fiitjee class 11th phase test 1 (jee mains)

FIITJEE Ltd., North West Delhi Centre, 31-32-33, Central Market, West Avenue Road, Punjabi Bagh (West), New Delhi - 110026, Ph: 011-45634000[

PHYSICS, CHEMISTRY & MATHEMATICS

Time Allotted: 3 Hours Maximum Marks: 360

Do not open this Test Booklet until you are asked to do so. Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose.

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3. The test is of 3 hours duration.

4. The Test Booklet consists of 90 questions. The maximum marks are 360.

5. There are three parts in the question paper A, B, C consisting of Physics, Chemistry and Mathematicshaving 30 questions in each part of equal weightage. Each question is allotted 4 (four) marks for correctresponse.

6. Candidates will be awarded marks as stated above in instruction No.5 for correct response of each question. (one fourth) marks will be deducted for indicating incorrect response of each question. No deduction fromthe total score will be made if no response is indicated for an item in the answer sheet.

7. There is only one correct response for each question. Filling up more than one response in any question willbe treated as wrong response and marks for wrong response will be deducted accordingly as per instruction 6above.

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Name of the Candidate (in Capital Letters) :_____________________________________

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FIITJEE - JEE (Mains)

Two Year CRP(1416)-PT-1_JEE (Mains)-PCM-IITJEE/16


2

SECTION IPHYSICS

1. A bob is hung from the ceiling of a train compartment. The train moves on an inclinetrack of inclination 300 with horizontal. Acceleration of the train up the plane is g/2. Theangle which the string supporting the bob makes with normal to the ceiling in equilibriumcondition, is(A) 300 (B) tan-1 (2)

(C) tan-1

32 (D) 450

2. A block of mass 2kg is gently placed over a massive plank moving horizontally over asmooth surface with velocity 6 m/s. The coefficient of friction between the block andplank is 0.2. The distance traveled by the block till it slides on the plank is (g=10 m/s2)(A) 4 m (B) 6 m(C) 9 m (D) 12 m

3. Power applied to a particle varies with time as 2P 3t 2t 1 watt, where t is insecond. Find the change in its kinetic energy between t = 2sec and t = 4sec(A) 32J (B) 46J(C) 61J (D) 100J

4. A heavy string of mass m hangs between two fixedpoints A and B at an angle with the horizontal asshown in the figure. The tension at the lowest point inthe string is

A B

(A) mg/(2 sin ) (B) mg/(2 cos )(C) mg/(2 tan ) (D) mg/(2 cot )

5. Find the minimum value of mass of hanging blockso 2 kg block slips over 4 kg block.(A) 30 kg(B) 20 kg(C) 10 kg(D) will not slip for any mass M

4 kg

=1.5

=0

2 kg

6. Find the ratio of the acceleration of m1 and m2. All the pulleys aresmooth and frictionless.

1 2m ma /a = ?

(A) 2 : 1(B) 1 : 2(C) 1 : 1(D) the system is not stable m2

m1

7. A particle is projected on inclined plane of inclination at angle of elevation to thehorizontal. If the particle strikes the plane horizontally then(A) tan 2 tan (B) tan cot (C) tan 2 tan (D) = 2



3

8. A block B is resting on movable wedge A. Thecoefficient of friction between A and B is . Theacceleration of the wedge for which B does notexperience any friction is/are :(A) g tan (B) g cot(C) g (D) g cos

A

B

9. A block 5 kg is kept on the floor of an elevator at rest. As theelevator starts descending with an acceleration of 12 m/s2,(Taking g = 10 m/s2) the displacement of the block during thefirst 0.2 sec.(A) 0.04 meter (B) 0.24 meter(C) 0.2 meter (D) 0.02 meter

a=12 m/s2

5 kg

10. A body of mass 1kg is thrown upwards with a velocity 20m/s. It momentarily comes torest after attaining a height of 18m. How much energy is lost due to air friction. (g = 10m/s2)(A) 10J (B) 20J(C) 30J (D) 40J

11. In system shown in figure Bm 4kg and Am 2kg .The pulleys are massless and friction is absenteverywhere. The acceleration of block A is 2g 10m/ s(A) 210 m / s

