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RET–7 FIITJEE (Hyderabad Classes) Limited., 5-9-14/B, Saifabad, (Opp. Secretariat) Hyderabad–500 063. Phone: 040-66777000-03 Fax: 040-66777004 FIITJEE RET – 7 (2017 – 2019)(1 ST YEAR_REGULAR) IIT2015 (P1) DATE: 21.08.2017 Time: 3 hours Maximum Marks: 264 INSTRUCTIONS: A. General 1. This booklet is your Question Paper containing 60 questions. 2. Blank papers, clipboards, log tables, slide rules, calculators, cellular phones, pagers and electronic gadgets in any form are not allowed to be carried inside the examination hall. 3. Fill in the boxes provided for Name and Enrolment No. 4. The answer sheet, a machine-readable Objective Response (ORS), is provided separately. 5. DO NOT TAMPER WITH / MULTILATE THE ORS OR THE BOOKLET. B. Filling in the OMR: 6. The instructions for the OMR sheet are given on the OMR itself. C. Question paper format: 7. The question paper consists of 3 parts (Physics, Chemistry and Mathematics). Each part consists of two sections. 8. Section I contains 8 questions. The answer to each question is a single digit integer, ranging from 0 to 9 (both inclusive). 9. Section II contains 10 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE are correct. 10. Section III contains 2 Match the following type questions and you will have to match entries in Column I with the entries in Column II D. Marking Scheme 11. For each question in Section I, you will be awarded 4 marks if you darken ALL the bubble(s) corresponding to the correct answer(s) ONLY. In all other cases zero (0) marks will be awarded. No negative marks will be awarded for incorrect answers in this section. 12. For each question in Section II, you will be awarded 4 marks if you darken ALL the bubble(s) corresponding to the correct answer(s) ONLY. In all other cases zero (0) marks will be awarded. –2 marks will be awarded for incorrect answers in this section. 13. For each question in Section III, you will be awarded 2 marks for each entry in Column I; if you darken ALL the bubble(s) corresponding to the correct answer(s) ONLY. In all other cases zero (0) marks will be awarded. –1 marks will be awarded for incorrect answers in this section. Don’t write / mark your answers in this question booklet. If you mark the answers in question booklet, you will not be allowed to continue the exam. NAME: ENROLLMENT NO.:

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Page 1: RET–7 FIITJEE RET – 7fiitjeehyderabad.com/documents/SFD/RET-7 Jr QP_C.pdfFIITJEE RET – 7 (2017 – 2019)(1ST ... An inclined plane makes an angle of 300 with the horizontal

RET–7 

FIITJEE (Hyderabad Classes) Limited., 5-9-14/B, Saifabad, (Opp. Secretariat) Hyderabad–500 063. Phone: 040-66777000-03 Fax: 040-66777004

FIITJEE RET – 7

(2017 – 2019)(1ST YEAR_REGULAR) IIT‐2015 (P1) 

DATE: 21.08.2017 Time: 3 hours Maximum Marks: 264 INSTRUCTIONS:

A. General

1. This booklet is your Question Paper containing 60 questions.

2. Blank papers, clipboards, log tables, slide rules, calculators, cellular phones, pagers and electronic gadgets in any form are not allowed to be carried inside the examination hall.

3. Fill in the boxes provided for Name and Enrolment No.

4. The answer sheet, a machine-readable Objective Response (ORS), is provided separately.

5. DO NOT TAMPER WITH / MULTILATE THE ORS OR THE BOOKLET.

B. Filling in the OMR:

6. The instructions for the OMR sheet are given on the OMR itself.

C. Question paper format:

7. The question paper consists of 3 parts (Physics, Chemistry and Mathematics). Each part consists of two sections.

8. Section I contains 8 questions. The answer to each question is a single digit integer, ranging from 0 to 9 (both inclusive).

9. Section II contains 10 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE are correct.

10. Section III contains 2 Match the following type questions and you will have to match entries in Column I with the entries in Column II

D. Marking Scheme

11. For each question in Section I, you will be awarded 4 marks if you darken ALL the bubble(s) corresponding to the correct answer(s) ONLY. In all other cases zero (0) marks will be awarded. No negative marks will be awarded for incorrect answers in this section.

12. For each question in Section II, you will be awarded 4 marks if you darken ALL the bubble(s) corresponding to the correct answer(s) ONLY. In all other cases zero (0) marks will be awarded. –2 marks will be awarded for incorrect answers in this section.

