236366883 Fiitjee Class 11th Phase Test 1 JEE Mains

FIITJEE - J EE (Ma ins) in s) 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 instructions carefully. carefully. You You are allotted allotted 5 minutes specifically specifically for this purpose.

I m p o r t a n t In In s t r u c t i o n s : 1.

Immediate Immediately ly fill fill in the partic particulars ulars on this this page page of the Test Test Booklet Booklet with Blue Blue / Black Black Ball Ball Point Point Pen. Pen. Use of of pencil is strictly prohibited. prohibited.

2.

The Answer Answer Sheet Sheet is kept inside inside this this Test Booklet. Booklet. When you you are direct directed ed to open the the Test Booklet, Booklet, take take out out the Answer Sheet and fill in the particulars carefully.

3.

The test is of 3 f 3 hours duration.

4.

The The Test Test Book Bookle lett con consi sist sts s of 90 of 90 questions. The maximum marks are 360. 360.

5.

There are t h r e e parts in the the question question paper A, B, C consisting consisting of Physics, Chemistry and Mathematics having 30 questions in each part of equal weightage. Each question is allotted 4 (fou (fourr) marks for correct response.

6.

Candidates will be awarded marks as stated stated above in instruction No.5 for correct response of each question. ¼ (one fourth) marks will be deducted for indicating incorrect response of each question. No deduction from the total score will be made if no response is indicated for an item in the answer sheet.

7.

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

8.

Use B l u e / B l a c k B a l l P o i n t P e n o n l y for writing particulars / marking responses on Side-1 and Side-2 of the Answer Sheet. U s e o f p e n c i l i s s t r i c t l y p r o h i b i t e d .

9.

No candidate candidate is is allowed allowed to carry carry any textua textuall material, material, printed printed or written written,, bits of of papers, papers, pager, pager, mobile mobile phone, phone, any electronic device, etc. except the Admit Card Card inside the examination hall / room. room.

10. On completion of the test, test, the candidate must must hand over the Answer S Sheet heet to the Invigilator on duty in the Room / Hall. H o w e v e r , t h e c a n d i d a t e s a r e a l l o w e d t o t a k e a w a y t h i s T e s t B o o k l e t w i t h t h e m . 11. Do not fold or make any stray marks on the Answer Answer Sheet.

Name of the Candidate Candidate (in Capital Letters) Letters) :____________ :___________________ _______________ _______________ __________ ___ Enrolment Number :_________________________________________________________ Batch :______________ :____________________ __________ ____ Date of Examinati Examination on : ______________ ____________________ __________ ____

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

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

2

SECTION – I PHYSICS 1.

A bob bob is hung hung fro from m the the cei ceili ling ng of of a trai train n comp compar artm tmen ent. t. The The trai train n move moves s on an inc incli line ne 0 track of inclination 30 with horizontal. Acceleration of the train up the plane is g/2. The angle which the string supporting the bob makes with normal to the ceiling in equilibrium condition, is (A) 300 (B) tan-1 (2) (C) tan-1

 2     3 

(D) 450

2.

A bloc block k of mas mass s 2kg 2kg is gen gentl tly y pla place ced d over over a mas massi sive ve pla plank nk mov movin ing g hori horizo zont ntal ally ly ove overr a smooth surface with velocity 6 m/s. The coefficient of friction between the block and plank is 0.2. The distance traveled by the block till it slides on the plank is (g=10 m/s 2) (A) 4 m (B) 6 m (C) 9 m (D) 12 m

3.

Pow Power appl appliied to a par partticl icle var varie ies s wi with time time as P   3t 2  2t  1 watt, where t is in second. Find the change in its kinetic energy between t = 2sec and t = 4sec (A) 32J (B) 46J (C) 61J (D) 100J

4.

A heavy avy string of mass m hangs between two fix fixed points points A and and B at at an angle angle  with the horizontal as shown shown in the figure. The tension tension at the lowest lowest point in the string is (A) mg/(2 sin ) (C) mg/(2 tan )

5.

6.





