Iit-jee Mock 1_paper i

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.

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.

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4.

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5.

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6.

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7.

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8.

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B.

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9.

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10.

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C. D.

Question paper format   Read the instructions printed on the back page of this booklet. Marking scheme 

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INSTRUCTIONS A.

C.

Question Paper Format:

11.

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

12.

Section–I contains 8 multiple choice questions. Each question has 4 choices (a), (b), (c) and (d) for its 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 has 2 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 instructions given 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 bubble corresponding 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 bubble corresponding to the correct answer and zero mark if no bubbles are darkened. No negative marks will be awarded in this section.

18.

For each question in Section III: you will be awarded 3 marks if you darken only the bubble corresponding 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 corresponding to the correct answer and zero mark if no bubble is darkened. No negative marks will be awarded for in this section.

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

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Part – I Section – I Single Correct Choice Type

Chemistry

This section contains 8 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) out of 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 for complete 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 atom is equal to (b) 2πr (c) 9πr (d) 3r (a) 6πr

3.

 4  If the salts M2X, QY2 and PZ3 have same solubilities  <  , their Ksp value are related as  27  (a) K sp (M2 X ) = K sp (QY2 ) > K sp (PZ3 )

(b) K sp (M2 X ) > K sp (QY2 ) = K sp (PZ3 )

(c) K sp (M2 X ) = K sp (QY2 ) = K sp (PZ3 )

(d) K sp (M2 X ) > K sp (QY2 ) > K sp (PZ3 )

4.

The rate of reaction gets doubled when temperature changes from 7° to 17°C. By what factor will it change 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°C Pt (H2)|HCl (aq) | | AgCl | Ag The 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

Mock Test–1 / Paper–I

Page 1

Chemistry 6.

Which of the following statement is correct about the folowing equilibrium

1 O2 ( g ) 2 on addition of NaNO3 the equilibrium shifts in forward direction on addition of NaNO2 the equilibrium shifts in backward direction on addition of O2 the equilibrium shifts in backward direction All of these

NaNO3 (s ) S NaNO2 (s ) + (a) (b) (c) (d) 7.

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

CHO OH–

8.

(X )

+ – C H 2= C H – P P h 3B r

(Y )

OH Product (Y) of the above reaction is (a)

O

(c)

(b) O

(d)

OH

OH

Space for rough work

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Mock Test–1 / Paper–I

Section – II Multiple Correct Choice Type

Chemistry

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

9.

+ Which among the following statement is/are correct (assuming aH+ = H  ) + (a) pH = − log10 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.

NaCN / BH3 P + Q  → C6H5 CH2NHCH2 CH3 methanol

(a) P is C6H5CHO (c) P is C6H6

(b) Q is C2H5NH2 (d) Q is CH3NHCH2CH3

Space for rough work

Mock Test–1 / Paper–I

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Chemistry 12.

Which of following can give CO2 as one of the byproduct of the reaction on heating alone or with metal oxide? (a) C H 2

C H 2 –C O O H C H 2 –C O O H

13.

(b) C H 2

COOH COOH

(c)

COOH COOH COOH

(d)

C H 2– C H 2– C O O H C H 2– C H 2– C O O H

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

NO2

NH2

NO2

NO2

(a) Aq. ethanolic (NH4)2S (c) Pt/H2

(b) Aq. Na2S (d) Zn | NaOH | C2H5OH

Space for rough work

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Mock Test–1 / Paper–I

Section – III Comprehension Type

Chemistry

This section contains 2 paragraphs. Based upon the first paragraph 3 multiple choice questions and based upon the second paragraph 2 multiple choice questions have to be answered. Each of these questions has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct. Passage for Question Nos. 14 to 16 Excess of KCN reacts with two different reagent as per the given reaction to make complex having coordination number four. KCN Ni (CN)2   → complex (1) Excess

KCN NiCl2   → complex (2 ) Excess

14.

The IUPAC name of complex 1 (a) Potassium tetracyanonicklate (IV) (c) Potassium tetrachloronicklate (II)

(b) Potassium tetracyanonicklate (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 (b) d2sp3 and dsp2 (c) dsp2 and sp3 (d) sp3 and dsp2 (a) sp3 and sp3d2

Space for rough work

Mock Test–1 / Paper–I

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Chemistry Passage for Question Nos. 17 and 18 Stability of alkenes can be compared by converting the compounds to a common product and comapring the amount of heat given off. One possibility would be to measure heats of combustion. Alkene of lowest heat 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 isomeric alkenes. Heat of hydrogenation is heat given off during catalytic hydrogenation. Lower is the heat of hydrogenation stable is the alkene. In case of cycloalkenes, cyacloalkanes having more angle strain are less 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.