13. For each question in Section III, you will be awarded 2 marks for each entry in Column I; if you darken ALL the bubble(s) corresponding to the correct answer(s) ONLY. In all other cases zero (0) marks will be awarded. –1 marks will be awarded for incorrect answers in this section.

Don’t write / mark your answers in this question booklet. If you mark the answers in question booklet, you will not be allowed to continue the exam.

NAME:

ENROLLMENT NO.:

Page 2: RET–7 FIITJEE RET – 7fiitjeehyderabad.com/documents/SFD/RET-7 Jr QP_C.pdfFIITJEE RET – 7 (2017 – 2019)(1ST ... An inclined plane makes an angle of 300 with the horizontal

RET–7 

FIITJEE (Hyderabad Classes) Limited., 5-9-14/B, Saifabad, (Opp. Secretariat) Hyderabad–500 063. Phone: 040-66777000-03 Fax: 040-66777004

PAPER–I PART I: PHYSICS

SECTION 1 (Maximum Marks: 32) This section contains EIGHT questions. The answer to each question is a SINGLE DIGIT INTEGER ranging from 0 to 9, both inclusive. For each question, darken the bubble corresponding to the correct integer in the ORS. Marking scheme:

+4 If the bubble corresponding to the answer is darkened. 0 In all other cases.

1. An inclined plane makes an angle of 030 with the horizontal. A

groove OA = 5m cuts in the plane makes an angle of 030 with OX. A short smooth cylinder is free to slide down under the influence of gravity. If time taken by the cylinder to reach from A to O is ‘a’ sec and speed of cylinder at the point ‘O’ is ‘b’ m/sec

then ab

2is________

2. A monkey of mass m =1 kg clings to a rope slung over a light

frictionless pulley. The opposite end of the rope is tied to a weight of mass M = 2m lying on a smooth horizontal plane. The tension in the rope for which the monkey moves upwards with an acceleration 2a 2m/ sec relative to the rope is T = W N (neglect the mass of pulley and rope). Find W.

3. Two blocks of mass m =10 kg and M= 20 kg are connected by a

string passing over a pulley B as shown in the figure. Another string connects the centre of pulley B and passes over another pulley A as shown. An upward force F is applied at the centre of pulley A. Both the pulleys are massless. When F is 600 N, then

The acceleration of mass m is _____

Space for rough work

Page 3: RET–7 FIITJEE RET – 7fiitjeehyderabad.com/documents/SFD/RET-7 Jr QP_C.pdfFIITJEE RET – 7 (2017 – 2019)(1ST ... An inclined plane makes an angle of 300 with the horizontal

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FIITJEE (Hyderabad Classes) Limited., 5-9-14/B, Saifabad, (Opp. Secretariat) Hyderabad–500 063. Phone: 040-66777000-03 Fax: 040-66777004

4. A ball of mass 200 gm is thrown with a speed 120ms . The ball

strikes a bat and rebounds along the same line at a speed of 140ms . Variation in the interaction force, as long as the ball

remain in contact with the bat, is as shown in the figure If ' ' is the speed of the ball in m/s at the instant the force

acting on it is maximum then 5

is _________

‘ms’ is millisecond.

5.

A sphere of mass 13

kg is placed on two inclined planes of

angle 30 and 60 with horizontal, as shown. Find the normal reaction at point P (in Newton)

6. 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 at speed of 5 m/s. If initial acceleration of the block is ‘a’ m/sec2 then value of (2a+1) is

7. You are designing an elevator for a hospital. The force exerted on a passenger by the floor of the elevator

is not to exceed 1.60 times the passenger’s weight. The elevator accelerates upward with constant acceleration for a distance of 3.0 m and them starts to slow down. What is the maximum speed (in ms–1) of the elevator ____

8. The elevator shown in fig is descending with an acceleration of

22ms . The mass of the block A = 0.5 kg. Find the force (in Newton) exerted by block A on block B.