Find Find the the min minim imum um valu value e of of mas mass s of of han hangi ging ng bloc block k so 2 kg block block slips over over 4 kg block. (A) 30 kg (B) 20 kg (C) 10 kg (D) will not slip for any mass

=1.5

=0

2 kg

4 kg

M

Find the ra ratio of th the ac accelerat ration of m1 and m2. All the pulleys are smooth and frictionless. am / am = ? 2

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

m1

m2

A par parti ticl cle e is is pro proje ject cted ed on incl inclin ined ed plan plane e of of inc incli lina nati tion on  at angle of elevation horizontal. If the particle strikes the plane horizontally then (A) tan   2 tan  (B) tan   cot  (C) tan   2 tan 

(D)  = 2

Centre, 31-32-33, 31-32-33, Central Central Market, Market, West Avenue Avenue Road, Punjabi Punjabi Bagh (West), (West), New Delhi - 110026, 110026, Ph: 011-4563400 011-45634000 0 FIITJEE Ltd., North West Delhi Centre, [

B

(B) mg/(2 cos ) (D) mg/(2 cot )

1

7.

A

 to the


8.

9.

3

A bloc block k B is res resting ting on mov movabl able wed wedge ge A. The The coefficient of friction between A and B is . The acceleration of the wedge for which B does not experience any friction is/are : (A) g tan (B) g cot (C) g (D) g cos

B A



A blo block ck 5 kg kg is is kep keptt on on the the floo floorr of of an an ele eleva vato torr at at res rest. t. As the the elevator starts descending with an acceleration of 12 m/s2, (Taking g = 10 m/s 2) the displacement displacement of of the block during the first 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 body of mass mass 1kg 1kg is throw thrown n upwards upwards with with a veloc velocity ity 20m/s. 20m/s. It mome momenta ntaril rily y comes comes to to rest after attaining a height of 18m. How much energy is lost due to air friction. (g = 10 m/s2) (A) 10J (B) 20J (C) 30J (D) 40J

11.

In sy system sh shown in in fifigure mB  4kg and m A  2kg . The pulleys are massless and friction is absent everywhere. The acceleration of block A is  g  10 m / s2  10 (A) m / s2 3 20 (B) m / s2 3 (C) 2 m / s 2 (D) 4 m/s2

12.

B A 0

30

A bea bead d of mass mass m is is loc locat ated ed on par parab abol olic ic wire wire wit with h its its axi axis s vertical and vertex at the origin as shown in figure and whose equation is x2 = 4ay. The wire frame is fixed and bead can slide on it without friction. The bead is released from the point y = 4a on the wire frame from rest. The tangential acceleration of the bead when it reaches the position given by y = a is (A) (C)

g 2 g 2

(B) (D)

3 g 2 g

y

m

O

5

13.

A body body is is proje project cted ed fro from m the the top top of of a towe towerr with with an an init initia iall velo veloci city ty of of 10 ms ms –1 horizontally (Assume g = 10 ms –2). The distance of the body from the point of projection after two seconds is (in m): (A) 20 (B) 40 (C) 28.8 (D) 14.4

14.

When When a trai train n is at rest rest,, rain rain drops drops fall fall verti vertical cally. ly. When it moves moves alon along g east east with with a veloci velocity ty equal 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 Centre, 31-32-33, 31-32-33, Central Central Market, Market, West Avenue Avenue Road, Punjabi Punjabi Bagh (West), (West), New Delhi - 110026, 110026, Ph: 011-4563400 011-45634000 0 FIITJEE Ltd., North West Delhi Centre,

[

x

4


15. 15.

Bloc Block k are are mov moving ing as as sho show wn. The The rat ratio io v1 / v 2 is (A) (C)

sin 1 sin 2 cos 2 cos 1

(B)

sin 2

(D)

cos 1

sin 1 cos 2

1 A

2 v1

B

v2

16.

A sprin spring g of force force cons constan tantt k is is cut cut into into two two pieces pieces such such that that one piece piece is is doubl double e the the length of the other. Then the long piece will will have a force constant constant of 2 3 (A) k (B) k 3 2 (C) 3k (D) 6k

17.