18.

The correct match for the following (A) 2-methyl-2-butene (B) trans-2-pentene (C) cis-2-pentene (D) 3-methyl-1-butene (a) A-(i), B-(iv), C-(ii), D-(iii) (c) A-(ii), B-(iv), C-(iii), D-(i)

(i) 27.6 (ii) 26.9 (iii) 30.3 (iv) 28.6 (b) A-(ii), B-(i), C-(iv), D-(iii) (d) A-(iii), B-(iv), C-(i), D-(ii)

Among the following pairs in which case the second compound has higher heat of hydrogenation than the first (a)

(c)

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

,

,

(d) 1-butene, 2-butene

Space for rough work

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Mock Test–1 / Paper–I

Section – IV Integer Type

Chemistry

This Section contains 10 questions. The answer to each question is a single digit integer ranging from 0 to 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°C and 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

A 2+

+0 .6 5 vo lt (E ° 1 )

A+

+1 .3 5 vo lt (E ° 2)

A

E ° 3 =X volt Calculate value of X. S3.

For an equilibrium reaction A + 2B S 2C + D; A and B are mixed in a reaction vessel at 300 K. The initial concentration of B was 1.5 times the initial concentration of A. At the equilibrium the concentration 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 radiation emitted is 1340.3 cm–1. The value of principal quantum number of the orbit from which this jump has taken 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 solution will 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-methyl pentane on catalytic reduction?

Space for rough work

Mock Test–1 / Paper–I

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Chemistry S7.

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

S8.

Consider the following reactions (i) At t = 0

→ C A  2M

(1st order reaction)

→ D (nth order reaction) B  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. After 15 minutes [B] = [A]. The value of ‘n’ is…

(ii)

S9.

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

x value of y .

(CH3 )x AlCly

AgNO3 → xCH4 (g ) + yCl− + Al3 +  → 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) a cylinder can last. [Assume 1 month = 30 days)

Space for rough work

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Mock Test–1 / Paper–I

Part – II Section – I Single Correct Choice Type

Mathematics

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

1.

If the point (0,λ ) is a point of the region bounded by the semicircle x = 9 − y 2 and the line x = 0 then the equation x 2 − 2x − λ = 0 has (a) atleast one real root in [2, 3] (c) two real roots in [–1, 3]

2.

(b) at least one real root in [–1, 0] (d) no real roots in (0, 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 ) sin t at a time ‘t’ where f is a thrice differentiable function. Then the velocity of the particle at time ‘t’ is (a) f ′′′ ( t ) 3.

4.

(b) f ′ ( t ) + f ′′′ ( t )

(c) f ′ ( t ) + f ′′ ( t )

(d) f ′ ( t ) − f ′′′ ( t )

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 along the normal at the point of opening to reach the next circle C2. Then it moves on the second circle C2 and leaves it likewise to reach the third circle C3 and so on. The total number of different paths in which the point can come out of the nth circle is (b) 2n–1 . n! (c) n! (d) nn–1 . (n – 1)! (a) 2n . n!

log x 7 4 If 2, log3x − 4 4, are in H.P. then x is equal to 3 + 2

(a) 1

(b) 2

(c) 4

(d) 0

Space for rough work

Mock Test–1 / Paper–I

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Mathematics 5.

The fractional part of the number (a)

6.

3 25

333 is 25

23 (b) 25

(c)

22 25

(d)

8 25

(d)

bn+1 − an+1 b−a

1 2 If (1 − ax )(1 − bx ) = a0 + a1x + a2 x + L then an equals

bn − an (a) b−a

an − bn (b) b − a

(c)

an+1 − bn+1 b−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 of B with integral coordinates is (a) 5 (b) 4 (c) 6 (d) 10

Space for rough work

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Mock Test–1 / Paper–I

Section – II Multiple Correct Choice Type

Mathematics

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

9.

−a 2 If a, b, c are three consecutive integers then the determinant ab ac

(a) 36 10.

(c) 48

ac

−b bc

bc is divisible by −c 2

2

(d) none of these

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

(a)

∫ (f ( x )) − (f (b ))

 dx = 

∫ ( ) 2x (b − f ( x )) dx

(b)

∫ (f ( x )) − (f (a ))

 dx = 

∫ ( ) 2x (b − f ( x )) dx

(c)

∫ f ( x ) dx

exists

(d)

∫ f ( x ) dx

doest not exists

b

2

2

a

b

11.

(b) 144

ab

2

2

a

b

a

b

a

−1

f a

f (b )

−1

f a

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

 4 14  (c) circumcentre of ∆ ABC is  − ,   5 5 

(d) circumcentre of ∆ ABC is (–1, 2)

Space for rough work

Mock Test–1 / Paper–I

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Mathematics 12.