Space for rough work

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FIITJEE (Hyderabad Classes) Limited., 5-9-14/B, Saifabad, (Opp. Secretariat) Hyderabad–500 063. Phone: 040-66777000-03 Fax: 040-66777004

SECTION 2 (Maximum Marks: 40) This section contains TEN questions. Each question has FOUR options (A), (B), (C) and (D). ONE OR MORE THAN ONE of these four option(s) is

(are) correct. For each question, darken the bubble(s) corresponding to all the correct option(s) in the ORS. Marking scheme:

+4 If only the bubble(s) corresponding to all the correct option(s) is (are) darkened. 0 If none of the bubbles is darkened. –2 In all other cases

9. At the moment t= 0 the force F = at is applied to a small body of mass m

resting on a smooth horizontal plane (a is a positive constant). The permanent direction of this force forms an angle with the horizontal. Then

(A) the velocity of the body at the moment of its breaking off the plane is 2

2

mg cos

asin

(B) the velocity of the body at the moment of its breaking off the plane is 2

2

mg sin

2acos

(C) the distance traversed by the body at the moment of it breaking off the

plane is 2 3

2 3

m g cos

6a sin

(D) the distance traversed by the body at the moment of it breaking off the

plane is 2 3

2 3

m g cos

3a sin

10. Consider the system as shown in fig. If mass of body 2 is

times as great as the mass of body 1 and the angle that

the inclined plane forms with the horizontal is equal to . The masses of the pulleys and the threads, as well as the friction, are assumed to be negligible. Then

(A) acceleration of body 2 is

g 2 sin

1 4

downward if

sin

2

(B) acceleration of body 2 is

2g 2 sin

1 4

upward if

sin

2

(C) acceleration of body 1 is

2g sin 2

1 4

down the inclined plane if if

sin

2

(D) For 2sin , the system does not move.

Space for rough work

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11. At the moment t=0, a stationary particle of mass m experiences a time – depended force F at t ,

where a is a constant vector, is the time during which the given force acts. then

(A) the momentum of the particle when the action of the force discontinued is 3a / 6 (B) the momentum of the particle when the action of the force discontinued is 3a /12 (C) the distance covered by the particle while till the force acted is 4a /12m (D) the distance covered by the particle while till the force acted is 4a / 6m 12. Which of the following are correct ? (A) A parachute of weight W strikes the ground with his legs and comes to rest with an upward

acceleration of magnitude 3g. Force exerted on him by ground during landing is 4 W. (B) Two massless spring balances are hung vertically in series from a fixed point and a mass M kg is

attached to the lower end of the lower spring balance. Each spring balance reads M kg –f (C) A body in equilibrium may be moving with a constant speed along a straight line path

(D) A man is standing at a spring platform. If man jumps away from the platform the reading of the spring balance first increases and then decreases to zero

13. The ring shown in the figure is given a constant horizontal

acceleration 0a g/ 3 . Maximum deflection of the string

from the vertical is 0 , then

(A) 00 30 (B) 0

0 60

(C) At maximum deflection, tension in string is equal to mg (D) At maximum deflection, tension in string is equal to

2mg

3

14. A body of mass 5 kg is suspended by the strings making angles 060

and 030 with the horizontal as shown in the figure 2g 10m/ s

(A) 1T 25N (B) 2T 25N

(C) 1T 25 3N (D) 2T 25 3N

Space for rough work

Page 6: RET–7 FIITJEE RET – 7fiitjeehyderabad.com/documents/SFD/RET-7 Jr QP_C.pdfFIITJEE RET – 7 (2017 – 2019)(1ST ... An inclined plane makes an angle of 300 with the horizontal

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FIITJEE (Hyderabad Classes) Limited., 5-9-14/B, Saifabad, (Opp. Secretariat) Hyderabad–500 063. Phone: 040-66777000-03 Fax: 040-66777004

15. In figures, the blocks A, B and C of mass m

each have acceleration 1 2a ,a and 3a ,

respectively, 1F and 2F are external force of

magnitude 2mg and mg, respectively. Then (A) 1 2 3a a a (B) 1 2 3a a a

(C) 1 2 3a a a (D) 1 2 3a a a

16. For the system shown in the figure, there is no friction anywhere.

Masses 1m and 2m can move up or down in the slots cut in mass M.

Two non –zero horizontal forces 1F and 2F ( 1 2F F ) are applied as

shown. The pulleys are massless and frictionless. Given

1 2m m then which of the following is / are correct

(A) It is not possible for the entire system to be in equilibrium (B) For some values of 1F and 2F , it is possible that entire system is

in equilibrium (C) It is possible that 1F and 2F are applied in such a way that 1m and

2m remain in equilibrium but M does not.