3

(B) 220 m / s3

(C) 22 m / s(D) 4 m/s2

300A

B

12. A bead of mass m is located on parabolic wire with its axisvertical and vertex at the origin as shown in figure andwhose equation is x2 = 4ay. The wire frame is fixed andbead can slide on it without friction. The bead is releasedfrom the point y = 4a on the wire frame from rest. Thetangential acceleration of the bead when it reaches theposition given by y = a is

(A) g2

(B) 3 g2

(C) g2

(D) g5

m

y

O x

13. A body is projected from the top of a tower with an initial velocity of 10 ms1 horizontally(Assume g = 10 ms2). The distance of the body from the point of projection after twosecondsis (in m):(A) 20 (B) 40(C) 28.8 (D) 14.4

14. When a train is at rest, rain drops fall vertically. When it moves along east with a velocityequal to that of rain, the rain will appear to fall, for a passenger in the train:(A) 45 to vertical (B) along north-west(C) from upwards (D) 30 to vertical



4

15. Block are moving as shown. The ratio 1 2v / v is

(A) 12

sinsin

(B)

2

1

sinsin

(C) 21

coscos

(D)

1

2

coscos

1 2v1 v2A B

16. A spring of force constant k is cut into two pieces such that one piece is double thelength of the other. Then the long piece will have a force constant of

(A) 2 k3

(B) 3 k2

(C) 3k (D) 6k

17. If wedge is moving with acceleration a as shown in thefigure then value of net force on m is(A) ma (B) 2 ma(C) mg ma (D) zero mM

M

aM

18. The acceleration-velocity graph of a particle moving in a straight lineis as shown in figure. Then slope of velocity-displacement graph(A) increases linearly(B) decreases linearly(C) is constant(D) increases parabolically V

a

19. A man is standing on a weighing machine with a block in his hand. The machine recordsW. When he takes the blocks upwards with some acceleration the machine records W1.When he takes the blocks down with some acceleration, the machine records W2. Thenchoose correct option.(A) 1 2W W W (B) 1 2W W W (C) 2 1W W W (D) 2 1W W W

20. A particle is moving on an elliptical path as shown, speed ofthe particle is constant. Its acceleration is maximum at(A) A(B) B(C) C(D) same everywhere A

B

C

21. If 1R A B

and 2R A B

, then 1 21 2

R RR R

will be along

(A) A

(B) B

(C) A B (D) A B



5

22. Two monkeys each of mass m move with acceleration 1 2ga a2

relative to the light inextensible string as shown in the figure. The ratioof tensions in the portions AB and BC of the string is(A) 1 : 2 (B) 3 : 1(C) 4 : 1 (D) 2 : 1

a2

a1

B

C

A

23. When a spring is stretched by a distance x, it exerts a force, given by 3F 5x 16x N. The work done, when the spring is stretched from 0.1M to 0.2M is

(A) 28.1 10 J (B) 212.2 10 J(C) 18.1 10 J (D) 112.2 10 J

24. A person walking at the rate of 3km/hour, the rain appears to fall vertically, when heincrease his to speed 6 km/hr it appears to meet him at angle of 450 with vertical. Thespeed of rain is

(A) 3 2 km / hr (B) 3 km / hr2

(C) 6 2 km / hr (D) 2 3 km / hr

25. In the figure shown there are two pendulums free to move in avertical circle about one pivoted end. The length of each is and mass of each bob is m. But AB is a light string while PQ isa light rigid rod. The ratio of minimum velocities v1 and v2 givento both as shown to complete the full vertical circle is v1

v2

A

B

P

Q

(A) 1 (B) 52

(C) 2 (D) 32

26. A weightless inextensible rope rests on a stationary wedgeforming an angle with the horizontal. One end of the ropeis fixed to the wall at point A. A small load is attached to therope at point B. The wedge starts moving to the right with aconstant acceleration a. The magnitude of acceleration ofthe load is given by:

(A) a (B) 2a sin2

(C) a sin (D) g sin

aB

A

27. The time taken by the projectile to reach from A to B is t.Then the distance AB is equal to

(A) ut3

(B) 3 ut2

(C) 3 ut (D) 2 ut30O

60O

u

A

B



6

28. Two steel balls A and B are placed inside a right circularcylinder of diameter 54 cm making contacts at point P, Qand R as shown. The radius rA = 12 cm and rB = 18 cm. Themasses are Am 60kg and mB = 15 kg. The forces exertedby the floor at the point Q and the wall at R are respectively(taking g = 10 m/s2)(all the surfaces are smooth)(A) 600N, 150N (B) 750N, 100N(C) 600N, 120N (D) 750N, 200N