The complex number with maximum modulus satisfying z + 1 − i ≤ 1 is (a)

(c) 13.

(

3π 3π   2 − 1  cos + isin  4 4  

)

(b)

3π 3π   2  cos + isin  4 4  

(

3π 3π   2 + 1  cos + isin  4 4  

)

1    ( −1 + i ) (d)  1 + 2 

A player tosses a coin. He sets one point for head and two points for tail. He is to play on till he reaches n. If Pn pe the probability that his score becomes ‘n’. Then (a) P2 =

1 2

(b) P2 =

3 2

(c) P1 =

1 2

(d) Pn =

1 (Pn−1 + Pn−2 ) 2

Space for rough work

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Mock Test–1 / Paper–I

Section – III Comprehension Type

Mathematics

This section contains 2 paragraphs. Based upon the first paragraph 3 multiple choice questions and based upon the second paragraph 2 multiple choice questions have to be answered. Each of these questions 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 distances between 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 must be (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

Space for rough work

Mock Test–1 / Paper–I

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Mathematics Passage for Question Nos. 17 and 18 Using the standard trigonometric inequality sinx < x < tanx where 0 < x <

π we can prove several other 2

 π inequalities. It must be noted that (0, 1) is a proper subset of  0,   2 17.

18.

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

(b) a < b for all x

 π π π (c) a > b in  0,  and a < b in  ,  4 2  2

 π π π (d) a < b in  0,  and a > b in  ,  4 2  4

π then 2 (a) log (sinx + cosx) < x (c) log (sinx + cosx) > x2

(b) log (sinx + cosx) >x (d) None of these

If 0 < x <

Space for rough work

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Mock Test–1 / Paper–I

Section – IV Integer Type

Mathematics

This Section contains 10 questions. The answer to each question is a single digit integer ranging from 0 to 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 [ ] denotes greatest integer less than or equal to x), then ‘k’ must be equal to

S3.

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

(

)

r r r r r k r r and r = 2a − b + µ a + 2b is a − b ; then the numerical quantity ‘k’ must be 3

(

S4.

)

(

)

r r r r 2, make angle of 60° with each other. If x × ( y × z ) = a , r r r r r r r r r r r r r b − aλ + a + b × c y × ( z × x ) = b and x × y = c, then z = , ‘ λ ’ must be 2

r r r Vector x,y and z each of magnitude

(

S5.

If x =

)

9 2 2 is a solution of the inequation loga ( x − x − 2 ) > loga ( − x + 2x + 3 ). Then the other solutions 4

 5 lie in the interval  k,  , ‘k’ must be equal to  2

Space for rough work

Mock Test–1 / Paper–I

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Mathematics 20

S6.

k If α = e2πi / 7 and f ( x ) = A 0 + ∑ A k x then the value of f ( x ) + f (αx ) + f(α 2 x) + Lf(α 6 x) is k =1

k(A0 + A7x7 + A14x14) then ‘k’ must be equal to S7.

Consider n × n graph paper where ‘n’ is a natural number. Consider the right angled isosceles triangle 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

2 n (n + 1)(2n + 1) then the numerical k

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

  y 2 / 3  intersection of normals at these points is x = 3 7   + 2 , then the numerical quantity ‘k’ should    k  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

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Mock Test–1 / Paper–I

Part – III Section – I Single Correct Choice Type

Physics

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

1.

At t = 0, a particle (of mass m) is projected on a horizontal plane (making some angle with the H horizontal) with velocity v . Which of these is the expression of the radial force acting on the particle at any time t, when the particle is airborne H H H H H H H H mg ( v − gt ) mg ( v + g t ) H mg ( v − g t ) H mg ( v + gt ) H H H H (b) (c) mg − H H (d) mg − H H (a) v − gt v + gt v − gt v + gt

2.

Water is flowing through a horizontal truncated cone having radii at the ends as 0.1m and 0.01m and pressure drop across the length is 5N/m2. The rate of flow of water approximately is (Neglect viscosity, density of water = 103 kg / m3 ) (a)

3.

π kg / s 10

π (b) 100 kg / s

(c) 10π kg / s

(d)

π kg / s 5

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

T

B A P (a) WA > WB

(b) WA < WB

(c) WA = WB

(d) Data insufficient

Space for rough work

Mock Test–1 / Paper–I

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Physics 4.

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

S1

t µ O

S S2

S creen (a) (b) (c) (d) 5.

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

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

 1  K =  4πε0  

O

Q

P

2Q

R

3R

3R

(a)

7 KQ towards right 16 R 2

(b)

(c)

KQ towards right R2

(d) zero

1 KQ towards right 8 R2

Space for rough work

Page 18

Mock Test–1 / Paper–I

Physics 6.