(D) None of the above 17. Small blocks A and B are simultaneously released from apex

of a smooth wedge as shown in figure. Select correct alternative(s)

(A) Relative acceleration of block B with respect to block A is zero (B) Magnitude of relative acceleration of block B with respect to block A is ‘g’ initially (C) Speed of block A and B will be same at the bottom of inclined plane (D) The time taken by A and B to reach the bottom of inclined plane will be same

Space for rough work

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FIITJEE (Hyderabad Classes) Limited., 5-9-14/B, Saifabad, (Opp. Secretariat) Hyderabad–500 063. Phone: 040-66777000-03 Fax: 040-66777004

18. Consider an infinite mass – pulley system

as shown. If this system is now released then

(A) The acceleration 1'a ' is g/2

(B) The acceleration 1'a ' is g/3

(C) Tension 1

3mgT

2

(D) Tension 1

4mgT

3

SECTION 3 (Maximum Marks: 16) This section contains TWO questions. Each question contains two columns, Column I and Column II Column I has four entries (A), (B), (C) and (D) Column II has five entries (P), (Q), (R), (S) and (T) Match the entries in Column I with the entries in Column II One or more entries in Column I may match with one or more entries in Column II. The ORS contains a 4 5 matrix whose layout will be similar to the one shown below:

(A) (P) (Q) (R) (S) (T) (B) (P) (Q) (R) (S) (T) (C) (P) (Q) (R) (S) (T) (D) (P) (Q) (R) (S) (T)

For each entry in Column I, darken the bubbles of all the matching entries. For example, if entry (A) in Column I matches with entries (Q), (R) and (T), then darken these three bubbles in the ORS. Similarly, for entries (V), (C) and (D). Marking entry in Column I.

+2 If only the bubble(s) corresponding to all the correct match (s) is (are) darkened. 0 If none of the bubbles is darkened. –1 In all other cases.

Space for rough work

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FIITJEE (Hyderabad Classes) Limited., 5-9-14/B, Saifabad, (Opp. Secretariat) Hyderabad–500 063. Phone: 040-66777000-03 Fax: 040-66777004

19 Column I gives four different situations involving two blocks of mass 1 2m and m placed in different ways

on smooth horizontal surface as shown. In each of the situations, horizontal force 1 2F and F are applied on

blocks of mass 1m and 2m , respectively and also 2m 1 1 2F m F . Match the statements in column I with the

corresponding results in column II Column – I Column – II

(A)

Both the blocks are connected by the

massless inelastic string. The magnitude of tension in the string is

(p) 1 2 1 2

1 2 1 2

m m F F

m m m m

(B)

m1 m2 F2 F1

Both the blocks are connected by the massless inelastic string. he magnitude of tension in the string is

(q) 1 2 1 2

1 2 1 2

m m F F

m m m m

(C)

m1 m2

F2 F1

The magnitude of normal reaction between the

blocks is

(r) 1 2 2 1

1 2 2 1

m m F F

m m m m

(D)

m1 m2

F2 F1

The magnitude of normal reaction

between the blocks is

(s) 1 21 2

1 2

F Fm m

m m

(t) 1 21 2

1 2

F Fm m

m m

Space for rough work

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20. Match the following

In column-I, different systems are shown. Match them with numerical values of accelerations given in column II. Consider all the surfaces smooth

Column I Column II

A)

A uniform rope of length 10 m and mass 5 kg is placed on a smooth fixed wedge as shown. Initially rope is released from rest. Both ends are at same horizontal level. Then initial acceleration of the rope is ________

37a = 53b=

P) 22 /m s

B) block is not slipping over the wedge Then acceleration of the block ‘A’ is ________

A

m

m

37o

m

Q) 3.33 2/m s

C)

A waterjet of cross sectional area 4 210 m- , moving with velocity of 10 m/s hits a vertical plate and comes to rest. If mass of plate is 5 kg, initial acceleration of plate is _______

R) 10 2/m s

D)

m

A

4m

Acceleration of block ‘A’ is _____

S) 8 2/m s

T) 2 /zero m s

Space for rough work

Page 10: RET–7 FIITJEE RET – 7fiitjeehyderabad.com/documents/SFD/RET-7 Jr QP_C.pdfFIITJEE RET – 7 (2017 – 2019)(1ST ... An inclined plane makes an angle of 300 with the horizontal

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FIITJEE (Hyderabad Classes) Limited., 5-9-14/B, Saifabad, (Opp. Secretariat) Hyderabad–500 063. Phone: 040-66777000-03 Fax: 040-66777004

PART II: CHEMISTRY SECTION 1 (Maximum Marks: 32)

This section contains EIGHT questions. The answer to each question is a SINGLE DIGIT INTEGER ranging from 0 to 9, both inclusive. For each question, darken the bubble corresponding to the correct integer in the ORS. Marking scheme:

+4 If the bubble corresponding to the answer is darkened. 0 In all other cases.