54 cm

R

P

A

B

Q

29. A weight W is attached to two weightless strings AB and AC

as shown in figure. The tension in each string will be

(A) W4

(B) W2

(C) 3W2

(D) W

TT

C B

120

W

A120

30. A projectile is projected at an angle (>450) with an initial velocity u (t=0). the time t atwhich its horizontal component velocity will equal to the vertical component velocity

(A) t = )sin(cos gu (B) t = )sin(cos

gu

(C) t = )cos(sin gu (D) t = )cos(sin 22

gu



7

SECTION IICHEMISTRY

1. Which of the following species has the greatest bond angle?(A) 4NH

(B) 2NO

(C) 3CH (D) 4PH

2. A vessel contains equal mass of methane and helium gases at 120oC and 800 mm Hgpressure. What is the partial pressure of methane in the vessel?(A) 600 mm Hg (B) 400 mm Hg(C) 160 mm Hg (D) 200 mm Hg

3. Which of the following compound of magnesium evolves NH3 gas when reacts withwater?(A) Mg(N3)2 (B) Mg3N2(C) Mg(NO3)2 (D) Mg(NO2)2

4. H2O2 decomposes as: 2 2 2 22H O 2H O O Which of the following structure of H2O2 explains its easiest decomposition?

(A)O

O

H

H

(B) OH

H

O

(C) OH

H

O (D) 222H O

5. 4 2 7 2 3 2 22NH Cr O Cr O 4H O N What is the equivalent weight of (NH4)2Cr2O7 (Molar mass = M g) in the above reaction?

(A) M4

(B) M3

(C) M6

(D) M8

6. What is the third ionization energy(I.E3) of lithium atom in electron volt unit?

(A) 9 13.64

(B) (9 13.6)

(C) 1 13.69

(D)4 13.69

7. Which of the following two elements have maximum number of identical properties?

(A) Si and Al (B) Mg and K(C) Be and Al (D) Na and Mg

8. Which of the following molecule contains identical covalent bonds?(A) SF6 (B) PF5(C) SF4 (D) IF7



8

9. Which of the following does not represent the root mean square velocity of an ideal gas?

(A) 3RTM

(B) 3Pd

(C) 2EM

(D) 2dM

10. In aqueous solution BeSO4 exists as(A) [Be(H2O)2]2+ and 24SO

(B) [Be(H2O)4]2+ and 24SO

(C) [Be(H2O)6]2+ and 24SO (D) [Be(H2O)3]2+ and 24SO

11. Which of the following solution of the given substance produces I2 when reacts withacidified H2O2?(A) NaIO3 (B) KI3(C) I2O5 (D) NaIO4

12. 0.7 g of Na2CO3.xH2O is dissolved in 100 mL of water, 20 mL of which required 19.8 mLof 0.1 N HCl. Therefore, x is:(A) 1 (B) 2(C) 3 (D) 4

13. How many maximum number of electrons of an atom will have n + = 5?n = principal quantum number = azimuthal quantum number(A) 6 (B) 8(C) 10 (D) 18

14. Which of the following species has maximum spin value?(A) 2O

(B) O2(C) 2O

(D) 22O

15. Which of the following substance has the highest value of second ionization energy?(A) Na (B) Mg(C) Al (D) Ca

16. The radius of each atom of helium is r. What would be the excluded volume for an atomof helium which touches other helium atoms in a vessel at high pressure and lowtemperature.

(A) 34 r3 (B) 38 r

3

(C) 316 r3 (D) 332 r

3

17. Which of the following gas reacts with NaOH?(A) NH3 (B) CO(C) H2 (D) C2H4

18. Which of the following substance forms a white colour product when reacts with H2O2?(A) K2Cr2O7 (B) FeSO4(C) PbS (D) Na2SO3

19. Which of the following molecule has zero dipole moment?



9

(A) SOF4 (B) SF4(C) XeF4 (D) XeOF4

20. Electrons with which of the following azimuthal quantum number, are present inmaximum number in an atom of zinc?(A) = 0 (B) = 1(C) = 2 (D) = 3

21. Reaction of P4O10 with MgO forms only magnesium phosphate. How many moles ofMgO can completely react with one mole of P4O10?(A) 4 (B) 5(C) 6 (D) 8