If wedge wedge is movi moving ng wit with h acc accel elera erati tion on a as as show shown n in in the the figure then value of net force on m is (A) ma (B) 2 ma (C) mg ma (D) zero

18.

The accele accelerat ration ion-ve -veloc locity ity graph graph of of a partic particle le moving moving in a stra straigh ightt line line is as shown in figure. Then slope of velocity-displacement graph (A) increases linearly (B) decreases linearly (C) is constant (D) increases parabolically

a M

m

a

V

19.

A man man is standi standing ng on on a weigh weighing ing machin machine e with with a block block in in his his hand. hand. The machin machine e recor records ds W. When he takes the blocks upwards with some acceleration the machine records W 1. When he takes the blocks down with some acceleration, the machine records W 2. Then choose correct option. (A) W1  W  W2 (B) W1  W  W2 (C) W2  W  W1 (D) W2  W1  W

20.

A part partic icle le is movi moving ng on an elli ellipt ptic ical al path path as show shown, n, speed speed of the particle is constant. Its acceleration is maximum at (A) A (B) B (C) C (D) same everywhere 

21.











If R 1  A  B and R2  A  B , then 

(A) A   (C) A  B









R1  R2 R1  R2

C

B A

will be along 

(B) B   (D) A  B



5 A

22. 22.

Two Two monk monkey eys s each each of of mass mass m move move with with acc accel eler erat atio ion n a1  a2 

g 2

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

B

a2

C

a1

23. 23.

When When a spr sprin ing g is is str stret etch ched ed by a dis dista tanc nce e x, x, itit exe exert rts s a forc force, e, give given n by by 3 F   5x  16x  N. The work done, when the spring is stretched from 0.1M to 0.2M is (A) 8.1 102 J (C) 8.1 101 J

(B) 12.2  102 J (D) 12.2  101 J

24.

A perso person n walki walking ng at the rate rate of 3km/ho 3km/hour, ur, the rain rain appear appears s to fall fall verti vertical cally ly,, when when he 0 increase his to speed 6 km/hr it appears to meet him at angle of 45 with vertical. The speed of rain is 3 (A) 3 2 km / hr (B) km/hr 2 (C) 6 2 km / hr (D) 2 3 km / hr

25.

In the the figur figure e sho shown wn ther there e are are two two pendu pendulu lums ms free free to to mov move e in a vertical 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 is is a light rigid rod. The ratio of minimum velocities v1 and v2 given to both as shown to complete the full vertical circle is

26.

27.

(A) 1

(B)

(C) 2

(D)

B

Q

2 3 2

(A) a

 (B) 2a sin 2

(C) a sin 

(D) g sin 

A

B a 

The The tim time e tak taken en by the the proj projec ecti tile le to to reac reach h from from A to B is is t. t. Then the distance AB is equal to ut 3 ut (A) (B) 2 3 (D) 2 ut

u

B

60 30 A


v2

v1

5

A wei weight ghtle less ss inex inexte tens nsib ible le rop rope e rest rests s on on a sta stati tion onar ary y wedg wedge e forming an angle  with the horizontal. One end of the rope is fixed to the wall at point A. A small load is attached to the rope at point B. The wedge starts moving to the right with a constant acceleration acceleration a. The magnitude of acceleration of the load is given by:

(C) 3 ut

P

A


28.

6

Two Two ste steel el ball balls s A and B are are pla place ced d ins insid ide e a right right circ circul ular ar cylinder of diameter 54 cm making contacts at point P, Q and R as shown. The radius r A = 12 cm and r B = 18 cm. The masses are m A  60kg and mB = 15 kg. The forces exerted by 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

B

P

R

A

Q 54 cm

29.

A wei weight ght W is atta attach ched ed to two two wei weight ghtle less ss stri strings ngs AB and AC

C

as shown in figure. The tension in each string will be (A) (C)

30. 30.

