MATHEMATICS

1. The real numbers x satisfying x15x

> 1are precisely those which satisfy

(A) x < 1 (B) 0 < x < 1 (C) � 5 < x < 1 (D) �1 < x < 1

2. Let tn denote the number of integral sided triangle with distinct sides chosen from {1, 2, 3 ���n). Then

t20

� t10

equals(A) 81 (B) 153 (C) 163 (D) 173

3. The number of pairs of reals (x, y) such that x = x2 + y2 and y = 2xy is(A) 4 (B) 3 (C) 2 (D) 1

4. How many positive real number x satisfy the equationx3 � 3 |x| + 2 = 0 ?(A) 1 (B) 3 (D) 4 (D) 6

5. Let (1 + 2x)20 = a0 + a

1x + a

2x2 + .... + a

20x20 . Then, 3a

0 + 2a

1 + 3a

2 + 2a

3 + 3a

4 + 2a

5 + .... 2a

19 + 3a

20.

equals to :

(A) 2

3�3.5 20

(B) 2

33.5 20

(C) 2

13.5 20

(D) 2

1�3.5 20

6. let P1, P

2, P

3, P

4, P

5 be five equally spaced points on the circumfercence of a circle of radius 1, centred

at O. Let R be the set of point in the plane of the circle that are closer to O than any of P1, P

2, P

3, P

4, P

5

Then R is a -(A) circular region (B) rectangular region(C) pentagonal region (D) oval region that is not circular

7. A company situated at (2,0) in the xy-plane charges Rs. 2 per km for delivery. A second company at (0,3)chargs Rs. 3 per km for delivery. The region of the plane where it is cheaper to use the first company is -(A) the inside of the circle (x + 5.4)2 + y2 = 18.72(B) the outside of the circle (x + 1.6)2 + (y � 5.4)2 = 18.72(C) the inside of the circle (x � 1.6)2 + (y + 5.4)2 = 18.72(D) the outside of the circle (x � 5.4)2 + (y + 1.6)2 = 18.72

8. In a right triangle ABC. the in circle touches the hypotenuse AC at D. If AD = 10 and DC = 3, the inradiusof ABC is -(A) 5 (B) 4 (C) 3 (D) 2

9. The sides of a quadrilateral are all positive integers and three of them are 5, 10, 20. How many possiblevalue are there for the fourth side ?(A) 29 (B) 31 (C) 32 (D) 34

10. If the volume of a sphere increases by 72.8%, then its surface area increases by -(A) 20% (B) 44% (C) 24.3% (D) 48.6%

www.examrace.com

PHYSICS

11. A boy standing on the foothpath tosses a ball straight up and catch it. The driver of a car passing bymoving with uniform velocity sees this.

The trajectory of the ball as seen by the driver will be -

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

12. Consider two spherical planets of same average density. Planet 2 is 8 times as massive as planet 1.The ratio of the acceleration due to gravity on the second planet to that on the first is.(A) 1 (B) 2 (C) 4 (D) 8

13. Two immiscible liquids, A and B are kept in a U-tube. If the density of liquid A is smaller than the densityof liquid B, then the equilibrium situation is.

(A)

A

(B)

A

(C)

A

(D) None of these

14. In !he figure below a ray of light travelling in a medium of refractive index µ passes through two differentconnected rectangular blocks of refractive indices µ

1 and µ

2 (µ

2 > µ

1).

µ µ1 µ2

The angle of incidence 1 is increased slightly. The angle

2

(A) increases.

(B) decreases.

(C) remains the same

(D) increases or decreases depending on the value of (µ1/µ

2).

www.examrace.com

15. Two charges of same magnitude move in two circles of radii 1R = R and R2 = 2R in a region of constant

uniform magnetic field 0B

.

The work W1 and W

2 done by the magnetic field in the Two cases, respectively are such that

(A) W1 = W

2 = 0 (B) W

1 > W

2(C) W

1 = W

2 0 (D)W

1 < W

2

16. Two charges +q and �q are placed at a distance b apart as shown in the figure below.

b/2

b

+q �q

B

AP

C

The electric field at a point P on the perpendicular bisector as shown as :

(A) along vector A (B) along vector B

(C) along vector C (D) Zero

17. A block of mass M is at rest on a plane surface inclined at an angle to the horizontal The magnitude of

force exerted by the plane on the block is :

(A) Mg cos (B) Mg sin (C) Mg tan (D) Mg

18. We are able to squeeze snow and make balls out of it because of -

(A) anomalous behaviour of water. (B) large latent heat of ice.

