2017 vidyamandir classes booster test 1 aceg

7/24/2019 2017 Vidyamandir Classes Booster Test 1 ACEG

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VMC/JEE-2017 1 Booster Test-1/ACEG

Booster Test - 1/[JEE-2017]07/12/2015 CODE : ACEG M.M. : 270

03.30 P.M. - 06.30 P.M. TIME : 3 Hrs

Read the following Instructions very carefully before you proceed

1. The question paper consists of 3 Subjects (Subject-I : Chemistry, Subject-II : Physics, Subject-III : Mathematics).

Each Part has 2 sections (Section I & Section II).

2. Section Icontains 10 Multiple Correct Answer Type Questions. Each question has 4 choices (A), (B), (C) and

(D), out of which ONE OR MORE CHOICES may be correct.

Marking scheme[5 Marks for Correct answer&1 NEGATIVE MARKINGfor wrong]

3. Section II contains 10 Single Integer Value Type Questions. The answer to each of the questions is a

single-digit integer, ranging from 0 to 9 (both inclusive)

Marking scheme[4 Marks for Correct answer&1 NEGATIVE MARKINGfor wrong]

4. For answering a question, an ANSWER SHEET (OMR SHEET) is provided separately. Please fill your Test Code,

Roll No.and GroupProperly in the space given in the ANSWER SHEET.

5. No candidate is allowed to carry any textual material, printed or written, bits of papers, pager, mobile phone,

any electronic device, etc., except the Admit Card inside the examination hall/room.

6. On completion of the test, the candidate must hand over the Answer Sheet to the Invigilator on duty in the

Room/Hall. However, the candidates are allowed to take away this Test Booklet with them.


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SUBJECT - I (CHEMISTRY) 90 MARKS

SECTION - I

MULTIPLE CORRECT ANSWERS TYPE

This section contains 10 Multiple Choice Questions. Each Question has 4 choices A, B, C & D, out of which ONE

or MORE Choices may be Correct :

1. Which of the following is correct about PF3Cl2?

(A) Both Cl are at equatorial position

(B) All F atoms are at equatorial position

(C) 2 Cl and 1 F atom are at equatorial position

(D) 0

2. Which of the following is isostructural and has same hybridization as XeF2 :

(A) 3I

(B) 2CO (C) 2HgCl (D) 2SnCl

3. Which of the following is false ?

(A) Critical temperature of gas is greater than Boyles temperature for all gases

(B) Critical temperature for CO2is higher than for H2O (Vap.)

(C) Critical temperature for H2O (Vap.) is higher than for CO2

(D) Critical temperature is higher for a gas with lower a

4. Which of the following has d orbitals involved in hybridization.

(A) H2SO4 (B) POCl3 (C) SF4 (D) XeF4

SPACE FOR ROUGH WORK


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5. Which of the following is correct ?

(A) free energy change for an irreversible iso-thermal is process positive

(B) free energy change is negative of work of non expansion

(C) free energy change is negative of maximum work done

(D) free energy for a system at equilibrium is constant

6. Which of the following comparison for theoretical and experimental value of combustionH are correct ?

(A) combustion(Theoritical) combustion (experimental)H H for benzene

(B) combustion (Theoritical) combustion(experimental)H H for ethane

(C) combustion ( theoritical ) combustion (experimental )H H for Buta-1,3-diene

(D) combustion ( theoritical ) combustion (experimental )H H for Benzene

7. For the above graph we can say that :

(A) Gas B has highest value of critical temperature

(B) GasA Cant be liquified(C) Gas B is earliest to be liquified

(D) Ease of liquifaction : A < D < C < B



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8. 3 2CaCO (s) CaO(s) CO (g) Kp= 3atm at 800 K.Above reaction goes forward when :

(A) CaO is removed (B) CaCO3is added

(C)2CO

P in atmosphere is 2 atm at 800 K (D) He is added at const. Pressure

9. 4 2 4 2Blue White

CuSO . 5H O(s) CuSO (anhy.) 5H O(g) Kp= 32 atm5

at 500 K.

Which of the following is correct ?

