3 3 3

a b c+ + is(a) 2 (b) 4

(c) 6 (d) both a and b.

15.

cos sin 0

( ) sin cos 0

0 0 1

x x

f x x x

− =

. Then value of ( ) ( ) f f θ φ ⋅ is

(a) 0 (b) 1

(c) Independent of θ (d) Independent of φ .

16. If 2 2 23a b ab+ = , then Arithmetic Mean of log a and log b is

(a) log( )a b+ (b)( )

log2

a b+

(c) log5

a b+

(d) log10

a b+

.

17. Whenever a player gets 1 on throwing a fair die, he gets one more chance to throw die.The probabil-

ity of obtaining a total score of exactly ( 6)r r > is

(a) 1

1 1

15 6r −

− (b) 6 1

1 1 1

5 6 6r r − −

(c) 1

1 1 1

5 6 6r r −

(d) None of these.

18. If the system of equations

5 ( )

2 3 9 ( )

3 ( )

x y z i

x y z ii

x y z iiiλ µ

+ + = →+ + = →+ + = →

has infinite solutions then

(a) 13, 5λ µ ≠ ≠ (b) 5, 13λ µ = =(c) 13, 5λ µ = = (d) 5, 13λ µ = ≠ .



LOCUS 9


19. Two of the lines given by the equation 4 3 2 2 3 4 0ay by x cy x dyx ax+ + + + = bisect the angle between

other two then the necessary and sufficient condition is

(a) 0a b c d + + + = (b) 2 2( ) ( 6 ) 0b d c a+ − + =

(c)

2 2

( ) ( 6 ) 0b d c a+ + + = (d) ( )( 6 ) 0b d c a+ + = .

20. ABC is an equelateral triangle L, M and N are foot of perpendiculars from a point P to the sides AB,

BC , CA respectively. P lies within the triangle and satisfies the condition PL PN

PM PL= . Then the locus

of P is

(a) a straight line not passing through origin

(b) a straight line passing through origin

(c) a circle with centre at origin

(d) a circle passing through origin.

21. The decimal parts of two numbers taken at random are found to be upto six places of decimal. The probability that the second number can be subtracted from first only when borrowing has to be done

at some place is

(a)

611

20

(b)

611

25

(c)

611

125

−

(d)

611

120

−

.

22. ‘ p’ is chosen at random from the closed interval [0, 5]. The probability of existence of three positive

numbers a, b and c in G.P. such that if the sum of their squares 2 2 2( )a b c+ + is 2S , then their sum

(a + b + c) is pS is

(a)1

5(b)

2

5

(c)3

5(d)

4

5.

23. Two numbers are selected randomly from the interval [0, 4]. The probability that the square of

exactly any one of the two numbers is greater than the other number is

(a) 13

(b) 58

(c)9

13(d)

4

13.

24.11 5 3 63

( )11 5 3 165

n n n nn N + + + ∈ is

(a) always a positive integer V n ∈ N (b) can be a fraction for some n ∈ N

(c) always an odd number V n ∈ N (d) none of these.



LOCUS 10


25. ( )

2

222

2 12 2

0

1( 1)

! (1 )

xn

xn

n

xn n x e

n x

− ∞

+ +=

∑ + − ⋅ ⋅+

is

(a) 2

1

1 x+

(b) 2

2

1

x

x+

(c)

2

21

x

x+(d)

2 xe .

26. If x and y are positive rational numbers such that1 1

1, x y

+ = then minimum value of3 5 x y

x y+ is

(a) 15 (b) 15

(c) 75 (d) 225.

27. If 2 3 1( ) 2 3 ..... ( 1)n n f x x x x nx−= − + + + − Then the value of (1 2) f ′ is

(a)

22 21

3 1

2 1 4 2( 1)

23 9 2

nn

n

n n−

−−

− + − + − ⋅ ⋅

(b)

2 2

3 1

2 1 3 4 21 ( 1)

23 9 2

nn

n

n n−

− + − − + − ⋅ ⋅

(c)

21

1

2 1 4 21 ( 1)

3 2 9 2

nn

n

n n−−

+ − − + − ⋅ ⋅

(d)

2 21

1

4 1 3 4 21 ( 1)

27 2 9 2

nn

n

n n−

−−

+ − − − + − ⋅ ⋅

.

28. If 1 0i i i L a x b y≡ + − = represent three sides of a triangle for i =1,2,3 whose orthocentre is at origin

then which of the following is true.

(a) 1 2 1 2 1a a b b= = (b)1 2 1 2

2 3 2 3

1a a b b

a a b b

+ =+

(c)1 2 2 1

2 3 3 2

1a b b a

a b b a

+=

+ (d) None of these.