(C) large specific heat of water. (D) low melting point of ice.

19. Which of the following phenomena can be demonstrated by light. But not with sound waves in an air

column?

(A) Reflection (B) Diffraction

(C) Refraction (D) Polarziation

20. The temperature of a metal coin is increased by 100°C and its diameter increases by 0.15%. Its areaincreases by nearly

(A) 0.15% (B) 0.60% (C) 0.30% (D) 0.0225%

www.examrace.com

CHEMISTRY

21. The element X which forms a stable product of the type XCI4 is -

(A) AI (B) Na (C) Ca (D) Si

22. A mixture of NH4CI and NaCI can be separated by -

(A) filtration (B) Distillation (C) Sublimation (D) Decantation

23. The pair in which the first compound is ionic and the second compound is covalent, is -

(A) Fe(OH)2,CH

3OH (B) CH

3OH, CH

3CH

2OH (C) Fe(OH)

2, Cu(OH)

2(D) Ca(OH)

2, Cu(OH)

2

24. In the reaction SO2 + 2H

2S 3S + 2H

2O, the substance that is oxidized is -

(A) SO2

(B) H2O (C) S (D) H

2S

25. Sodium oxide dissolves in water to give sodium hydroxide which indicates its -

(A) acidic character (B) basic character

(C) amphoteric character (D) ionic character

26. For an ideal gas, Boyle�s law is best described by -

(A)

P

T

(B)

P

V

(C)

P

V

(D)

P

T

27. The pH values of

(i) 0.1 M HCl aq (ii) 0.1 M KOH

(iii) tomato juice and (iv) pure water

follow the order -

(A) (i) < (iii) < (iv) < (ii) (B) (iii) < (i) < (iv) < (ii) (C) (i) < (ii) < (iii) < (iv) (D) (iv) < (iii) < (ii) < (i)

28. When calcium carbide is added to water, the gas that is evolved is -

(A) carbon dioxide (B) hydrogen (C) acetylene (D) methane

29. Atomic radii of alkali metals follow the order -

(A) Li > Na > K > Cs (B) K > Cs > Li > Na (C) Na > K > Cs > Li (D) Cs > K > Na > Li

30. The number of possible structural isomers of C3H

4 is :

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

www.examrace.com

BIOLOGY

31. Which one of the following is the smallest in size ?

(A) Bacteria (B) Mitochondrion

(C) Mammalian cell (D) Virus

32. If birds are moved from 30°C to 10ºC, their body temperature :(A) changes from 30ºC to 10°C (B) increases by 10ºC(C) does not changes at all (D) decreases by 10ºC

33. Ascorbic acid is a/an.

(A) Strong inorganic acid (B) Hormone

(C) Vitamin (D) Enzyme

34. Bile salts :

(A) break down polypeptide chains (B) emulsify fats and solubilize them

(C) digest fats (D) help breakdown of polysaccharides

35. Dietary fibers are composed of :

(A) Cellulose (B) Amylase (C) Proteins (D) Unsaturated fats

36. �On the origin of species , by means of Natural selection�was written by.(A) Hugo de vires (B) Charles Darwin (C) Charles dickons (D) Alfred Russell wallace

37. Unlike humans, dogs cannot perspire to get rid to excess metabolic heat. They lose metabolic heat by:

(A) Panting (B) running in windy conditions

(C) taking a bath (D) rolling in the mud

38. Haemodialysis is a treatement option for patients with malfunctions of :

(A) Kidney (B) Heart (C) Liver (D) Lungs

39. An individual has O blood group if his/her blood sample.

(A) Clumps only when antiserum A is added

(B) Clumps only when antiserum B is added

(C) Clumps when both antiserum A and antiserum B are added

(D) Does not clump when either antiserum A or antiserum B is added

40. In warmer, weather, curds from milk forms faster because :

(A) bacteria diffuse better in warmer milk (B) the rate of bacterial multiplication increases

(C) lactogen is better dissolved (D) it is easier to separate protein from water

www.examrace.com

MATHEMATICS

1. The radius of a cone is 2 times the height of the cone. A cube of maximum possible volume is cut from

the same cone. What is the ratio of the volume of the cone to the volume of the cube ?

2. Three equal circles of unit radius toucher each other. Then find area of the circle circumscribing the three

circle is (in sq. unit).

3. What will be the last digit of 4554 33 22 .

PHYSICS

4. A needle 10 cm long is placed along the axis of a convex lens of focal length 10 cm, such that the middle

point of the needle is at a distance of 20 cm from the lens. Find the length of the image of the needle.