21. In the reaction, 4 2 34A 2B 3C A B C , the number of moles of product formed, starting from 1.5 mol of

A, 0.8 mol of B and 0.9 mol of C is X. Then the value of 10X is 22. Hydrazine reacts with KIO3 in the presence of HCl as

2 4 3 2 2N H IO 2H Cl ICl N 3H O

The number of equivalents of N2H4 present in 40g of it is ____ 23. In the manufacture of 2 4H SO from iron pyrites 2FeS following reaction takes place.

2 2 2 3 24FeS 11O 2Fe O 8SO

2 2 32SO O 2SO

3 2 2 4SO H O H SO

How many mole of iron pyrites is required for the formation of 196 grams of sulphuric acid?

24. Consider the following reaction 2 3 3 2 3 4 2 43As S 28HNO 4H O 6H AsO 9H SO 28NO

If the moles of electrons are lost by 1mole of 2 3As S is x, then what is the value of x/4?

25. If the number of litres of liquid CCl4 (density = 1.5g/ml) must be measured out to contain

1 1025 CCl4 molecules, is equal to y. Then what is the value of y/0.25? 26. The hydrated salt Na2CO3. xH2O undergoes 46% loss is mass on heating and becomes anhydrous. The

value of ‘x’ is 27. When the following redox reaction Cr2O7

2– + 14H+ + xCl– 2Cr3+ + Cl2 + 7H2O is balanced, what is the value of x/2.

28. The molarity of 18% w

v

aqueous solution of urea is 0.6 x. What is the value of x ?

Space for rough work

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FIITJEE (Hyderabad Classes) Limited., 5-9-14/B, Saifabad, (Opp. Secretariat) Hyderabad–500 063. Phone: 040-66777000-03 Fax: 040-66777004

SECTION 2 (Maximum Marks: 40)

This section contains TEN questions. Each question has FOUR options (A), (B), (C) and (D). ONE OR MORE THAN ONE of these four option(s) is

(are) correct. For each question, darken the bubble(s) corresponding to all the correct option(s) in the ORS. Marking scheme:

+4 If only the bubble(s) corresponding to all the correct option(s) is (are) darkened. 0 If none of the bubbles is darkened. –2 In all other cases

29. 1gm of mg was burnt in a closed vessel containing 2gm oxygen. Which of the following are not correct ? (A) 0.25 gm of Mg will be left unburnt (B) 1.33 gm of O2 will be left unreacted (C) 2.5 gm of MgO will be formed (D) The mixture at the end will have a total weight of 3gm 30. When equimolar mixture of Cu2S and CuS is titrated with 4 2

Ba MnO in acidic medium. The final products

contain Cu2+, SO2 and Mn2+. If the mol. Wt of Cu2S, CuS and Ba(MnO4)2 are M1, M2 and M3 respectively then.

(A) Eq. wt of Cu2S is 1M

8 (B) Eq. wt of CuS 2M

6

(C) Eq. wt of Ba 4 2MnO is 3M

5 (D) Cu2S and CuS both have same n–factor

31. If 1 litre of 1 M H3PO4 is reacted with 1 litre of 1M X(OH)2 as : 3 4 4 22

H PO X OH XHPO 2H O then :

(A) The equivalent weight of base is mol.wt.

2

(B) The eq. wt. of H3PO4 is 98

3

(C) The resulting solution is required 1 mole NaOH for complete neutralization (D) 1 mole of X(OH)2 more required for complete neutralization of XHPO4. 32. Which molecules are representing the underlined atoms in their highest oxidation state ? (A) H2S2O8 (B) P4O10 (C) CrO2Cl2 (D) Mn2O7 33. An oxide of nitrogen has 30.43% nitrogen (At. Wt .of N = 14) and its one molecule weight 1.527 x 10–22g.