29. A circle 2 2 4 4 4 0 x y x y+ − − + = is inscribed in a triangle whose two sides are 0 x = and 0 y = .

The locus of circumcentre of the triangle is 2 2 0. x y xy x yλ + − + + = Then value of λ is

(a) –1 (b) 1

(c) 4 (d) –4.

30. 2 2

1 26

1 4 AX I ×

− =

. Then matrix A is

(a)2 4

1 1

−

(b)1 1

4 2

−

(c)4 2

1 1

−

(d) None of these.



LOCUS 11


CYCLE-2, QUIZ-3, PHYSICS

1. A ray of light travels from a medium of refractive index µ to air. Its angle of incidence in the

medium θ , measured from the normal to the boundary and its angle of deviation is δ . Which of the

following best represent the plot of δ .

(a)

!2

!1

!

O " # /2

$

(b)

!2

!1

!

O " # /2

$

(c)

!2

!1

!

" # /2

$

(d)

!2

!1

!

" # /2

2. Two moles of an ideal monatomic gas, initially at pressure p1 and volume v

1, undergo an adiabatic

compression until its volume becomes v2. Then the gas is given heat Q at constant volume v

2. What

will be the final temperature of the gas?

(a)1 1 2

2 3

P v v Q

R R

+

(b)

5/ 3 2 /3

1 1 2

3

P v v Q

R

− +

(c)1 1

2 3

P v Q

R R

+ (d)

7 / 2 5/3

1 1 2 2

2 3

P v v Q

R R

− +

3. A wave pulse starts propagating in + x-direction along a non-uniform wire of length 10m with mass

per unit length given by 0m m x= + α and under a tession of 100N. Find the time taken by the pulse

to travel from lighter end to heavier end. 2 3 3

0( 10 / , 10 / )m kg m kg m− −= α = 9×(a) 3.52 sec (b) 2.33 sec

(c) 5.91 sec (d) 1.5 sec

4. Two parallel beams of light P and Q are incident normally ona prism and the transmitted rays are brought to focus with the

help of a convergent lens as shown in fig. If the intensities of

the upper and lower beams immediately after transmission from

face AC are 4I and I respectively. Find the resultant intensity

at the focus:

(a) 5 I (b) 3 I

L

A

B C

P

Q

(c) 10 I (d) 9 I

5. A convex lens of focal length f is placed somewhere between an object and a screen. The distance between

the object and the screen is x. If the magnification is m, the focal length of the lens is given by

(a) 2( 1)

mx

m + (b)

2( 1)m x

m

−

(c) 2( 1)

mx

m − (d)

2( 1)m x

m

+



LOCUS 12


6. A point source of light B, placed at a distance L in front of the

centre of a plane mirror of weidth d , hangs vertically on a

wall. A man walks in front of the mirror along a line parallel to

the mirror at a distance 2 L from it as shown. The greatest

distance over which he can see the image of the light source in

the mirror is:(a) / 2d (b) d 2L

L

d B

(c) 2d (d) 3 d

7. Two coherent point sources S 1 and S

2 vibrating in phase emit light of wavelength λ . The Separation

between the sources is 2λ . The smallest distance from S 2 on a line passing through S

2 and

perpendicular to S 1 S

2, where a minimum of intensity occurs is:

(a)7

12

λ(b)

15

4

λ

(c)2λ (d) 3

4λ

8. What should be the minimum value of i1 so that finally ray comes out along AC . µ is refractive

index of material of prism. Angle of prism is

(a)1sin 1− 2 µ −

(b) [ ]1sin sin cos A A

− µ −

A

B C

i 1

(c)1 2sin 1sin cos A A− µ − −

(d) 45°

9. Three moles of an ideal gas at 300K are isothermally expanded to five times its volume and heated

at this constant volume so that the pressure is raised to its initial value before expansion. In the

whole process 83.14 kJ heat is required.

The value of ( )/ P V C C will be:

8.31 / mol R J =log 5 1.61e =

(a) 1.42 (b) 1.33

(c) 1.0 (d) 1.75

10. A body cools in 7 minutes from 60°C to 40°C. What will be its temperature after next 7 minutes?

The temperature. of surrocuding is 10°C

(a) 20 °C (b) 25 °C

(c) 28 °C (d) 10 °C

11. A sphere of diameter 7 cm and mass 266.5 g floats in a bath of liquid. As the temperature is raised, the

sphere begins to sink at a temperature of 35 °C. If the density of the liquid is 1.527 g/cc at 0 °C. Find the

Coefficient of cubical expression of liquid. Neglect the expression of sphere.

