iit-jee mock 1_paper i

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IIT-JEE Mock Test – 1 (Paper – I) Time : 3 Hours Maximum Marks : 252 Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose. INSTRUCTIONS A. General 1. This booklet is your Question Paper containing 84 questions. The booklet has 27 pages. 2. The question paper Test ID is printed on the left hand top corner of this page. 3. The question paper contains blank spaces for your rough work. No additional sheets will be provided for rough work. 4. 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. 5. Fill in the boxes provided below on this page and also write you Name and Enrollment ID in the space provided on the back page of this booklet. 6. The answer sheet, a machine-readable Objective Response Sheet (ORS), is provided separately. 7. DO NOT TAMPER WITH/ MUTILATE THE ORS OR THE BOOKLET. 8. Do not break the seals of the question-paper booklet before being instructed to do so by the invigilators. B. Filling the ORS: 9. Please read the instruction box printed in the OMR sheet. 10. Make sure to fill in your name, Enrollment ID, Date of birth, gender on side 1 and complete of side 2 of the OMR sheet before proceeding. Use HB pencil only. C. Question paper format D. Marking scheme Read the instructions printed on the back page of this booklet. DO NOT BREAK THE SEAL WITHOUT BEING INSTRUCTED TO DO SO BY THE INVIGILATOR Name of the Candidate I have read all the instructions and shall abide by them. ........................................................ Sig nature of the Candidate Enrollment ID I have verified all the information filled in by the Candidate in OMR. ........................................................ Sig nature of the Invi g ilator

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Page 1: Iit-jee Mock 1_paper i

IIT-JEEMock Test – 1 (Paper – I)

Time : 3 Hours Maximum Marks : 252

Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose.

INSTRUCTIONSA. General

1. This booklet is your Question Paper containing 84 questions. The booklet has 27 pages.

2. The question paper Test ID is printed on the left hand top corner of this page.

3. The question paper contains blank spaces for your rough work. No additional sheets will be provided

for rough work.

4. 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.

5. Fill in the boxes provided below on this page and also write you Name and Enrollment ID in the

space provided on the back page of this booklet.

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

7. DO NOT TAMPER WITH/ MUTILATE THE ORS OR THE BOOKLET.

8. Do not break the seals of the question-paper booklet before being instructed to do so by the

invigilators.

B. Filling the ORS:

9. Please read the instruction box printed in the OMR sheet.

10. Make sure to fill in your name, Enrollment ID, Date of birth, gender on side 1 and complete of side2 of the OMR sheet before proceeding. Use HB pencil only.

C. Question paper format

D. Marking schemeRead the instructions printed on the back page of this booklet.

DO

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TH

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EA

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ITH

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T B

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G IN

ST

RU

CT

ED

TO

DO

SO

BY

TH

E IN

VIG

ILA

TOR

Nam e of the Candidate

I have read all the instructions and shall ab ide by them .

........................................................Signature of the Candidate

Enrollment ID

I have verified all the inform ationfilled in by the Candida te in OM R.

.... .. ... .. ... .. .. ... .. ... .. .. ... .. .. ... .. ... .. .. ... .. ..Signature of the Invigilator

Page 2: Iit-jee Mock 1_paper i

C. Question Paper Format:

11. The question paper consists of 3 Parts (Chemistry, Mathematics and Physics), and each Partconsists of four Sections.

12. Section–I contains 8 multiple choice questions. Each question has 4 choices (a), (b), (c) and (d) forits answer, out of which only one is correct.

13. Section–II contains 5 multiple choice questions. Each question has 4 choices (a), (b), (c) and (d)for its answer, out of which one or more is/are correct.

14. Section–III contains 2 groups of questions. One group has 3 questions and second group has2 questions based on a paragraph. Each question has 4 choices (a), (b), (c) and (d) for its answer,out of which only one is correct.

15. Section–IV contains 10 questions. The answer to each of the questions is a single-digit integer,ranging from 0 to 9. The answer will have to be appropriately bubbled in the ORS as per the instructionsgiven at the beginning of the section.

D. Marking Scheme:

16. For each question in Section I: you will be awarded 3 marks if you have darkened only the bubblecorresponding to the correct answer and zero mark if no bubbles are darkened. In all other cases,minus two (–2) mark will be awarded.