5. An iceberg is floating partially immersed in sea water. If the denssity of sea water is 1.03 g/cc and that of

ice is 0.92 g/cc, find the fraction of the total volume of iceberg above the level of sea water.

6. An infinite wire bent in the form of L carries current . Find the magnetic field at the point O

www.examrace.com

CHEMISTRY

7. The solubility product constant of Ag2CrO4 and AgBr are 1.1 ×10�12 and 5.0 ×10�13 respectively. Calculatethe ratio of the molarities of their saturated solutions.

8. (i) The solution of salt (A) in dilute HCl gives a dirty yellow precipitate on passing H2S gas. The precipitatedissolves in yellow ammonium sulphide.(ii) The salt (A) gives chromyl chloride test.(iii) (A) first forms a white precipitate with NaOH which dissolves in excess of NaOH forming a compound(B).(iv) The alkaline solution of (B) when added to bismuth chloride gives a black precipitate (C).(v) (A) reduces HgCl2 in solution to a white precipitate (D) which changes to grey. Identify (A), (B), (C) and(D). Give reactions at steps (i) to (v).

9. Identify the gas (X) :(i) (X) is a colourless with pungent smell.(ii) (X) turns lime water milky(iii) (X) turns acidified K

2Cr

2O

7 solution green.

(iv) (X) gives white turbidity when H2S is passed through it aqueous solution.

(v) A white precipitate insoluble in conc. HNO3 is formed when the aqueous solution of (X) in NaOH is treated

with barium chloride and bromine water.

BIOLOGY

10. Answer the following questions :(a) What is the name given to cytoplasmic connections in between two adjacent plant cells .What is itssignificance in phloem tissue ?

(b) What is phylogenetic classification ?

(c) �Bat and whales are mammals� comment on this statement.

(d) Define syndrome ?

(e) What are interferons ?

11. Answer the following question :

(i) Give one example each of insectivore and a sanguivore animal.

(ii) In which animal group first complete alimentary canal was developed ?

(iii) Name the digestive juice that contains no digestive enzyme ?

(iv) Name any two proteolytic enzymes ?

(v) Name the plant structure which helps in attaching the bryophytes to the substratum ?

12. Coin one word or two words equivalent for the following :

(i) Science that deals with the study of inheritance.

(ii) Alternative forms of some genes.

(iii) The person who coined the term chromosome.

(iv) The diagrammatic representation of karyotype.

(v) Name the term used for transfer of pollen grains with the help of insects.

www.examrace.com

MATHEMATICS

1. 5x 0 1� x 0

x < 1 ...(i)

5x > 1 � xx + 5 > 1 + x2 � 2xx2 � 3x � 4 < 0(x � 4) (x +1) < 0x (�1, 4) ....(ii)Using (i) & (ii) x (�1, 1)

3. x = x2 + y2 & y = 2 xy when y = 0 x = x2

x = 0, x = 1 solutions are (0,0) (1,0)

when x = 21

21

�41

= y2 41

= y2 y = ±21

solutions

21

,21

21

,�21

4. x3 � 3 |x| + 2 = 0 [Let x > 0]x3 � 3x + 2 = 0(x � 1) (x2 + x � 2) = 0

x = 1, x = 2

91� = 1

Now, let x < 0x3 + 3x + 2 = 0no solutionx = 1 only one solution

5. (1 + 2x)20 = a0 + a

1x + a

2x2 + ------- + a

20x20

put x = 1 320 = a0 + a

1 + a

2 + ------- + a

20

x = �1 1 = a0 � a

1 + a

2 � a

3 ------- + a

20

subtract 320� 1 = 2(a1 + a

3 + -------- + a

19]

add 320 + 1 = 2 (a0 + a

2 + -------- +a

20]

HINTS & SOLUTIONS (PRACTICE PAPER-2)

Ques. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15Ans. D A A A C C B D D B C B C B A

Ques. 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30Ans. A D A D C D C A D B C A C D B

Ques. 31 32 33 34 35 36 37 38 39 40Ans. D C C B A B A A D B

www.examrace.com

2 (a1 + a

3 + ------- + a

19) + 3 [a

0 + a

2 + --------- + a

20] = (320�1) +

23

(320 + 1)

= 2

13.5 20

6. Points which are equidistant from O and P1 lies on perpendicular bisector of OP

1

O

P2

P1

P5

P3

P4

Similarly for others In figure points on pentagon are equdistant from points P

1, P

2, ...... and O

interior region of pentagon is closed to �O�

7. Let (x, y) be any point

Using given condition 2 22 y)2x( < 3 22 )3y()0x(

5x2 + 5y2 � 54y + 16x + 65 > 0x2 + y2� 10.8y + 3.2x + 13 > 0

It is a circle, radius = 72.18

Centre (� 1.6, 5.4)Hence region is exterior of (x + 1.6)2 + (y � 5.4)2 = 18.72.