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

C

B µ

y=x 2

h A (a) h = µ 2 7.

(c) h =

µ2 + 2 3

(d) h =

µ2 − 1 4

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

8.

(b) h = µ 2 / 3

3mg 4b

(b)

5g (c) 11b

g b

11g (d) 5b

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

10 m /s 2

C ross section al view (a) 1 atm

(b) 1.4 atm

(c) 1.14 atm

(d) 2.4 atm

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Section – II Multiple Correct Choice Type

Physics

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

9.

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

2 a = m ag nitude of accelera tio n o f elevator E levator K

m

45°

µ= 0.5 g , block slides on the floor of elevator 2 (b) for a > g, block slides on the floor of elevator (a) for a >

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

mg 2K

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

mg K

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Physics 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 g

is

11.

3 v0

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

3λ, 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

3λ S1

O

S2 D

(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

5D from point O 2

(d) A minima will be observed at a distance

5D from point O 2

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Physics 12.

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

O

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

R 5 mR2 3

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

(c) The acceleration of centre of mass will be (d) Force exerted by the hinge on the bowl is 13.

3g just after its release 5R

3g 2 5 mg 2

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

π  v = 3 sin  314t +  and current from the supply is 6   π  i = 2sin  314t +  . Which of the following is/are correct? 3  (a) Impedance of circuit is 1.5Ω (c) Resistance of circuit is

3 3 Ω 4

(b) Reactance of circuit is

4 Ω 3

(d) Wattless component of current is

1 2

A

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Mock Test–1 / Paper–I

Section – III Comprehension Type

Physics

This section contains 2 paragraphs. Based upon the first paragraph 3 multiple choice questions and based upon the second paragraph 2 multiple choice questions have to be answered. Each of these questions 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

2mg l0 . An impulse imparts a horizontal velocity v0 to the block in this position

v0 14.

If v0 is the minimum velocity for which the block loses contact with the base, then the distance covered by the block before it loses contact is (a)

15.

(b)

3 l0

(c)

3 l0 2

(d)

2l0 3

The minimum velocity v0 for which the block will loose contact with the base is (a)

16.

l0 2

g l0

(b)

gl0

(c)

2gl0

(d)

1 gl0 2

If the spring is replaced by a string, then the net force acting on the block, just after the velocity equal to v0 (found in previous question) is imparted, is (a) 3 mg

(b) 2 mg

(c)

mg 2

(d) mg

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Physics 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 hinged at O. The system is on a smooth horizontal table. An electric field is switched on in perpendicular direction to rod.

Final position

l E

l Initial position

17.

The speed of the block when rod becomes parallel to the field is (a)

18.

3qEl 2m

(b)

2qEl 3m

(c)

qEl m

(d)

2qEl 5m

The tension developed at midpoint of the rod when rod becomes parallel to the field is (a)

49 qE 16

(b)

33 qE 8

(c)

5 qE 3

(d)

q qE 2

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Mock Test–1 / Paper–I

Section – IV Integer Type

Physics

This Section contains 10 questions. The answer to each question is a single digit integer ranging from 0 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 is projected 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?

v0 30° S2.

At any instant the ratio of the amount of two radioactive substances is 2 : 1. If their half lives be respectively 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 performs pure rolling on the horizontal surface, then find the acceleration of the centre of mass (in m/s2) of the disc. (Take

F = 3m / s2 )? m 2F F

O

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Physics S4.

Two capacitors of capacitance 2µf and 6µf 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 switch S1 is opened and S2 is closed. Find the ratio of heat loss in resistance 2Ω when only switch S1 was closed (for a long time) to the heat loss in the same resistance when switch S2 only is closed (for a long time)?

2 µF 6 µF

2Ω 1Ω

S2

S1

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. What is 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 a certain resistance is connected in parallel with the voltmeter, the reading decreases two times while the reading of the ammeter increases to same number of times. Find the reading of the voltmeter after connection of resistance?

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Mock Test–1 / Paper–I

Physics S7.

A particle of mass m is executing oscillations about the origin, on the x-axis. Its potential energy is U(x) = K | x |3 where K is some positive constant. If the amplitude of oscillation is ‘a’, then its maximum 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

 πx  displacement of the wire is y1 = A sin   sin ωt and energy is E1 and in another experiment, its  L  E2  3πx  sin3ωt and energy is E2. Then displacement is y 2 = A sin   E1 is  L  S9.

n moles of an ideal gas undergoes a process in which the temperature changes with volume as T = KV2, where K is positive constant. The work done by the gas as the temperautre changes from  nRT0 T0 to 4T0 is x   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 , then ( y + z ) is given by z R

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