17. For each question in Section II, you will be awarded 3 marks if you darken only the bubblecorresponding to the correct answer and zero mark if no bubbles are darkened. No negative markswill be awarded in this section.

18. For each question in Section III: you will be awarded 3 marks if you darken only the bubblecorresponding to the correct answer and zero mark if no bubbles are darkened. In all other cases,minus one (–1) mark will be awarded.

19. For each question in Section IV: you will be awarded 3 marks if you darken the bubble correspondingto the correct answer and zero mark if no bubble is darkened. No negative marks will be awardedfor in this section.

Note: Fill all the data correctly in OMR sheet otherwise it will not be checked.

Corporate Office / Registered Office

Corporate Office: Career Launcher India Limited.15A, Knowledge Park – II, Greater Noida, UP

Registered Office: R – 90, Greater Kailash – 1, New Delhi

Website: www.careerlauncher.com

Page 3: Iit-jee Mock 1_paper i

Page 1Mock Test–1 / Paper–I

ChemistryPart – ISection – I

Single Correct Choice Type

This section contains 8 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) outof which ONLY ONE is correct.

1. 0.7 gm of Na2CO3.xH2O is dissolved in 100 ml of water, 20 ml which required 19.8 ml of 0.1NHCl forcomplete neutralisation. The value of x is(a) 4 (b) 3 (c) 2 (d) 1

2. If the radius of first Bohr orbit is r, the wavelength of an electron in the third orbit of a hydrogen atomis equal to

(a) 6 rπ (b) 2 rπ (c) 9 rπ (d) 3r

3. If the salts M2X, QY2 and PZ3 have same solubilities 4

27 <

, their Ksp value are related as

(a) ( ) ( ) ( )sp 2 sp 2 sp 3K M X K QY K PZ= > (b) ( ) ( ) ( )sp 2 sp 2 sp 3K M X K QY K PZ> =

(c) ( ) ( ) ( )sp 2 sp 2 sp 3K M X K QY K PZ= = (d) ( ) ( ) ( )sp 2 sp 2 sp 3K M X K QY K PZ> >

4. The rate of reaction gets doubled when temperature changes from 7° to 17°C. By what factor will itchange when the temperature change from 17°C to 27°C (log 1.91 = 0.28)(a) 2 (b) 2.1 (c) 1.91 (d) 2.3

5. The EMF of the following cell is 0.265 V at 25°C and 0.2595 V at 35°CPt (H2)|HCl (aq) | | AgCl | AgThe heat of reaction, taking place at 25°C is(a) –90.8 kJ (b) –80.8 kJ (c) –82.8 kJ (d) + 35.5 kJ

Space for rough work

Page 4: Iit-jee Mock 1_paper i

Mock Test–1 / Paper–IPage 2

Chemistry

6. Which of the following statement is correct about the folowing equilibrium

( ) ( ) ( )3 2 2

1NaNO s NaNO s O g

2+

(a) on addition of NaNO3 the equilibrium shifts in forward direction(b) on addition of NaNO2 the equilibrium shifts in backward direction(c) on addition of O2 the equilibrium shifts in backward direction(d) All of these

7. In which of the following both compounds of the pair has p pπ − π back bonding(a) SiCl4 and N(SiH3)3 (b) BF3 and BCl3(c) N(SiH3)3 and N(CH3)3 (d) SiF4 and SiO2

8.O H –

(X) CH =CH–P P h B r2 3

+

(Y)CHO

OH

Product (Y) of the above reaction is

(a) O

(b) O

(c)

OH

(d) OH

Space for rough work

Page 5: Iit-jee Mock 1_paper i

Page 3Mock Test–1 / Paper–I

ChemistrySection – IIMultiple Correct Choice Type

This section contains 5 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) outof which ONE OR MORE may correct.