(A) CuSO4(anhy.) is hygroscopic (water absorbing) when 2H OP in atmosphere is 3 atm

(B) CuSO4(anhy.) is hygroscopic (water absorbing) when 2H OP in atmosphere is 1 atm

(C) CuSO4 crystal is of blue colour when 2H OP in atmosphere is 3 atm

(D) Reactant has covalent, ionic, coordinate bond

10. 2 4 2N O (g) 2NO (g) at 300 K 1 atm mean molar mass of mixture of N2O4, NO2of equilibrium is 69,

then:(A) is equal to 1/3(B) Kpis equal to 1/2

(C) Increase in pressure causes decrease in paramagnetism

(D) Increase in volume increase



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SECTION - II

SINGLE INTEGER VALUE CORRECT TYPE

This section contains 10 single Integer Value Correct type Questions. Each question has an integer answer

between 0 and 9. Fill the answer bubbles in the OMR Sheet APPROPRIATELY and CAREFULLY.

1. Number of Paramagnetic species among the following :

NO, NO2, 2O , KO2, NaAlO2,

22O

, 2 2 2 6 2O , ClO , O [AsF ], B

2. Number of atoms on the same plane in the following molecule :

3. For which of the following average bond energy predicted theoretically is different than experimental

value?

2 23 2 3 6 6 2 4 3O , NO , CO , C H , C H , SO

, 3 4 3BF , ClO , NO

4. How many gases will diffuse to a longer distance in same time as compared to CO under similar physical

condition.

CO2, NO, NO2, NH3, CH4, He, 2 2 2N O, O , N

5. P d is present in the structure for how many of the following:

3 2 2 3 3 3 3 4 3 4 10 3 2SO , SO Cl , (SiH ) N, BF , POCl , XeF , SF N, P O , (SiH ) O



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6. Number of molecules with 0 among the following ?

7. For a equilibrium : 2 2 3N (g) 3H (g) 2NH (g) H 0

How many of following result in increase of cQ ?

Addition of N2 Increase in pressure increase in temperature removal of NH3 decrease in volume addition of He const volume

8. For a gas slope of P-V Curve for reversible adiabatic expansion is 1.4 times the Slope of P-V Curve for

reversible isothermal expansion. Cvof the gas is expressed as xR/2 value of x will be ________.

9. One mole of each H2and I2is kept in a 1Lt. flask, at 300 K to establish equilibrium :

2 2 pH (g) I (g) 2HI(g) K 4

How many moles of NaOH are required to neutralize HI formed at equilibrium.

10. For a monatomic gasp

v

C

Cis expressed as

21

x value of x will be ___________.



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SUBJECT - II (PHYSICS) 90 MARKS

SECTION - I



or MORE Choices may be Correct:

1. In the figure acceleration of bodiesA,BandCare shown with directions. Valuesbandc are w.r.t. ground

whereas a is acceleration of blockAw.r.t. wedgeC. Acceleration of blockAw.r.t. ground is :

(A) 2 2 a c a

(B)2 2

2 a c ac cos

(C) 2 2

2 b c c b c c.cos

(D) 2 2

2 b c c b c c .cos

2. All the blocks shown in the figure are at rest. The pulley is smooth and the strings are light. Coefficient of

friction at all contacts is 0.2. A frictional force of 10Nacts betweenAandB. The blockAis about to slide

on blockB.

(A) the normal reaction exerted by the ground on the blockB is 110N

(B) the normal reaction exerted by the ground on the blockBis 50N

(C) the frictional force exerted by the ground on the blockBis 20N

(D) the frictional force exerted by the ground on the blockBis zero



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3. In the figure, the blocks are of equal masses. The pulley is fixed. In the position shown, Amoves down

with a speedu, andvB= the speed ofB, along surface.

(A) B will never lose contact with the ground

(B) The downward acceleration ofA is equal to

magnitude of the horizontal accelerationB

(C) Bv u cos

(D) Bv u / cos

4. A smooth track in the form of a quarter circle of radius 6mlies in

the vertical plane (see figure). A particle of weight 4N moves from

P1 toP2under the action of forces 1 2 F , F , and 3

F . Force 1F

is

always towards P2 and is always 20 N in magnitude, force 2F

always acts horizontally and is always 30Nin magnitude, force 3F

always acts tangentially to the track and is of magnitude (15 10s)

N whens is distance travelled in meters. If the particle has speed4m/s atP1, then :

(A) Work done by force 1 is 169 7F .