Which of the following statement regarding the oxide is (are) true ? (A) Its empirical formula is N2O (B) Its empirical formula is NO2 (C) its molecular formula is N2O4 (D) Its molecular formula is N4O2

Space for rough work

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34. 100 ml of H2O2 is oxidised to O2 by 100 ml of 0.01 M KMnO4 in acidic medium (MnO 4 reduced to 2Mn ).

100 ml of same H2O2 is oxidised to O2 by V ml of 0.01 M KMnO4 in basic medium (MnO 4 reduced to

MnO2). Hence V is : (A) 500 (B) 100 (C) 100/3 (D) 500/3 35. Which of the following represents redox reactions?

(A) 2 22 7 4 2Cr O 2OH 2CrO H O

(B) 4 4Zn CuSO ZnSO Cu

(C) 24 2 22MnO 3Mn 4OH 5MnO 2H O

(D) 22Cu Cu Cu

36. For the reaction : I2 + NaOH NaIO3 + NaI + H2O. Identify the correct statements ( At wt. of Na = 23) (A) Reaction is an example of disproportionation

(B) Equivalent weight of 2 23

I mol.wtof I5

(C) Eq. wt of NaOH in the reaction is 6.66 (D) Eq. wt of NaOH in the reaction is 48 37. In which of the following compounds, the halogen atom exists in a positive oxidation state ? (A) OCl2 (B) OF2 (C) OBr2 (D) ClO2 38. 1 mole of H2SO4 can be completely neutralized by (A) 2 mole of NaOH (B) 2 mole of Ca(OH)2 (C) 1 mole of Ba(OH)2 (D) 1 mole of Ca(OH)2

SECTION 3 (Maximum Marks: 16)

This section contains TWO questions. Each question contains two columns, Column I and Column II Column I has four entries (A), (B), (C) and (D) Column II has five entries (P), (Q), (R), (S) and (T) Match the entries in Column I with the entries in Column II One or more entries in Column I may match with one or more entries in Column II. The ORS contains a 4 5 matrix whose layout will be similar to the one shown below:

(A) (P) (Q) (R) (S) (T) (B) (P) (Q) (R) (S) (T) (C) (P) (Q) (R) (S) (T) (D) (P) (Q) (R) (S) (T)

For each entry in Column I, darken the bubbles of all the matching entries. For example, if entry (A) in Column I matches with entries (Q), (R) and (T), then darken these three bubbles in the ORS. Similarly, for entries (V), (C) and (D). Marking entry in Column I.

+2 If only the bubble(s) corresponding to all the correct match (s) is (are) darkened. 0 If none of the bubbles is darkened. –1 In all other cases.

Space for rough work

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39. Match the underlined substance in the reactions listed in column I with their equivalent masses listed in

column II.(M = molecular mass of the substance in question) Column – I Column – II

(A) 22 4 2 7FeC O Cr O H Pr oducts (p)

M

6

(B) 3 4 4Fe O MnO H Pr oducts (q)M

2

(C) 2 4 4KHC O MnO H Pr oducts (r) M

(D) 22 2 2 7H O Cr O H products (s)

M

3

40.

Column – I Column – II

(A) Molecular weight

Eq. wt.33

(p) When CrI3 oxidises into 22 7Cr O and 4IO

(B) Molecular weight

Eq. wt.27

(q)When Fe(SCN)2 oxidises into Fe3+, 2

4SO , 23CO and 3NO

(C) Molecular weight

Eq. wt.61

(r) When NH4SCN oxidizes into 2

4SO , 23CO

and 3NO

(D) Molecular weight

Eq. wt.24

(s) When K4[Fe(CN)6] oxidizes into K+, Fe3+,

23CO and 3NO

Space for rough work

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PART III: MATHEMATICS SECTION 1 (Maximum Marks: 32)

This section contains EIGHT questions. The answer to each question is a SINGLE DIGIT INTEGER ranging from 0 to 9, both inclusive. For each question, darken the bubble corresponding to the correct integer in the ORS. Marking scheme:

+4 If the bubble corresponding to the answer is darkened. 0 In all other cases.