9. Which among the following statement is/are correct (assuming H

a H++ = )

(a) 10pH log H+ = − (b) pH decreases with increase of temperature(c) pH can not be zero, negative or more than 14(d) If a solution is diluted ten times, its pH increases by 1

10. Which is/are property/properties of ethanenitrile(a) It gives carbylamine reaction with chloroform(b) It undergoes acidic hydrolysis to give methylisocyanide(c) It undergoes acidic hydrolysis to give carboxylic acid(d) It undergoes alkaline hydrolysis to give salt of carboxylic acid

11. 3NaCN/BH6 5 2 2 3methanol

P Q C H CH NHCH CH+ →(a) P is C6H5CHO (b) Q is C2H5NH2

(c) P is C6H6 (d) Q is CH3NHCH2CH3

Space for rough work

Page 6: Iit-jee Mock 1_paper i

Mock Test–1 / Paper–IPage 4

Chemistry

12. Which of following can give CO2 as one of the byproduct of the reaction on heating alone or withmetal oxide?

(a) CH 2

CH –COO H2

CH –COO H2

(b) C H 2

C O O H

C O O H(c)

COO HCOO H

COO H(d)

C H –C H – C O O H2 2

C H –C H – C O O H2 2

13. The reagent(s) which can be used for the following conversion

NO 2

NO 2

NO 2

NH 2

(a) Aq. ethanolic (NH4)2S (b) Aq. Na2S(c) Pt/H2 (d) Zn | NaOH | C2H5OH

Space for rough work

Page 7: Iit-jee Mock 1_paper i

Page 5Mock Test–1 / Paper–I

ChemistrySection – IIIComprehension Type

This section contains 2 paragraphs. Based upon the first paragraph 3 multiple choice questions andbased upon the second paragraph 2 multiple choice questions have to be answered. Each of thesequestions has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

Passage for Question Nos. 14 to 16Excess of KCN reacts with two different reagent as per the given reaction to make complex having coordinationnumber four.

( ) ( )KCNExcess2

Ni CN complex 1→

( )KCN2 Excess

NiCl complex 2→

14. The IUPAC name of complex 1(a) Potassium tetracyanonicklate (IV) (b) Potassium tetracyanonicklate (II)(c) Potassium tetrachloronicklate (II) (d) Potassium tetrachloronicklate (IV)

15. Which of the following statement is correct about complex (1) and complex (2)(a) Both the complexes are diamagnetic(b) Both the complexes are paramagnetic(c) Complex (1) is diamagnetic and complex (2) is paramagnetic(d) Complex (1) is paramagnetic and complex (2) is diamagnetic

16. The hybridization of central metal atom in complex (1) and complex (2) respectively is(a) sp3 and sp3d2 (b) d2sp3 and dsp2 (c) dsp2 and sp3 (d) sp3 and dsp2

Space for rough work

Page 8: Iit-jee Mock 1_paper i

Mock Test–1 / Paper–IPage 6

Chemistry

Passage for Question Nos. 17 and 18

Stability of alkenes can be compared by converting the compounds to a common product and comapringthe amount of heat given off. One possibility would be to measure heats of combustion. Alkene of lowestheat of combustion among isomeric alkenes is of lowest energy and most stable.The measure of heats of hydrogenation is another possibility to compare the relative stability of isomericalkenes. Heat of hydrogenation is heat given off during catalytic hydrogenation. Lower is the heat ofhydrogenation stable is the alkene. In case of cycloalkenes, cyacloalkanes having more angle strain areless stable.Heats of combustion are large numbers and measuring small difference in these large numbers is difficult.However heats of hydrogenation are smaller numbers and provide more accurate energy difference.

17. The correct match for the following(A) 2-methyl-2-butene (i) 27.6(B) trans-2-pentene (ii) 26.9(C) cis-2-pentene (iii) 30.3(D) 3-methyl-1-butene (iv) 28.6(a) A-(i), B-(iv), C-(ii), D-(iii) (b) A-(ii), B-(i), C-(iv), D-(iii)(c) A-(ii), B-(iv), C-(iii), D-(i) (d) A-(iii), B-(iv), C-(i), D-(ii)

18. Among the following pairs in which case the second compound has higher heat of hydrogenationthan the first

(a),

(b) cis-2-butene, trans-2-butene

(c) , (d) 1-butene, 2-butene

Space for rough work

Page 9: Iit-jee Mock 1_paper i

Page 7Mock Test–1 / Paper–I

ChemistrySection – IVInteger Type

This Section contains 10 questions. The answer to each question is a single digit integer ranging from 0to 9. The correct digit below the question number in the ORS is to be bubbled.

S1. A hydrocarbon contains 10.5 gm of carbon per gm of H. One litre vapours of hydrocarbon at 127°Cand 1 atm pressure weighs 2.8 gm. Find out number of carbon atom(s) in a molecule of hydrocarbon.