(a) 28.5 10−× (b) 37.5 10−×(c) 4

7.5 10

−

×(d) 4

8.5 10

−

×



LOCUS 13


12. Suppose we create an artificial atmosphere of gas for the verification of second law of thermodynamics

suppose the mass of gas taken is m. It is slowly heated from T 1 to T

2. What will be the change in

entropy of the atmosphere, if its heat capacity is C?

(a)1 2

2 2

1 2

T T mc

T T

+ (b)

2

1

lnT

mc

T

(c)2 1

1

T T mc

T

−

(d) zero as the process is reversible

13. Two bodies of A and B have thermal emissivities of 0.01 and 0.81 respectively. The outer surface

areas of the two bodies are same. They emit total rodiant power at the same rate. The wavelength Bλ

corresponding to maximum spectral radiancy in the radiation from B is shifted from the wavelength

corresponding to maximum spectral radiancy in the radiation -from A by 1.00 pm. If the temperature

of A is 5202 K, wavelength Bλ will be

(a) 2 mµ (b) 1.5 mµ(c) 7400 A° (d) 2000 A°

14. Suppose we have two covalent molecules, which individually can be

treated as dipole. The molecules are oriented perpendicular to each

other.

The force on 2 due to 1 will be

(a)1 2

4

0

1

4

P P

r π∈ (b)1 2

4

0

1 3

4

P P

r π∈

P 2

2

1

P 1

r

(c) 1 24

0

14 4

P P r π∈ (d) 1 2

4

0

1 24

P P r π∈

15. A 10 F µ capacitor is charged through a resistance of 0.1 M Ω from a battery of 1.5V. The time

required for the capacitor to get char.ged upto 0.75V for the situations shown will be respectively

(a) 0.693 & 0.693

(b) 0 & 0

(c) 0 & 0.693R E C E C

( )a ( )b

R

(d) 2 Cu 2 & Cu 2

16. The first overtone of an open organ pipe beats with the first overtone of a closed organ pipe with a beat frequency of 2.2 Hz. The fundamental frequency of the closed organ pipe is 110 Hz. The lengths

of pipe will be 1 0( closed; open) L L= =(a) 1 00.75 & 0.75 L m L m= = (b) 1 01 & 2.13 L m L m= =(c) 00.75 & 0.99C L m L m= = (d) 01 & 1.5C L m L m= =

17. The specific heat of many solids at low temperatures varies with absolute temperature T according to the

relation 3 , s aT = where a is a constant. Find the heat energy required to raise the temperature of a mass m

of such a solid from 0 to 20K.

(a) 44 10 ma× (b) 43 10 ma×(c) 42 10 ma× (d) 41 10 ma× .



LOCUS 14


18. The first allowed excited state of hydrogen atom is 10.2 eV above its lowest energy (ground) state. To what

temperature should hydrogen gas be raised so that inelastic collisions may excite an appreciable number of

atoms to their first excited state?

(a) 68.0 10 K × (b)47.88 10 K ×

(c) 46.44 10 K × (d) 58.80 10 K × .

19. The PV diagram shown in figure for a thermodynamic process

is a semicircle. Find the work done on the gas in the process

ABC .

(a) /2 atm-lt.π

(b) /2 atm-lt.−π

(c) /4 atm-lt.π

3

A

B

C

1 2

P(atm)

V(litre)

1

(d) None of these.

20. The two ends of a uniformly tapered rod are maintained at

temperatures 100°C and 0°C respectively. Under steady state,

the temperature of the section AA exactly at the mid point

(a) is more than 50°C

(b) is 50°C 0°C

100°CA

A

(c) is less than 50°C

(d) none of these.

21. For the electric field

( ) !1/ 3 E kx x="# Z

Y

X l l

l

l

where k is a constant, compute the electric flux throughthe face of the cubic region depicted in figure.

(a) 5/ 2 ( 2 1)kl −(b) 3/ 2 ( 2 1)kl +(c) 3/ 2 ( 2 1)kl −(d) 5/ 2 ( 2 1)kl +

22. For the electric field

( ) !1/ 3 E kx x="#

where k is a constant, compute the charge confined

Z

Y

X l l

l

l

inside the cube?

(a) 5/ 20 ( 2 1)kl ∈ −

(b) 3/20 ( 2 1)kl ∈ −

(c) 3/20 ( 2 1)kl ∈ +

(d) 5/ 20 ( 2 1)kl ∈ + .



LOCUS 15


23. The region between two concentric spheres of radii a b< contains

volume charge density ( ) ,C

r r

ρ = where C is constant and r is the

radial distance, as shown in figure. A point charge q is placed at the

origin, r = 0.