(B) Work done by force 1 is 60F J

(C) Work done by force 3 is 302 8 F . J

(D) Speed of particle atP2 is 11.42m/s



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5. A small block of mass 0 50aM . kg is placed on a long slab

of mass 3 0sM . kg as shown above. Initially, the slab is at

rest and the block has a speed 0v of 4.0m/sto the right. The

coefficient of kinetic friction between the block and the slab

is 0.20, and there is no friction between the slab and the

horizontal surface on which it moves.

At some moment later, before the block reaches the right end of the slab, both the block and the slab attain

identical speeds fv . (Takeg= 10m/s2)

(A) The value of fv is nearly 0.52m/s

(B) The distance the slab has travelled at the moment it reaches fv is nearly 0.49m

(C) The work done by friction on the slab from the beginning of its motion until is reaches fv is

nearly 0.49 Joule

(D) Displacement of block w.r.t. slab till it reaches fv is nearly 3.42m

6. A U shaped smooth tube of mass 2m is placed on a smooth horizontal

surface. Two identical spherical balls each of massmand of diameter

slightly less than the inner diameter of tube enters into the tube with a

velocityuas shown in figure. (Assume no loss of energy anywhere

and all collisions to be elastic).

(A) Speed of each ball, just before their collision is2

u

(B) At the time of collision, angle between direction of motion of spherical ballsAandBis12 2tan

as observed in the ground frame

(C) Speed of each ball just before their collision is3

2

u

(D) At the time collision angle between direction of motion of balls as observed in ground frame is

12 3

tan



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7. One of the forces acting on a certain particle depends on the particles

position in thexyplane. This forceF, expressed in newtons, is given by

the expression 21

F xy i xy j N / m , wherexandyare expressed

in meters.

(A) Work done by force for pathOACis 1J

(B) Work done by force for pathOACis 1/2J

(C) Work done by force for pathOCis 2/3J

(D) Work done by force for pathOBCis 1J

8. The cross-section of a fixed cylinder (not allowed to rotate and

translate) with horizontal axis is as shown. One end of a light inelastic

string is fixed at top of cylinder of radiusRand a small block of mass

m is tied to the other end of string. Initially the block is at rest with

the portion of string not in contact with cylinder being vertical and

having lengthLas shown. At the lowest position the block is given

initial horizontal velocity 2u gL and the block moves in vertical

plane. When the block reaches the highest point of its trajectory, the

length of string not in contact with cylinder is3

R

L

(whereg is

acceleration due to gravity).

(A) The distance between block and centre of cylinder when block is at highest position will be 3R

(B) The least tension in string is 3 2mg /

(C) Tangential acceleration of block at highest position is 3 2g /

(D) Least tension in string is2

mg



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9. A particle of 500gmmass moves along a horizontal circle of radius 16 msuch that normal acceleration of

particle varies with time as2

9na t

(A) Tangential force on particle att= 1 second is 5 Newton

(B) Total force on particle att= 1 second is 7.5 Newton

(C) Power delivered by total force att= 1 is 72 watts.

(D) Average power delivered by total force over first one second is 36 watts.

10. The magnitudes of the gravitational field at distance 1r and 2r from the centre of a uniform sphere of

radiusRand massmare 1 2andF F respectively. Then :

(A)1 1

1 2

2 2

and F r

if r R r RF r

(B)

21 2

1 222 1

if and F r

r R r RF r

(C)1 1

1 2

2 2

if andF r

r R r RF r

(D)2

1 11 22

2 2

if andF r

r R r RF r



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SECTION - II




1. From the given position, as shown in the figure, the plank starts

moving towards left with initial velocity zero and acceleration

8m/s2.The rod flies in the air and falls back on the plank. With all

surfaces smooth, If the least required length of plank , isKmeter

then value of50

121

Kis ________ .