22. Which of the following atom attains a half-filled electronic configuration by gaining oneelectron?(A) Boron (B) Carbon(C) Nitrogen (D) Oxygen

23. Which of the following ion has the largest ionic radius?(A) N3 (B) O2(C) C4 (D) F

24. Which of the following molecule is formed by overlapping of pure half-filled p-orbitalsaccording to valence bond theory?(A) H2 (B) H2O(C) CH4 (D) F2

25. The pressure of an ideal gas increases by one atm when the gas was transferred from a9 L vessel to a 6 L vessel at constant temperature. What is the pressure of the gas in thesmaller vessel?(A) 4 atm (B) 2 atm(C) 3 atm (D) 6 atm

26. Which of the following is not a product of the reaction between sodium and oxygen?(A) Na2O (B) Na2O2(C) NaO2 (D) NaO

27. Which of the following type of hydrogen is formed in the hydrogen torch which is used forwelding of metals?(A) Atomic hydrogen (B) Nascent hydrogen(C) Ortho hydrogen (D) Para hydrogen

28. How many gram of NaOH can be completely neutralized by 200 mL of 0.4 M HClsolution?(A) 2.8 (B) 0.08(C) 3.2 (D) 0.04

29. Which of the following ratio of the characteristics of an orbit and electron is equal toprincipal quantum number of the orbit?

(A) Area of orbitFrequency of electron motion

(B) Circumference of orbitWavelengthof electron motion

(C) Radius of orbitWave number of electron motion

(D) Area of orbitCircumference of orbit



10

30. The energy change of which of the following process is called the ionization energy ofsodium? (s = Solid state and g = gaseous state)(A) Na g Na s (B) Na s Na s(C) Na g Na g (D) Na s Na g



11

SECTION IIIMATHEMATICS

1. If 32 ,2 then 2 2 2cos 4 is equal to

(A) 2cos (B) 2sin (C) 2cos (D) 2sin

2. The numerical value of 3 cosec20 sec 20 is equal to(A) 2 (B) 4(C) 6 (D) none of these

3. The maximum value of 212sin 9sin is equal to(A) 3 (B) 4(C) 21 (D) none of these

4. If 1 1sin , cos2 3

and 0 ,2 , then lies in the interval

(A) (60, 90) (B) (90, 120)(C) (120, 300) (D) (150, 180)

5. Given thatn

3m

m 0nsin x.sin3x c cosmx, c 0,

is an identity. The value of n is

(A) 2 (B) 4(C) 6 (D) cannot be calculated

6. The number of positive integral values of m for which the x-coordinate of the point ofintersection of the lines 3x + 4y = 9 and y = mx + 1 is an integer, is(A) 0 (B) 1(C) 2 (D) infinitely many

7. If the point , lies on the line 2x 3y 6 , the smallest value of 2 2 is(A) 36

13(B) 6 13

13(C) 6 (D) 13

8. The distance of the point 4,1 from the line y 3x measured along a line with gradient1 is

(A) 11 22

(B) 11 24

(C) 1 (D) none of these

9. A point P 4,1 undergoes the following three transformations successively:(i) reflection about the line y x,(ii) translation through 2 units along the positive direction of x-axis, and

(iii) rotation through an angle4 about the origin in the anticlockwise sense.

The final position of P is

(A) 1 7,2 2

(B) 2,7 2



12

(C) 1 7,2 2

(D) 2,7 210. A line passing through the point 21,30 and normal to the curve y 2 x has its slope

equal to(A) 2 (B) 3(C) 2 (D) 5

11. The number of common tangents to the circles 2 2x y 6x 14y 48 0 and2 2x y 6x 0 is

(A) 1 (B) 2(C) 0 (D) 4

12. The equation of the circle passing through the points (2, 0) and (0, 4) and having theminimum possible radius is(A) 2 2x y x y 3 (B) 2 2x y 2x 4y 0 (C) 2 2x y 7x y 8 0 (D) none of these

13. The incentre of the triangle formed by the lines y x and y 1 is(A) 0,2 2 (B) 2 2,0(C) 2 2,0 (D) 0,2 2

14. The common chord of the circles 2 2x y 4x 4y 0 and 2 2x y 16 subtends at theorigin an angle equal to

(A)6 (B)