Find the value ofC for which the electric field in the region betweenthe spheres is constant.

(a) 2

4q

a(b) 2

3q

a

%( )t r a q

b

(c) 2

2q

a(d) 2

q

a.

24. A solid insulating ball of radius a is surrounded by a conducting

spherical shell with an inner radius of b and an outer radius of

c (see figure). The inner ball has a charge Q, which is uniformlydistributed throughout its volume. The conducting spherical

shell is charged with charge – Q.

Compute the electric potential at P .

+Q a

b

c

–Q

r 1

(a)1 1

Qr b

+

(b)2 1

Qr b

−

(c)2 1

Qr b

+

(d)1 1

Qr b

−

.

25. A solid insulating ball of radius a is surrounded by a

conducting spherical shell with an inner radius of b

and an outer radius of c (see figure). The inner ball has

a charge Q, which is uniformly distributed throughout

its volume. The conducting spherical shell is charged

with charge – Q.

Compute the electric potential at R.

+Q a

b

c

–Q

R r 2

(a)1 1

Q

r b

−

(b)2 1

Q

r b

−

(c)1 1

Qr b

+

(d) zero.



LOCUS 16


26. A thin conducting plate is inserted in halfway between the plates of a parallel plates capacitor (see figure).

d /2

d /2

A (area of each plate)

Compute the capacitance before the plate was inserted.

(a)0 A

d

∈(b)

0

A

d ∈

(c)02 A

d

∈(d)

03 A

d

∈.

27. A thin conducting plate is inserted in halfway between the plates of a parallel plates capacitor (seefigure).

d /2

d /2


What is the capacitance after the plate was inserted?

(a) 0 Ad ∈ (b)

0

A

d ∈

(c)02 A

d

∈(d)

03 A

d

∈.

28. A thin conducting plate is inserted in halfway between the plates of a parallel plates capacitor (see

figure).

d /2

d /2


What does the value of capacitance become when the thin plate and the upper plate are shortened

(i.e. connected by a conducting wire)?

(a)0 A

d

∈(b)

0

A

d ∈

(c)02 A

d

∈(d)

03 A

d

∈.



LOCUS 17


29. A capacitor is composed of two very long conducting

cylinders of radii a and b, where a < b. A constant

voltage difference V is kept fixed across the capacitor

(see figure).

Compute the capacitance per unit length of the system.

a b

V +&1=+Q

– &1= – Q

(a) 0.5 µF(b) 1.5 µF

(c) 2 µF

(d) 2.5 µF.

30. A capacitor is composed of two very long conducting

cylinders of radii a and b, where a < b. A constant

voltage difference V is kept fixed across the capacitor

(see figure).

a

b

V +&1=+Q

– &1= – Q

One adds a third concentric long conducting cylinder

of radius c, where c > b. V is then turned off and its

positive terminal is reconnected to the new cylinder c.

What is the capacitance per unit length between the

cylinders of radii a and c?

(a)2 2

1 2

1( )

4C V V − (b)

2 21 2

1( )

4C V V +

(c)2

1 2

1( )

4C V V − (d)

21 2

1( )

4C V V + .



LOCUS 18

PHYSICS1 (a) 11 (d) 21 (a)

2 (b) 12 (b) 22 (a)

3 (b) 13 (b) 23 (d)

4 (d) 14 (b) 24 (d)

5 (a) 15 (c) 25 (d)

6 (d) 16 (c) 26 (a)

7 (a) 17 (a) 27 (a)

8 (c) 18 (b) 28 (c)

9 (a) 19 (b) 29 (c)

10 (c) 20 (a) 30 (c)

ANSWERS

MATHEMATICS

DATE (8TH JANUARY,

2008)

1 (b) 11 (c) 21 (d)

2 (a) 12 (c) 22 (b)

3 (c) 13 (d) 23 (b)

4 (b) 14 (b) 24 (a)

5 (c) 15 (b) 25 (c)

6 (d) 16 (c) 26 (a)

7 (a) 17 (b) 27 (d)

8 (c) 18 (b) 28 (b)

9 (c) 19 (c) 29 (b)10 (b) 20 (d) 30 (c)

CHEMISTRY

1 (a) 11 (a) 21 (a)2 (b) 12 (b) 22 (a)

3 (d) 13 (d) 23 (a)

4 (a) 14 (d) 24 (c)

5 (d) 15 (a) 25 (b)

6 (c) 16 (c) 26 ( )

7 (b) 17 (a, d) 27 (b)

8 (d) 18 (b) 28 (a)

9 (c) 19 (c) 29 (d)

10 (b) 20 (b,c,d) 30 (b)

cycle 2 quize 3.pdf

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