2. A plank of massm1= 8kgwith a bar of massm2= 2kgplaced on its rough

surface, lie on a smooth floor of elevator ascending with an accelerationg/4.

The coefficient of friction is 1 5/ betweenm1 andm2.A horizontal forceF= 30N is applied to the plank. If acceleration of plank

and the bar in the reference frame of elevator are,a1anda2respectively then

value of1

2

4

5

a

ais _________.



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3. A block of massm= 2kg is placed on a plank of mass M= 10kg

which is placed on a smooth horizontal plane. The coefficient of

friction between the block and the plank is1

3 . A horizontal force

F is applied on the plank. If the maximum value ofFfor which the

block and the plank move together is KN then value of K/10is _______. (Takeg= 10m/s

2and neglect height of plank).

4. A rectangular plate lie in the horizontal plane as shown in the figure. At one

end a peg is situated and a particle of mass mtied with a string of length

through the peg and initially particle is just below the peg. A horizontal

velocity of magnitude 130g is given to the particle then after how many

collisions particle does not touch the plate if coefficient of restitution between

the plate and the particle is 1/2.

5. The spool shown in figure is placed on a rough horizontal surface has

inner radiusrand outer radiusR. A tangential forceF is applied as

shown at angle with horizontal. The angle for which the spool

does not roll and remains stationary is given by1 nr

cosR

then

value ofnis ___________.



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6. Consider the two bobs as shown in the figure. The bobs are

pivoted to the hinges through massless rods. Let At be the time

taken by the bobA to reach the lowest position and Bt be the

time taken by the bobBto reach the lowest position. (Both bobs

are released from rest from a horizontal position) If the ratio

A Bt / t is given by k then value ofkis ________.

7. Two vertical walls are separated by a distance of 2 meters. Wall A is

smooth while wall B is rough with a coefficient of friction 0 5. . A

uniform rod is probed between them. If the length of the longest rod that can

be probed between the walls is17

Kmeters then value ofKis ________.

8. A small solid sphere A of massm and radiusrrolls without slipping inside a

large fixed hemispherical bowl of radius R r as shown in figure.

The sphere starts from rest at the top point of the hemisphere. If the normal

force exerted by the small sphere on the hemisphere when it is at the bottom

Bof the hemisphere is 17mg/Kthen the value ofKis _______________.



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9. A hollow smooth uniform sphere A of mass m rolls without sliding on a

smooth horizontal surface. It collides head on elastically with another

stationary smooth solid sphereBof the same massmand same radius. If the

ratio of kinetic energy ofB to that ofA just after collision is,K : 4 thenK

is_______________.

10. A spaceship is sent to investigate a planet of mass M and radius R. While

hanging motionless in space at a distance 5R, from the centre of the planet,

the spaceship fires an instrument package with speed 0v as shown in the

figure. The package has massm, which is much smaller than the mass of the

spaceship. If the angle for which package just graze the surface of the

planet is 12

0

1 81

5

GMsin

KV R

, the value ofKis ________.



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SUBJECT - III (MATHEMATICS) 90 MARKS

SECTION - I



or MORE Choices may be Correct :

1. Forr= 0, 1, , 10 letAr,Br andCr denote respectively, the coefficients ofxr in the expansions of

10 20 30

1 1 and 1x x x then ; 10

10 10

1

r r r

r

A B B C A

is:

(A) 10 10B C (B) 10 10C B

(C) Not divisible by 2 (D) Not divisible by 3

2. Consider all 3 elements subsets of the set {1, 2, 3, . 300} then :

(A) Number of these subsets for which Sum of the three elements is multiple of 3 is 100 333 100C (B) Number of these subsets for which sum of the three elements is not a multiple of 3 is

3 100 33300 3 100C

(C) Number of these subsets for which sum of the three elements is even is 151 1503 2149C C

(D) Number of these subsets for which sum of the three elements is even is 300 1503 3C C

3. For all values of , the lines represented by the equation :

3 2sin cos x + 3 5cos sin y 5 2cos sin

(A) pass through 2 fixed points

(B) pass through a fixed point whose reflection with respect to the line 2x y is 2 1 2 1 (C) pass through a fixed point lying on 5 2 3 0x y

(D) pass through a fixed point whose distance from 0y along 0x y is 1



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4.