8. (r + 3)2 + (r + 10)2 = (13)2

AB

C

D3

10

3

r

r 10

r2 + 9 + 6r + r2 + 100 + 20r = 169 2r2 + 26r � 60 = 0 r2 + 13r � 30 = 0 (r + 15) (r �2) = 0 r = 2

9. To find possible intergal value of 4th sier minimum possible value of 4th side greater than 0 is 1.For maximum possible value.

AB

C

20

D

let angle , are slightly smaller than 180ºif , = 180ºAD = 35 maximum value of 4th side is 34 1, 2, 3, ------------- 34 are possible value of 4th side 34 values are possible.

www.examrace.com

10.V

'V =

1008.172

= 3

3

R34

'R34

R'R = 1.2

Now, ratio of surface area = S

'S = 3

2

R4

'R4

=

= S

'S = 1.44

Hence surface area increased by 44%

PHYSICS12. given mass of planet A = m

A

and mass of planet B = mB

mB = 8 m

A

gA =

2A

A

rGm

and gB =

2B

B

rGm

or

2

A

B

B

A

B

A

rr

mm

gg

.......(i)

mB = 8 m

A

dr

34

8dr34 3

A3B

A

B

rr

= 2

21

481

gg

B

A

gB = 2g

A

20. A = r2

rA

2AA

100rA

2%AA

15.02%AA

= 0.30%

www.examrace.com

CHEMISTRY

21. Silicon is tetravalent, so it forms SiCl4 .

22. NH4Cl undergoes sublimation while NaCl does not.

24. SO + 2H S2 2 3S + 2H O2

Reduction

Oxidation

26. As per Boyle�s lawPV = constant

and P V1

28. CaC2 + 2H

2O Ca(OH)

2 + C

2H

2

Calcium Water Calcium Ethynecarbide hydroxide (acetylene)

29. As we move downwards in a group, atomic radii increases. So the order will be Li < Na < K < Cs.

30. CH3 � C CH (Propyne) and (cyclo propene) are two possible structural isomers of C

3H

4 .

www.examrace.com

MATHEMATICS

1.h

a�h =

h2

2a2

h

a

h2

h22

h�a

1a�h

= 2a

2h � 2a = a2h = 3a

cubeofvolumeconeofvolume

= 3

2

a

hr31

= 3

2

3h2

h)h2(31

= 2.25

2.

M

O1

O2 O3

O1O

2 = O

2O

3 = O

3O

1 = 1 + 1 = 2 unit

Height of equilateral triangle O1 O

2 O

3

= 23

× 2 = 3 unit.

Centre of the bigger circle O will be the centroid of the triangle.

O1O =

323

= 3

2.

So, the radius of bigger circle

=

3

21 =

3

23

Hence, area of the bigger circle

2

3

23

= 3 2)32( sq. unit

www.examrace.com

3. 45 5343 22

Now as 45 > 54

{for x > 2,(x)x + 1 > (x + 1)x always }

4554 33 22

Now all even power of 3 are of the form 4n + 1 last term of first digit is 2also all odd powers of 3 are of the form 4n + 3. last digit of the term is 8[ By cyclicity of last digit]Thus, the last digit of expression 2 � 8 = 4.

PHYSICS

4.

BC FA O20 cm

10 cm

In the given figure AB is the needle of length 10 cm.

CO = 20 cm, AO = 25 cm, BO = 15 cm

For the image of end A of the needle:

u1 = �25 cm, f = 10 cm.

f1

u1

�v1

11

251

101

v1

1 �

251

101

v1

1

� 503

v1

1

v1 = 16.67 cm

For the image of end B of the needle:

u2 = �15 cm, f = 10 cm.

f1

u1

�v1

22

101

151

v1

2

�

� 151

101

v1

2

�

301

v1

2

v2 = 30 cm

Size of image of the needle AB = v2 � v

1

= 30 � 16.67 = 13.33 cm.