41. The position vectors of the points A, B, C and D are ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ3i 2 j k, 2i 3 j 4k, i j 2k and 4i 5 j k . It is

known that these points are coplanar, then the value of 17

73

must be

42. 1 2ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆa i j k, b 4i 3 j 4k and c i x j x k

are coplanar vectors and c

= 2, then the value of 2x1

2 +

3x2 must be

43. ABCD is parallelogram. If L and M are the middle points of BC and CD, then k

AL AM AC2

, then the

value of k is

44. If G is the centroid of the triangle ABC, then GA GB GC

= 45. If M and N are the mid points of the diagonals AC and BD respectively of a quadrilateral ABCD, then

AB AD CB CD

= kMN, then the value of k is

46. If the vectors ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆa i j k, i bj k and i j ck (a b c 1) are coplanar, then the value of

1 1 1

1 a 1 b 1 c

.

47. The value of a such that the vectors ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ2i j k, i 2 j 3k and 3i aj 5k are coplanar, is p, then the value

of |p| is 48. In a OAB, E is the mid point of OB and D is a point on AB such that AD : DB = 2 : 1. If OD and AE

intersect at P, then the ratio OP : PD is 3 : k, then the value of k is

Space for rough work

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SECTION 2 (Maximum Marks: 40) This section contains TEN questions. Each question has FOUR options (A), (B), (C) and (D). ONE OR MORE THAN ONE of these four option(s) is

(are) correct. For each question, darken the bubble(s) corresponding to all the correct option(s) in the ORS. Marking scheme:

+4 If only the bubble(s) corresponding to all the correct option(s) is (are) darkened. 0 If none of the bubbles is darkened. –2 In all other cases

49. The two vectors ˆ ˆ ˆ ˆ ˆ ˆa 2i j 3k, b 4i j 6k

are parallel if is equal to

(A) 2 (B) –3 (C) 3 (D) –2

50. In a triangle ABC, if 2

CB3AC , then

OB3OA2 equals

(A)

OC5 (B)

OC (C)

OC (D) None of these

51. If kjia

, k4j3i4b

and kjic

are linearly dependent vectors and

c

= 3 , then

(A) =1, = – 1 (B) = 1, = 1 (C) = –1, = 1 (D) = 1, = 1

52. Let a, b, c be three non coplanar vectors such that 1r a b c , 2r b c a ,

3r a b c , 4r 2a 3 b 4c . If 14 1 2 2 3 3r p r p r p r then

(A) 1p 7 (B) 1 3p p 3 (C) 1 2 3p p p 4 (D) 2 3p p 0

53. If (x, y, z) (0, 0, 0) and ˆ ˆ ˆi j 3k x 3i 3j k y 4i 5j z xi y j zk where ˆi, j,k are unit

vectors along the coordinate axes, then (A) = 0 (B) = 2 (C) = 1 (D) = –1 54. If ABC is a triangle with sides a, b, c, O, G, H and I be its circumcentre, centroid, orthocentre and incentre

respectively. Answer the following questions. Then OG

is equal to

(A) GH

(B) 1

GH2

(C)

1GH

3

(D) GI

Space for rough work

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55. The unit vector parallel to the resultant of the vectors ˆ ˆ ˆ ˆ ˆ ˆ2i 3 j k and 4i 3 j 2k is

(A) 1 ˆ ˆ6i k37

(B) 1 ˆ ˆ6i j37

(C) 1 ˆ ˆ6 j k37

(D) none of these

56. If a

= (2, 1, –1), b

= (1, –1, 0) and c

= (5, –1, 1), then the unit vector parallel to a b c

, but in the opposite direction is

(A) 1 ˆ ˆ ˆ2i j 2k3

(B) 1 ˆ ˆ ˆ2i j 2k

3 (C) 1 ˆ ˆ ˆ2i j 2k

3 (D) none of these

57. ABC is any triangle and O any point in the plane of the same. If AO, BO and CO meet the sides BC, CA

and AB in D, E, F respectively, then OD OE OF

AD BE CF =

(A) 1 (B) –1 (C) 0 (D) none of these

58. The sides of a parallelogram are ˆ ˆ ˆ ˆ ˆ ˆ2i 4 j 5k and i 2 j 3k . Then the unit vector parallel to one of the

diagonals is

(A) 1 ˆ ˆ ˆ3i 6 j 2k7

(B) 1 ˆ ˆ ˆ3i 6 j 2k7

(C) 1 ˆ ˆ ˆi 2 j 8k69

(D) 1 ˆ ˆ ˆi 2 j 8k69

SECTION 3 (Maximum Marks: 16)

This section contains TWO questions. Each question contains two columns, Column I and Column II Column I has four entries (A), (B), (C) and (D) Column II has five entries (P), (Q), (R), (S) and (T) Match the entries in Column I with the entries in Column II One or more entries in Column I may match with one or more entries in Column II. The ORS contains a 4 5 matrix whose layout will be similar to the one shown below:

(A) (P) (Q) (R) (S) (T) (B) (P) (Q) (R) (S) (T) (C) (P) (Q) (R) (S) (T) (D) (P) (Q) (R) (S) (T)

For each entry in Column I, darken the bubbles of all the matching entries. For example, if entry (A) in Column I matches with entries (Q), (R) and (T), then darken these three bubbles in the ORS. Similarly, for entries (V), (C) and (D). Marking entry in Column I.