S2. The reduction potential diagram for ‘A’ in acid solution is

E° =X volt3

+0 .65 vo lt (E° )1A + +1.35 vo lt (E° )2A 2+ A

Calculate value of X.

S3. For an equilibrium reaction A 2B 2C D;+ + A and B are mixed in a reaction vessel at 300 K. Theinitial concentration of B was 1.5 times the initial concentration of A. At the equilibrium theconcentration of A and D are same. Calculate KC for the above equation.

S4. An electron jumps from a certain Bohr’s orbit of H atom to the 5th orbit. The wave number of radiationemitted is 1340.3 cm–1. The value of principal quantum number of the orbit from which this jump hastaken place (RH = 109670 cm–1) is…

S5. A solution has pH = 5. If one ml of this solution is diluted to 1 litre, then the pH of resulting solutionwill be… (Round off the value to nearby whole number if required)

S6. How many alkene(s) is/are possible with the molecular formula C6H12 each of which gives 3-methylpentane on catalytic reduction?

Space for rough work

Page 10: Iit-jee Mock 1_paper i

Mock Test–1 / Paper–IPage 8

Chemistry

S7. The number of next nearest neighbour ions of Cl– in rock salt structure is/are…

S8. Consider the following reactions

(i) A → C (1st order reaction)At t = 0 2M

(ii) B → D (nth order reaction)At t = 0 1M

When conc. of A was 2M and conc. of B was 1M the t1/2 for each reaction was 5 min. After15 minutes [B] = [A]. The value of ‘n’ is…

S9. The reaction given below yields 0.222 gm CH4(g) when 0.643 gm (CH3)x AlCly is ignited. The residualsolution on treatment with AgNO3(aq) results in 0.996 gm AgCl as white precipitate. Find out the

value of xy .

( ) ( ) ( )3AgNO33 y 4x

CH AlCl xCH g yCl Al y AgCl s− +→ + + →

S10. The cooking gas cylinder is assumed to contain 9.82 kg isobutane having heat of combustion–2658 KJ/mole. If a family needs 15 × 103 KJ energy per day for cooking how long (in months) acylinder can last. [Assume 1 month = 30 days)

Space for rough work

Page 11: Iit-jee Mock 1_paper i

Page 9Mock Test–1 / Paper–I

MathematicsPart – IISection – I

Single Correct Choice Type

This section contains 8 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) outof which ONLY ONE is correct.

1. If the point ( )0,λ is a point of the region bounded by the semicircle 2x 9 y= − and the line x = 0

then the equation 2x 2x 0− − λ = has(a) atleast one real root in [2, 3] (b) at least one real root in [–1, 0](c) two real roots in [–1, 3] (d) no real roots in (0, 2)

2. A particle moving on a curve has the position given by ( ) ( )x f t sin t f t cos t,′ ′′= +

( ) ( )y f t cos t f t sint′ ′′= − at a time ‘t’ where f is a thrice differentiable function. Then the velocity of

the particle at time ‘t’ is

(a) ( )f t′′′ (b) ( ) ( )f t f t′ ′′′+ (c) ( ) ( )f t f t′ ′′+ (d) ( ) ( )f t f t′ ′′′−

3. Let C1, C2, … Cn… be a sequence of concentric circles. The nth circle has the radius ‘n’ and it has‘n’ openings. A point P starts travelling on the smallest circle C1 and leaves it at an opening alongthe normal at the point of opening to reach the next circle C2. Then it moves on the second circle C2and leaves it likewise to reach the third circle C3 and so on. The total number of different paths inwhich the point can come out of the nth circle is(a) 2n . n! (b) 2n–1 . n! (c) n! (d) nn–1 . (n – 1)!

4. If 2, x3 4log 4,

− x 73

2

log 4+ are in H.P. then x is equal to

(a) 1 (b) 2 (c) 4 (d) 0

Space for rough work

Page 12: Iit-jee Mock 1_paper i

Mock Test–1 / Paper–IPage 10

Mathematics

5. The fractional part of the number 333

25 is

(a)3

25(b)

2325 (c)

2225

(d) 8

25

6. If ( )( )2

0 1 2

1a a x a x

1 ax 1 bx= + + +

− − then an equals

(a) n nb ab a

−−

(b)

n na bb a

−− (c)

n 1 n 1a bb a

+ +−− (d)

n 1 n 1b ab a

+ +−−

7. A real valued function f(x) satisfies the functional equation f(x – y) = f(x) f(y) – f(a – x) f(a + y) where‘a’ is a given constant and f(0) = 1. Then f(2a – x) equals(a) f(x) (b) – f(x) (c) f(–x) (d) f(a) + f(a – x)