www.examrace.com

5. waterseaofDensityiceofDensity

)v(volumeTotal)u(waterinsideVolume

03.192.0

vu

103.192.0

1vu

10310392

v)vu(

or 10311

v)vu(

%10010311

volumeTotalwatersideoutVolume

= %11~1031100

6. Magneitc field due to straight wirePQ at O,B

1 = 0

Magnetic field due to straight wire QR at O

B2 = )sin(sin

d4 210

I

Here 1 = 45º and = 90º

B2 = .O1

2

1d4

0

I

Magnetic field due to were QS at O

B3 = )sin(sin

d4 210

I

Here 1 = 45º and

2 = 90º

So, B3 =

1

2

1d4

0I

Net magnetic field at OB = B

1 + B

2 + B

3 = 0

www.examrace.com

CHEMISTRY7. Molarility of Ag2 CrO4 solution.

Ag2CrO4(s) + aq 2Ag+(aq) + CrO42�(aq)

Let the solubility of Ag2CrO4 in water be S mol litre�1. Then[Ag+(aq)] = 2S and [CrO4

2�(aq)] = SNow, Ksp = [Ag+(aq)]2[CrO4

2�(aq)] = (2S)2 × S = 4S3

or S = 31

sp

4

K= 3

1 12�

4101.1

= 0.65 × 10�4

= 6.5 ×10�5 mol L�1

(b) Molarity (or molar solubility) of Ag Br solution.

AgBr(s) + aq Ag+(aq) + Br�(aq)

Let the solubility of AgBr be S mole L�1. Then [Ag+(aq)] = S and [Br�(aq)] = S

Now, Ksp = [Ag+(aq)][Br�(aq)] = S × S = S2

or S = spK = 13�100.5

= 0.707 × 10�6 mol L�1 = 7.07 × 10�7 mol L�1

Ratio of molarities of the saturated solutions

= AgBrofMolarityCrOAgofMolarity 42

= 7�

5�

1007.7

105.6

= 91.9

8. (i) )A(

2SnCl + H2S yellowDirty

SnS + 2HCl

SnS + (NH4)2S2 SnS2 + (NH4)2S

SnS2 + (NH4)2S2 lelubSo324 SnS)NH(

(ii) SnCl2 + H2SO4 SnSO4 + 2HCl

K2Cr2O7 + H2SO4 K2SO4 + 2CrO3 + H2O

CrO3 + 2HCl

chlorideChromyl

22ClCrO + H2O

(iii) SnCl2 + 2NaOH .pptWhite2)OH(Sn + 2NaCl

Sn(OH)2 + 2NaOH

lelubSo)B(

22SnONa (Sodium stannite)

(iv) )B(

22SnONa3 + 6NaOH + 2BiCl3

.pptBlack)C(

Bi2 + 3Na2SnO3 + 6NaCl + 3H2O

(v) SnCl2 + 2HgCl2

)chlorideMercurous(.pptWhite

)D(22ClHg + SnCl4

HgCl2 + SnCl2 Grey

Hg2 + SnCl4

www.examrace.com

9. [Hints : (i) (X) is SO2. It is colourless and pungent. Rest of properties are observed with SO

3.

(ii) Ca(OH)2 + SO

2 CaSO

3 + H

2O

Lime water Milky

(iii) K2Cr

2O

7+ H

2SO

4 + 3SO

2 K

2SO

4 + Cr

2(SO

4)

3 + H

2O

Green

(iv) SO2 + 2H

2S 3S + 2H

2O

White turbidity

(v) H2SO

3 + 2NaOH Na

2SO

3 + 2H

2O

Na2SO

3 + BaCl

2 BaSO

3 + 2NaCl

Br2 + H

2O 2HBr + [O]

BaSO3 + [O] BaSO

4

White ppt. (Insoluble in conc. HNO

3)

BIOLOGY10. (a) plasmodesmata. Due to this the sieve tube cells which lacks nucleus at maturity remains alive

through cytoplasmic transfer from companion cells.

(b) System of classification based on evolutionary relationships of organism.

(c) Both posses mammary glands and diaphragm which is characteristic feature of mammals.

(d) A group of symptoms that collectively indicate or characterize a disease, psychological disoder orother abnormal condition is called syndrome.

(e) Interferons are specific type of proteins which are released by virus infected cells during viral infectionand stops further multiplication of virus in body.

11. (i) Lizard and leech

(ii) Annelids

(iii) Bile juice

(iv) Pepsin & trypsin.

(v) Root like structures are called Rhizoids.

12. (i) Genetics (ii) Alleles (iii) Waldeyer

(iv) Idiograms (v) Entomophily

www.examrace.com