2015

40302015 20140 1 2015

11

ax a x a x ........

x x

then :

(A) 1 3 5 1a a a ...... (B)0 4 8

2 6 10

1a a a ..........

a a a .........

(C) Middle term is

1007

2015 22

0

kk k

k

C C

(D)0 1 3 4 6 7

2 5 82

a a a a a a ........

a a a ...........

5. If letters of the word THING are arranged in all possible manner and words thus formed are written in

dictionary order. If K is the number of words lying between NIGHT and THING (both exclusive) in

that dictionary then :

(A) Number of zeros at the end of is 4K

(B) Number of divisors ofKis 6

(C) Number of integral coordinates (both abscissa and ordinate integer) lying strictly inside triangle

formed by 0 0y x , x y K is 171

(D) Kdoes not divide number of words in that dictionary

6. Let 0 3 2 0A B and 6 1C be the vertices of ABCand 1D K K be a moving point then :

(A) Dlies on 1y x

(B) DandA lies on same side ofBCif6

7K

(C) Dlies outside the ABCif6 3

7 2K

(D) Locus ofDdivides the area of ABCin the ratio 1 : 1



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7. Consider all possible permutations of the letters of the word INDIANOIL then :

(A) Number of permutations containing the word INDIA is 5

(B) Number of permutations in which letter I occurs in first and the last position is 63 5

(C) Number of permutations in which none of the letters D, L, N occurs in the last 5 positions is 2 5!

(D) Number of permutations in which the letters, A, I, O occurs only in odd position is 2 5

8. If the coefficients of3 4

andx x in the expansion of 1821 1 2ax bx x in the powers ofxare bothzero then :

(A) a= 14 (B) a= 16 (C)272

3b (D)

251

3b

9. IfA(a, 0) andB(0,b) are end points of a diagonal of a parallelogram then:

(A) If parallelogram is square the other end points are2 2

a b a b

and

2 2

a b b a

(B) If parallelogram is rhombus with other diagonal twice of AB then other end points are2 2

2 2

a b b a

2 2and

2 2

a b b a

(C) If parallelogram is rectangle with other diagonal makes 45 with positive x-axis then other end

points are

2 2 2 22 2

2 2 2 2

a a b b a b

(D) Parallelogram cannot be square until and unlessa=b

10. The equation of the bisectors of the angles between the two intersecting lines,

1 1 1 1and are

x x y y x x y y

cos sin cos sin

1 1 1 1and then

x x y y x x y y

cos sin A B

:

(A)2

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



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SECTION - II




1. In the expansion of 2 3 4 5

1 1 1 1x y z w the sum of the coefficients of the terms of degree

2 is then number of divisors of is ________.

2. 6 6

2 1 3 1

, then sum of digits of is ________. (where [.] denotes greatest integer

function)

3. 5 1 1 7 1 4A B C are vertices of ABC,Ibe its incentre,AIintersectBCatDwhen extended.

IfAI:ID = , then 25 is _________.

4. Number of ways of selecting 4 letter from the letters of the word VIDYAMANDIR isK1and coefficient of

7x in 35 2

1 1x x x is 2K then 2 1K K is _________.

5. Number of rectangles in a chess board (8 8 unit area squares), which are not squares and both length and

breadth are even isK, then43

Kis ________.



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6. If is the image of origin about the line 1x y

a b 0 0a b , then maximum value

a b

is _________.

7. If 2 2 2 2

19 19 19 190 1 2 9 19nC C C ............ C C then number of divisors ofnis _________.

8. If 3 1 3 3

2 02 2 3 2 2

cos sin

are collinear then number of values of 0 5 is ________.

9. Number of ways in which sum of upper faces of 4 distinct dices can be 12 is , then sum of digits of

is ________.

10. The line 0ax by c intersect the line x cos y sin c 0c at Pand angle between them is

3

. If the line 0x sin y cos also passes throughP, then2 2

a b is ___________.



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End of Booster Test-1/JEE-2017

2017 vidyamandir classes booster test 1 aceg

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