8. Let A = (3, 4) and B is a variable point on the lines |x| = 6. If AB 4≤ then the number of positions ofB with integral coordinates is(a) 5 (b) 4 (c) 6 (d) 10

Space for rough work

Page 13: Iit-jee Mock 1_paper i

Page 11Mock Test–1 / Paper–I

MathematicsSection – IIMultiple Correct Choice Type

This section contains 5 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) outof which ONE OR MORE may correct.

9. If a, b, c are three consecutive integers then the determinant

2

2

2

a ab ac

ab b bc

ac bc c

−−

− is divisible by

(a) 36 (b) 144 (c) 48 (d) none of these

10. Let a real valued differentiable function f(x) be strictly monotonic on [a, b] then

(a) ( )( ) ( )( ) ( )( )( )

( )b f b2 2 1

a f af x f b dx 2x b f x dx− − = − ∫ ∫

(b) ( )( ) ( )( ) ( )( )( )

( )b f b2 2 1

a f af x f a dx 2x b f x dx− − = − ∫ ∫

(c) ( )b

af x dx∫ exists

(d) ( )b

af x dx∫ doest not exists

11. In a triangle ABC, A and B are (1, –1) and (3, 1) respectively. The equation of perpendicular bisectorof AC is 3x – 2y + 8 = 0 then(a) mid point of AC is (–2, 1) (b) C is (–5, 3)

(c) circumcentre of ABC∆ is 4 14

,5 5

− (d) circumcentre of ABC∆ is (–1, 2)

Space for rough work

Page 14: Iit-jee Mock 1_paper i

Mock Test–1 / Paper–IPage 12

Mathematics

12. The complex number with maximum modulus satisfying z 1 i 1+ − ≤ is

(a) ( ) 3 32 1 cos isin

4 4π π − +

(b) ( ) 3 32 1 cos isin

4 4π π + +

(c)3 3

2 cos isin4 4π π +

(d) ( )11 1 i

2

+ − +

13. A player tosses a coin. He sets one point for head and two points for tail. He is to play on till hereaches n. If Pn pe the probability that his score becomes ‘n’. Then

(a) 2

1P

2= (b) 2

3P

2= (c) 1

1P

2= (d) ( )n n 1 n 2

1P P P

2 − −= +

Space for rough work

Page 15: Iit-jee Mock 1_paper i

Page 13Mock Test–1 / Paper–I

Mathematics

Space for rough work

Section – IIIComprehension Type

This section contains 2 paragraphs. Based upon the first paragraph 3 multiple choice questions andbased upon the second paragraph 2 multiple choice questions have to be answered. Each of thesequestions has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

Passage for Question Nos. 14 to 16

Let S be the set of points in a plane, we define the diameter of the set S as the maximum of the distancesbetween arbitrary pairs of points of S. Thus the diameter d of S′ is given by d = max d(P,Q) where P, Q∈S

14. If S be the set of interior points of an equilateral triangle of side 2 units then the diameter of S mustbe

(a) 1 (b) 2 (c) 2 (d) 3

15. If S be the set of interior points of the ellipse x2 + 2y2 = 4 then diameter of S must be

(a) 2 (b) 2 (c) 1 (d) 4

16. The diameter of the set of points forming a square of side ‘a’ must be

(a) a (b) 2a (c) a 2 (d) a

2

Page 16: Iit-jee Mock 1_paper i

Mock Test–1 / Paper–IPage 14

Mathematics

Space for rough work

Passage for Question Nos. 17 and 18

Using the standard trigonometric inequality sinx < x < tanx where 0 x2π< < we can prove several other

inequalities. It must be noted that (0, 1) is a proper subset of 0,2π

17. If a = cos (sinx), b = sin (cosx) then(a) a > b for all x (b) a < b for all x

(c) a > b in 0,2π

and a < b in ,

4 2π π

(d) a < b in 0,

and a > b in ,

4 2π π

18. If 0 x2π< < then

(a) log (sinx + cosx) < x (b) log (sinx + cosx) >x(c) log (sinx + cosx) > x2 (d) None of these

Page 17: Iit-jee Mock 1_paper i

Page 15Mock Test–1 / Paper–I

Mathematics

Space for rough work

Section – IVInteger Type

This Section contains 10 questions. The answer to each question is a single digit integer ranging from 0to 9. The correct digit below the question number in the ORS is to be bubbled.