W 4

(B)

3W 2

(D) W

B 120

°

T

W 2

A 120°

W

A pro proje ject ctil ile e is is pro proje jec cted ted at at an an an angle gle (>450) with an initial velocity u (t=0). the time t at which its horizontal component velocity will equal to the vertical component velocity u u (A) t = (cos   sin ) (B) t = (cos   sin ) g g (C) t =

u g

(sin   cos )

(D) t =

u g

(sin

2

  cos 2 )


T


7

SECTION – II CHEMISTRY 1.

Whic Which h of of the the foll follow owin ing g spec specie ies s has has the the gre great ates estt bon bond d ang angle le? ?   (A) NH4 (B) NO2 (C) CH3

(D) PH4

2.

A ves vesse sell con conta tain ins s equ equal al mass mass of meth methan ane e and and heli helium um gase gases s at at 120 120oC and 800 mm Hg pressure. What is the partial pressure pr essure of methane in the vessel? (A) 600 mm Hg (B) 400 mm Hg (C) 160 mm Hg (D) 200 mm Hg

3.

Whic Which h of of the the foll follow owin ing g com compo poun und d of of mag magne nesi sium um evol evolve ves s NH NH3 gas when reacts with water? (A) Mg(N3)2 (B) Mg3N2 (C) Mg(NO3)2 (D) Mg(NO2)2

4.

H2O2 decomposes as: 2 H2O2   2 H2O  O2 Which of the following structure of H 2O2 explains its easiest decomposition? H

H

O

(A)

(B)

O

O

O

H

H H

(C)

O

O

(D)

 2 H  O22 

H

5.

 NH4  2 Cr2O7  Cr2O3  4 H2 O  N2 What is the equivalent weight of (NH4)2Cr 2O7 (Molar mass = M g) in the above above reaction? M M (A) (B) 4 3 M M (C) (D) 6 8

6.

Wha What is is th the th third ioniz nization en energy ergy((I.E3) of lithium atom in electron volt unit? 9  (A)   13.6  (B) (9  13.6) 4  (C)

1   9  13.6   

(D)

4   9  13.6   

7.

Which Which of of the the foll follow owin ing g two two eleme element nts s have have max maxim imum um num number ber of ide ident ntic ical al pro prope perti rties es? ? (A) Si and Al (B) Mg and K (C) Be and Al (D) Na and Mg

8.

Which Which of the the follo followi wing ng mole molecu cule le cont contai ains ns iden identi tica call cova covale lent nt bonds bonds? ? (A) SF6 (B) PF5 (C) SF4 (D) IF7



9.

Which Which of of the the foll follow owin ing g does does not not repr repres esen entt the the root root mea mean n squa square re vel veloc ocit ity y of an an idea ideall gas? gas? 3 RT 3P (A) (B) M d (C)

10.

8

2E M

(D)

2d M

In aq aqueous so solution Be BeSO4 exists as 2+ (A) [Be(H2O)2] and SO24

(B) [Be(H2O)4]2+ and SO24

(C) [Be(H2O)6]2+ and SO24

(D) [Be(H2O)3]2+ and SO24

11.

Which Which of of the the foll follow owin ing g solu soluti tion on of of the the give given n subs substa tanc nce e produ produce ces s I2 when reacts with acidified 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 mL of 0.1 N HCl. Therefore, x is: (A) 1 (B) 2 (C) 3 (D) 4

13.

How How many many max maxim imum um num numbe berr of elec electr tron ons s of an ato atom m wil willl have have n +  = 5? n = principal quantum number  = azimuthal quantum number (A) 6 (B) 8 (C) 10 (D) 18

14.

Which Which of the the fol follo lowi wing ng spe speci cies es has has maxi maximu mum m spi spin n val value? ue?  (A) O2 (B) O2 (C) O2

(D) O22

15.

Which Which of of the follow following ing subs substan tance ce has has the the highes highestt value value of of second second ioni ionizat zation ion ener energy? gy? (A) Na (B) Mg (C) Al (D) Ca

16.

The radius radius of of each each atom atom of of helium helium is r. r. What What would would be the the exclu excluded ded volu volume me for for an atom atom of helium which touches other helium atoms in a vessel at high pressure and low temperature. 4 8 (A) r 3 (B) r 3 3 3 16 3 32 3 r r (C) (D) 3 3

17. 17.