4

(C)3 (D)

2

15. The chord of contact of the pair of tangents to the circle 2 2x y 1 drawn from any pointon the line 2x y 4 passes through the point(A) 1 1,

2 4 (B)

1 1,4 2

(C) 11,

2 (D)

1, 12

16. If a circle passes through the point a,b and cuts the circle 2 2 2x y p orthogonally,then the equation of the locus of its center is(A) 2 2 22ax 2by a b p 0 (B) 2 2 22ax 2by a b p 0 (C) 2 2 2 2 2x y 3ax 4by a b p 0 (D) 2 2 2 2 2x y 2ax 3by a b p 0

17. If the circle 2 2x y 4x 22y c 0 bisects the circumference of the circle2 2x y 2x 8y d 0 , then c d equals

(A) 60 (B) 50(C) 40 (D) none of these



13

18. If one vertex of an equilateral triangle of side 2 is the origin and another vertex lies onthe line x 3y , then the third vertex can be(A) 0,2 (B) 3, 1 (C) 2, 2 (D) 3,1

19. The sum of the squares of the length of the chord intercepted by the line x y n, n N on the circle 2 2x y 4 is(A) 11 (B) 22(C) 33 (D) none of these

20. The statement ~ p ~ q is(A) a tautology (B) a fallacy(C) equivalent to p q (D) ~ p q

21. The number of integral solutions of 3x 1 x 2 x 4

0x 2

is(A) 0 (B) 2(C) 3 (D) 4

22. If x a t sin t , y a 1 cos t , then dydx

is equal to

(A) sin t1 cos t (B)

1 cos tsin t

(C) cos t1 sin t (D)

cos t1 sin t

23. The set of real values of x for which 2log x 12 x 5 is(A) , 1 4, (B) 4,(C) , 1 (D) 1,4

24. If2

2 2

1 t 2tx , y ,1 t 1 t then

dydx

(A) yx

(B) yx

(C) xy

(D) xy

25. If 4log 5 a and 5log 6 b, then 3log 2 (A) 1

2a 1 (B)1

2b 1(C) 2ab 1 (D) 1

2ab 1



14

26. 7dx

x x 1

(A)7

7

1 xln c7 x 1

(B)

7

7

1 xln c7 x 1

(C)

7

7

xln cx 1

(D) none of these

27. If/3

2 2/4

1 dx k,sin x cos x

then k is equal to

(A) 23

(B) 3

(C) 2 (D) 5

28.4 2

3x

1x sin xxlim

1 x

(A) 0 (B) 1(C) 1 (D) doesnt exist

29. If A = tan 6 tan 42 and B = cot 66 cot 78, then

(A) A = 2B (B) 1A B3

(C) A = B (D) 3A = 2B

30. The maximum value of sin cos x is equal to(A) sin1 (B) 1

(C) 1sin2

(D)3sin

2



15

FIITJEE INTERNAL TESTPHASE IBATCHES:

ANSWERS IIT MAINSQP CODE:

SR.NO PHYSICS C.CODE CHEMISTRY C. CODE MATHS C.CODE

1. C P110403 B C110305 D M1113032. C P110401 C C111207 B M1114023. B P110504 B C110903 B M1114114. C P110403 C C111006 B M1114035. D P110403 C C111101 C M1114076. B P110320 B C110103 A M1107017. C P110310 C C110702 A M1107148. A P110405 A C110306 B M1107189. C P110326 D C111206 C M110728

10. B P110502 B C110902 D M11071211. A P110404 B C111006 D M11082212. C P110415 B C110202 B M11080213. C P110326 D C110107 A M11070414. A P110320 B C110112 D M11082015. C P110416 A C110703 A M11080916. B P110404 C C111204 A M11082117. B P110404 B C110808 B M11081518. C P110325 C C111006 A M11070219. C P110404 C C110304 B M11082320 C P110318 B C110107 C -21. A P110201 C C110202 C M11010922. C P110403 B C110108 B M12050923. A P110507 C C110706 B M11020324. A P110320 D C110306 C M12050825. B P110508 C C111202 D M11020226. B P110409 D C110803 A M12070127. A P110314 A C111003 A M12080328. D P110405 C C111102 B M11060629. D P110403 B C110103 C M11140230. C P110310 C C110704 A M111308

fiitjee class 11th phase test 1 (jee mains)

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