S1. There is a point from which length of the tangent drawn to the three circles 2x2 + 2y2 + x +7y+3 = 0,2x2 + 2y2 – 3x + 5y + 9 = 0 and x2 + y2 + y = 0 are equal. This length must be

S2. The k is the number of values taken by the function f(x) = [x2] + [2x2] over [0, 1] (where [ ] denotesgreatest integer less than or equal to x), then ‘k’ must be equal to

S3. If a and b

are non-collinear vectors, then the point of intersection of the lines r a 2b= − + λ ( )b 2a+

and ( )r 2a b a 2b= − + µ +

is ( )ka b

3−

; then the numerical quantity ‘k’ must be

S4. Vector x,y and z

each of magnitude 2, make angle of 60° with each other. If ( )x y z a× × =

,

( )y z x b× × =

and x y c,× =

then ( )b a a b c

z ,2

− λ + + ×=

‘ λ ’ must be

S5. If 9

x4

= is a solution of the inequation ( ) ( )2 2a alog x x 2 log x 2x 3 .− − > − + + Then the other solutions

lie in the interval 5

k, ,2

‘k’ must be equal to

Page 18: Iit-jee Mock 1_paper i

Mock Test–1 / Paper–IPage 16

Mathematics

S6. If 2 i / 7e πα = and ( )20

k0 k

k 1

f x A A x=

= + ∑ then the value of ( ) ( ) 2 6f x f x f( x) f( x)+ α + α + α is

k(A0 + A7x7 + A14x

14) then ‘k’ must be equal to

S7. Consider n × n graph paper where ‘n’ is a natural number. Consider the right angled isoscelestriangle whose vertices are integer points of this graph and whose sides forming right angle are

parallel to x and y-axis. If the number of such triangles is ( )( )2n n 1 2n 1

k+ + then the numerical

quantity ‘k’ must be

S8. Two sides of a triangle are of lengths 6 and 4 and the angle opposite to smaller side is 30°. If the

possible areas of the triangle are equal to 2 k 2,± then the numerical quantity ‘k’ must be equal

to

S9. The ordinates of two points on the parabola y2 = 12x are in the ratio 1 : 2. If the locus of point of

intersection of normals at these points is 2 / 3

yx 3 7 2 ,

k

= + then the numerical quantity ‘k’ should

be

S10. If the line y = 2x + a neither intersects nor touches the circles x2 + y2 – 2x – 2y + 1 = 0 and x2 + y2

– 16x – 2y + 61 = 0 and the circles lie on the opposite side of the line then ‘a’ must lie in the interval

( )2 5 k, 5 1 ;− − − the numerical quantity ‘k’ must be equal to

Space for rough work

Page 19: Iit-jee Mock 1_paper i

Page 17Mock Test–1 / Paper–I

PhysicsPart – IIISection – I

Single Correct Choice Type

This section contains 8 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) outof which ONLY ONE is correct.

1. At t = 0, a particle (of mass m) is projected on a horizontal plane (making some angle with thehorizontal) with velocity v

. Which of these is the expression of the radial force acting on the particleat any time t, when the particle is airborne

(a)( )mg v gt

v gt

−−

(b) ( )mg v gt

v gt

++

(c) ( )mg v gt

mgv gt

+−

+

(d)

( )mg v gtmg

v gt

−−

2. Water is flowing through a horizontal truncated cone having radii at the ends as 0.1m and 0.01m andpressure drop across the length is 5N/m2. The rate of flow of water approximately is (Neglect

viscosity, density of water = 3 310 kg /m )

(a) kg / s10π

(b) kg / s100

π(c) 10 kg/ sπ (d) kg / s

3. Temperature pressure graph for the two gases A and B is shown in the figure. If work done by thegases A and B during the processes shown are WA and WB respectively, then choose the correctstatement

P

T

A

B

(a) WA > WB (b) WA < WB (c) WA = WB (d) Data insufficient

Space for rough work

Page 20: Iit-jee Mock 1_paper i

Mock Test–1 / Paper–IPage 18

Physics

4. In YDSE, one of the slits is covered by a transparent slab, which transmits only 90% of the incidentlight, then select the incorrect statement from the following.