Whic Which h of of the the foll follow owin ing g gas gas rea react cts s wit with h NaO NaOH? H? (A) NH3 (B) CO (C) H2 (D) C2H4

18.

Which Which of the follow following ing substa substance nce forms forms a whit white e colo colour ur prod product uct when when react reacts s with with H2O2? (A) K2Cr 2O7 (B) FeSO4 (C) PbS (D) Na2SO3

19.

Which Which of the the fol follo lowi wing ng mol molec ecul ule e has has zer zero o dipo dipole le momen moment? t? Centre, 31-32-33, 31-32-33, Central Central Market, Market, West Avenue Avenue Road, Punjabi Punjabi Bagh (West), (West), New Delhi - 110026, 110026, Ph: 011-4563400 011-45634000 0 FIITJEE Ltd., North West Delhi Centre,

[


(A) SOF4 (C) XeF4

9

(B) SF4 (D) XeOF4

20.

Electr Electrons ons with with whic which h of the followi following ng azim azimuth uthal al quan quantum tum number number,, are are prese present nt in in maximum 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 of MgO can completely react with one mole of P4O10? (A) 4 (B) 5 (C) 6 (D) 8

22.

Which Which of of the the follow following ing atom atom atta attains ins a half half-fi -fille lled d elec electro tronic nic configu configurat ration ion by gaining gaining one electron? (A) Boron (B) Carbon (C) Nitrogen (D) Oxygen

23.

Which Which of the the fol follo lowi wing ng ion ion has has the the larg larges estt ion ionic ic rad radiu ius? s? 3– 2– (A) N (B) O 4– (C) C (D) F –

24.

Which Which of the follow following ing molecu molecule le is formed formed by overla overlappi pping ng of of pure pure half-f half-fill illed ed p-orbit p-orbitals als according to valence bond theory? (A) H2 (B) H2O (C) CH4 (D) F2

25.

The pressur pressure e of an ideal ideal gas incre increase ases s by one atm when when the the gas was transfe transferre rred d from from a 9 L vessel to a 6 L vessel at constant temperature. What is the pressure of the gas in the smaller vessel? (A) 4 atm (B) 2 atm (C) 3 atm (D) 6 atm

26.

Which Which of of the the foll followi owing ng is not a produc productt of the reactio reaction n betwe between en sodi sodium um and and oxy oxygen? gen? (A) Na2O (B) Na2O2 (C) NaO2 (D) NaO

27.

Which Which of of the follow following ing type type of hydro hydrogen gen is is formed formed in the the hydro hydrogen gen torc torch h which which is used used for welding of metals? (A) Atomic hydrogen (B) Nascent hydrogen (C) Ortho hydrogen (D) Para hydrogen

28.

How many gram of NaOH NaOH can can be be compl complete etely ly neutra neutraliz lized ed by by 200 200 mL mL of 0.4 M HCl HCl solution? (A) 2.8 (B) 0.08 (C) 3.2 (D) 0.04

29.

Which Which of of the followi following ng ratio ratio of the the chara characte cteris ristic tics s of an orbit orbit and elec electr tron on is equal equal to principal quantum number of the orbit? Area of orbit Circ Circumf umfer erenc ence e of orbit orbit (A) (B) Freq Freque uenc ncy y of elec electr tron on motio motion n Waveleng Wavelengthof thof elect electro ron n motion motion (C)

Radi Radius us of orbi orbitt Wave Wave numb number er of elec electr tron on moti motion on

(D)

Area of orbit Circ Circumf umfer eren ence ce of orbi orbitt



30.

10

The ener energy gy chan change ge of whic which h of the the follo followin wing g proces process s is called called the ioniz ionizati ation on energy energy of sodium? (s = Solid state and g = gaseous state)  Na  s   Na  s  (A) Na  g  (B) Na  s  

 Na  g (C) Na  g  

 Na  g  (D) Na  s  



11

SECTIO SEC TION – III MATHEMATICS 1.