+2 If only the bubble(s) corresponding to all the correct match (s) is (are) darkened. 0 If none of the bubbles is darkened. –1 In all other cases.

Space for rough work

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59. Consider the triangle formed by the lines y + 3x + 2 = 0, 3y – 2x – 5 = 0, 4y + x – 14 = 0

Column I Column II(A) Value of a if (0, ) lies inside

triangle

p. 7 13, ,3 4

(B) Values of a if (, 0) lies inside triangle

q. 4 1

3 2

(C) Value of a if (, 2) lies inside triangle

r. No value of

(D) Value of a if (1, ) lies outside triangle

s. 5 7

3 2

60.

Column I Column II (A) If lines 3x + y – 4 = 0, x – 2y – 6 = 0 and x + 4y + 2 = 0 are concurrent,

then value of is p. –4

(B) If the points ( + 1, 1), (2 + 1, 3) and (2 + 2, 2) are collinear, then the value of is

q. 1

2

(C) If line x + y – 1 –

2

= 0, passing through the intersection of x – y + 1 = 0

and 3x + y – 5 = 0, is perpendicular to one of them, then the value of is

r. 4

(D) If line y – x – 1 + = 0 is equidistant from the points (1, –2) and (3, 4), then is

s. 3

Space for rough work

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FIITJEE RET – 7

(2017 – 2019)(1ST YEAR_REGULAR) IIT‐2015 (P1)_SET–A DATE: 21.08.2017

ANSWERS PHYSICS

1. 5 2. 8 3. 5 4. 4

5. 5 6. 6 7. 6 8. 4

9. C 10. BONUS 11. A, C 12. A, B, C, D

13. A, D 14. A, D 15. A, C 16. A

17. B, C 18. A, C 19. A q, B r, C BONUS, D r

20. A t, B q, C p, D r

CHEMISTRY

21. 3 22. 5 23. 1 24. 7

25. 7 26. 5 27. 3 28. 5

29. A, C 30. A, B 31. A, C 32. A, B, C, D

33. B, C 34. D 35. B, C, D 36. A, B, D

37. A, C, D 38. A, C, D

39. BONUS 40. A q ; B p ; C s ; D r

MATHEMATICS

41. 2 42. 7 43. 3 44. 0

45. 4 46. 1 47. 4 48. 2

49. D 50. A 51. D 52. B, C

53. BONUS 54. B 55. A 56. B

57. A 58. A, D 59. A s; B r; C q; D p,q

60. A p ; B Bonus; C p, r; D Bonus

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FIITJEE RET – 7

(2017 – 2019)(1ST YEAR_REGULAR) IIT‐2015 (P1)_SET–B DATE: 21.08.2017

ANSWERS PHYSICS

1. 5 2. 6 3. 6 4. 4

5. 5 6. 8 7. 5 8. 4

9. A, D 10. A, C 11. A 12. B, C

13. A, C 14. C 15. Bonus 16. A, C

17. A, B, C, D 18. A, D 19. A t, B q, C p, D r

20. A q, B r, C Bonus, D r

CHEMISTRY

21. 7 22. 5 23. 3 24. 5

25. 3 26. 5 27. 1 28. 7

29. D 30. B, C, D 31. A, B, D 32. A, C, D

33. A, C, D 34. A, C 35. A, B 36. A, C

37. A, B, C, D 38. B, C 39. A q ; B p ; C s ; D r

40. Bonus

MATHEMATICS

41. 4 42. 1 43. 4 44. 2

45. 2 46. 7 47. 3 48. 0

49. B 50. A 51. B 52. A

53. A, D 54. D 55. A 56. D

57. B, C 58. A, D 59. A p; B Bonus; C p, r; D Bonus

60. A s; B r; C q; D p, q

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