t S 1

S 2

S O

µ

Screen

(a) a maxima can occur at O(b) central maximum position on the screen is the point at which the path difference is zero(c) the point on the screen at which destructive interference occur, intensity will be equal to zero(d) dark fringe will not be formed on the screen

5. A solid conducting sphere of radius 2R, carrying charge Q is surrounded by two point charges Q and2Q as shown in the figure. The electric field at point P due to the charges on conducting sphere is

0

1K

4

= πε

Q

3R 3R

R

O P2Q

(a) 2

7 KQ16 R

towards right (b) 2

1 KQ8 R

towards right

(c) 2

KQR

towards right (d) zero

Space for rough work

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6. ABCA is a cross section of a transparent material of refractive index µ is shown in the figure. One ofits refracting surfaces AC is given by y = x2. A ray of light travelling parallel to x-axis is incidentnormally on the face AB and refracted. The minimum height h of the incident ray from point A to geta refracted ray from surface AC is

y=x 2

CB

Ah

µ

(a) 2h = µ (b) 2h / 3= µ (c) 2 2

h3

µ += (d) 2 1

h4

µ −=

7. A light rod is povited at one end show that it can swing freely as a pendulum. Two masses 2m andm are attached to it at distances b and 3b respectively from the pivot. The rod is held horizontal andthen released. The angular acceleration at the instant it is released is

(a)3mg4b

(b) gb

(c) 5g

11b (d) 11g5b

8. A cylindrical tank of radius 1 m is half filled with water. The axis of the cylinder is horizontal. The tankis given a horizontal acceleration being of 10 m/s2. The acceleration is perpendcular to the axis ofthe cylinder. The maximum value of pressure in the cylinder is

10 m /s 2

Cross sectional view

(a) 1 atm (b) 1.4 atm (c) 1.14 atm (d) 2.4 atm

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Section – IIMultiple Correct Choice Type

This section contains 5 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) outof which ONE OR MORE may correct.

9. Consider a spring block arrangement placed on a rough floor of an elevator accelerating in thedirection as shown. The elevator started accelerating at t = 0, when the spring-block system was atrest with the spring (massless) relaxed.

m

µ= 0.5

E levator

K 45°

2 a = m agnitude ofaccelera tion o f elevator

(a) for g

a ,2

> block slides on the floor of elevator

(b) for a > g, block slides on the floor of elevator

(c) for a = 2g, maximum compression in the spring is mg2K

(d) for a = 2g, maximum compression in the spring is mgK

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10. A particle is projected with speed v0 from the ground by making an angle of 30° with the horizontal.After some time it lands on the ground. Choose the correct statement (s)(a) The average speed of projectile first decreases and then increases(b) Angular momentum of the projectile about the point of projection first increases and then decrease(c) Change in linear momentum of projectile during the time of flight is mv0

(d) Instantaneous angular velocity of projectile when it hits the ground, about the point of projection

is 0

g

3 v

11. Two sound sources, each emitting sound of wavelength ,λ in same phase are placed at a distance

3 ,λ as shown in figure. A detector is moved along a line perpendicular to S1S2. The distance D of

this line from the midpoint of the sources is very large as compared to λ

O

D

S 1 S 2

(a) Total 5 maxima will be observed on the line(b) Total 6 minima will be observed on the line

(c) A maxima will be observed at a distance 5 D2

from point O

(d) A minima will be observed at a distance 5 D2

from point O

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12. A hollow hemispherical bowl of mass m and radius R is hinged at O as shown in figure. Just afterreleasing the hemisphere, choose the correct statement (s)

RO

(a) The moment of inertia of bowl about O is 25

mR3

(b) The angular acceleration of bowl about O will be 3g5R

just after its release

(c) The acceleration of centre of mass will be 3g

2 5

(d) Force exerted by the hinge on the bowl is mg2

13. In a series L-C-R circuit, voltage applied is

v 3sin 314t6π = +

and current from the supply is

i 2sin 314t .3π = +

Which of the following is/are correct?