If   2 

3 2

, then

2  2  2 cos 4 is equal to

(A) 2cos  (C) 2cos 

(B) 2sin  (D) 2sin 

2.

cos ec ec 20  sec 20 20 is equal to The numerical value of 3 co (A) 2 (B) 4 (C) 6 (D) none of these

3.

The maximum value of 12 sin   9 sin2  is equal to (A) 3 (B) 4 (C) 21 (D) none of these

4.

5.

 1 1 , co cos   and 0  ,   , then    lies in the interval 2 3 2 (A) (60°, 90°) (B) (90°, 120°) (C) (120°, 300°) (D) (150°, 180°) If s in  

Given that sin3 x. sin 3 x 

n

c

m

cos mx, c n

 0, is an identity. The value of n is

m 0

(A) 2 (C) 6

(B) 4 (D) cannot be calculated

6.

The The numb number er of of posi positi tive ve int integr egral al val values ues of ‘m’ ‘m’ for for whic which h the the x-co x-coor ordi dina nate te of of the the poin pointt of intersection 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  3 y  6 , the smallest value of  2

36 13 (C) 6

6 13 13 (D) 13

(A)

8.

 2 is

(B)

The distance of the point  4,1 from from the the lin line e y  3x measured along a line with gradient

1 is 11 2 2 (C) 1

11 2 4 (D) none of these

(A)

9.

(B)

A point P  4,1 undergo undergoes es the follow following ing three three transfor transformat mation ions s success successive ively: ly: (i) reflection about the line y  x, (ii) translation through 2 units along the positive direction of x-axis, and (iii) rotation through an angle The final position of P is  1 7  (A)  ,   2 2

 4

about the origin in the anticlockwise sense.

(B)

 2, 7 2 



(C)

10. 10.

12

 1 7   ,   2 2

(D)

(B) 3 (D) 5

 6 x  0 is (B) 2 (D) 4

 y2  7x  y  8  0

(D) none of these

The The inc incen entr tre e of of the the tria triang ngle le form formed ed by the the lin lines es y  x and y  1 is

 (C)  2 

 2, 0 

  (D)  0, 2  2 

(A) 0, 2  2

14. 14.

(B) 2  2, 0

The The commo ommon n cho chord of the the circl ircles es x 2 origin an angle equal to (A) (C)

15.

 y 2  4 x  4 y  0 and x 2  y 2  16 subtends at the



(B)

6



(D)

3

 4

 2

The The cho chord rd of cont contac actt of of the the pai pairr of of tan tangen gents ts to the the circ circle le x 2 on the line 2x  y  4 passes through the point

 1, 1  2 4    1 (C)  1,   2

 y 2  1 drawn from any point

 1, 1 4 2   1  (D)  , 1 2 

(A)

16. 16.

 y 2  6 x  14 y  48  0 and

The equati equation on of of the circle circle passin passing g throu through gh the the poin points ts (2, (2, 0) 0) and and (0, (0, 4) and having having the minimum possible radius is (A) x 2  y 2  x  y  3 (B) x 2  y 2  2x  4 y  0 (C) x 2

13. 13.



The The num numbe berr of of com commo mon n tan tange gent nts s to to the the circ circle les s x2 x 2  y2 (A) 1 (C) 0

12.

2, 7 2

A line ine pass passiing throu hrough gh the the poin pointt  21, 30 30  and normal to the curve y  2 x has its slope equal to (A) 2 (C) 2

11. 11.



(B)

If a ci circle rcle pass passes es thro throug ugh h the the poin pointt  a,b  and and cut cuts s the the circ circle le x 2

 y 2  p2 orthogonally,

then the equation of the locus of its center is (A) 2ax  2by   a2  b2  p2   0 (B) 2ax  2by   a2  b2 (C) x 2 17.

 y 2  3ax  4by   a2  b2  p2   0

(D) x 2

 p2   0

 y 2  2ax  3by   a2  b2  p2   0

 y 2  4 x  22y  c  0 bisects the circumference of the circle x 2  y 2  2x  8 y  d  0 , then c  d equals

If the circle (A) 60 (C) 40

x2

(B) 50 (D) none of these


13


18.

If one one vert vertex ex of of an equil equilate ateral ral tria triangl ngle e of side side 2 is the origin origin and and anoth another er vert vertex ex lies lies on the line x  3y , then the third vertex can be

  3, 1 (D)  3,1

(A)  0, 2  (C) 19.

 2, 2

The sum of the square squares s of of the the lengt length h of of the the chor chord d inte interce rcepte pted d by the line line x  y  n, n  N on the circle x 2 (A) 11 (C) 33

20.

(B)

 y 2  4 is (B) 22 (D) none of these

The statement ~  p  ~ q is (A) a tautology (C) equivalent to p  q

(B) a fallacy (D) ~ p  q 3

21. 21.

The The num numbe berr of of in integr tegral al solut olutio ions ns of

 x  1  x  2  x  4  x2 (B) 2 (D) 4

(A) 0 (C) 3 22.

dy is equal to dx 1  cos t (B) sint cost (D) 1  sin t

If x  a  t  sin t  , y  a  1  cos t  , then sint 1  cos t cost (C) 1  sin t (A)

23.

log

The set of re real values of x for which 2

 , 1   4,   (C)  , 1 (A)

24.

25.

1  t2 2t dy  If x  , y , then 1  t2 1  t2 dx y (A)  x x (C)  y

 0 is

2

 x 1

 x  5 is (B)  4,  (D)  1, 4 

 y x x (D) y (B)

If l og4 5  a and log5 6  b, then log3 2  (A)

1 2a  1

(C) 2ab  1

1 2b  1 1 (D) 2ab  1 (B)



26.

dx

 x x

7

 1

14



1  x7  (A) ln  7 c 7  x  1

 x7  c 7  x 1  

(C) ln 

27.



If

 /3

 /4

(A)

2

(B)

3

lim

x 

1  x2 x 1  x3

(A) 0 (C) 1

 (B) 1 (D) doesn’t exist

If A = tan tan 6° tan tan 42° 42° and and B = cot cot 66° 66° cot cot 78° 78°, the then n (A) A = 2B (C) A = B

30.

3

(D) 5

x4 s siin

29. 29.

(D) none of these

1 dx  k, then k is equal to sin2 x co cos2 x

(C) 2

28.

1  x7  (B)  ln  7 c 7  x  1

1 3 (D) 3A = 2B (B) A

 B

The maximum value of sin  cos x  is equal to (A) sin1

 1    2

(C) sin 

(B) 1

 3  2   

(D) sin 



15

INTERNAL TEST PHASE – I BATCHES: ANSWERS IIT MAINS

QP CODE: SR. NO 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20 21. 22. 23. 24. 25. 26. 27. 28. 29. 30.

PHYSICS

C.CODE

CHEMISTRY

C. CODE

M ATHS

C.CODE

C C B C D B C A C B A C C A C B B C C C A C A A B B A D D C

P110403 P110401 P110504 P110403 P110403 P110320 P110310 P110405 P110326 P110502 P110404 P110415 P110326 P110320 P110416 P110404 P110404 P110325 P110404 P110318 P110201 P110403 P110507 P110320 P110508 P110409 P110314 P110405 P110403 P110310

B C B C C B C A D B B B D B A C B C C B C B C D C D A C B C

C110305 C111207 C110903 C111006 C111101 C110103 C110702 C110306 C111206 C110902 C111006 C110202 C110107 C110112 C110703 C111204 C110808 C111006 C110304 C110107 C110202 C110108 C110706 C110306 C111202 C110803 C111003 C111102 C110103 C110704

D B B B C A A B C D D B A D A A B A B C C B B C D A A B C A

M111303 M111402 M111411 M111403 M111407 M110701 M110714 M110718 M110728 M110712 M110822 M110802 M110704 M110820 M110809 M110821 M110815 M110702 M110823 -

M110109 M120509 M110203 M120508 M110202 M120701 M120803 M110606 M111402 M111308


236366883 Fiitjee Class 11th Phase Test 1 JEE Mains

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