(a) Impedance of circuit is 1.5Ω (b) Reactance of circuit is 43

Ω

(c) Resistance of circuit is 3 3

4Ω (d) Wattless component of current is

1A

2

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PhysicsSection – IIIComprehension Type

This section contains 2 paragraphs. Based upon the first paragraph 3 multiple choice questions andbased upon the second paragraph 2 multiple choice questions have to be answered. Each of thesequestions has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

Passage for Question Nos. 14 to 16

In the arrangement shown in the figure, the spring is in its natural length l0 and spring constant of the spring

is 0

2mgl . An impulse imparts a horizontal velocity v0 to the block in this position

v 0

14. If v0 is the minimum velocity for which the block loses contact with the base, then the distancecovered by the block before it loses contact is

(a) 0l

2(b) 03 l (c) 03 l

2(d) 02l

3

15. The minimum velocity v0 for which the block will loose contact with the base is

(a)0

gl

(b) 0gl (c) 02gl (d) 0

1gl

2

16. If the spring is replaced by a string, then the net force acting on the block, just after the velocityequal to v0 (found in previous question) is imparted, is

(a) 3 mg (b) 2 mg (c) mg2

(d) mg

Space for rough work

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Passage for Question Nos. 17 and 18

A block of mass m and charge q is attached to a rod of same mass m. The other end of the rod is hingedat O. The system is on a smooth horizontal table. An electric field is switched on in perpendicular directionto rod.

l

l E

Final position

Initial position

17. The speed of the block when rod becomes parallel to the field is

(a) 3qEl2m

(b) 2qEl3m (c)

qElm

(d) 2qEl5m

18. The tension developed at midpoint of the rod when rod becomes parallel to the field is

(a) 49

qE16

(b) 33

qE8

(c) 5

qE3

(d) q

qE2

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Section – IVInteger Type

This Section contains 10 questions. The answer to each question is a single digit integer ranging from0 to 9. The correct digit below the question number in the ORS is to be bubbled.

S1. A body of mass m slips down an inclined plane with a constant velocity. When the same body isprojected up the inclined plane from the bottom with a speed v0 = 10 m/s, find the total displacement(in m) of the body up the plane?

v 0

30°

S2. At any instant the ratio of the amount of two radioactive substances is 2 : 1. If their half lives berespectively 12 and 16 hours, then the ratio of the substances after two days is x : y. Find | x – y |?

S3. A disc of mass m and radius R is subjected to two forces as shown in the figure. If the disc performspure rolling on the horizontal surface, then find the acceleration of the centre of mass (in m/s2) of the

disc. (Take 2F3m / s

m= )?

O

2F

F

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S4. Two capacitors of capacitance 2 fµ and 6 fµ are connected in a circuit as shown in the figure.

Initially both the capacitors are uncharged and switch S1 remains closed for a long time. Now switchS1 is opened and S2 is closed. Find the ratio of heat loss in resistance 2Ω when only switch S1 wasclosed (for a long time) to the heat loss in the same resistance when switch S2 only is closed(for a long time)?

6 Fµ

2 Fµ

S 1

S 2

S5. A ball of mass 0.5 kg is projected with a speed of 5 m/s at an angle of 37° from the horizontal. Whatis the average torque (in Nm) of weight about the point of projection in time 0.6 s?

S6. An ammeter and a voltmeter are connected in series to a battery with an emf E = 6V. When acertain resistance is connected in parallel with the voltmeter, the reading decreases two times whilethe reading of the ammeter increases to same number of times. Find the reading of the voltmeterafter connection of resistance?

Space for rough work

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S7. A particle of mass m is executing oscillations about the origin, on the x-axis. Its potential energy isU(x) = K | x |3 where K is some positive constant. If the amplitude of oscillation is ‘a’, then itsmaximum speed is proporitonal to ax/y. Here x and y are integers. Find (x + y)?

S8. The ends of a stretched wire of length L are fixed at x = 0 and x = L. In one experiment, the

displacement of the wire is 1

xy A sin sin t

Lπ = ω

and energy is E1 and in another experiment, its

displacement is 2

3 xy A sin sin3 t

Lπ = ω

and energy is E2. Then 2

1

E

E is

S9. n moles of an ideal gas undergoes a process in which the temperature changes with volume asT = KV2, where K is positive constant. The work done by the gas as the temperautre changes from

T0 to 4T0 is 0nRTx

2

. Find x?

S10. If the potential energy at the surface of the earth is assumed to be zero, the total energy of a moving

satellite at a radius of 2R is given by y GMm

,z R

then ( )y z+ is given by

Space for rough work