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Test - 7A (Paper-1) (Code A) All India Aakash Test Series for JEE (Advanced)-2018

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PART - I : PHYSICS

SECTION - 1

This section contains SEVEN questions. Each question has FOUR options [A], [B], [C] and [D]. ONE OR MORE THAN

ONE of these four option(s) is(are) correct.

1. A partition divides a container having insulated walls into two compartments I and II as shown in figure. The same

gas is filled in the two compartments.The partition is a conducting wall which can move freely without friction.

Which of the following statements is/are correct, with reference to the final equilibrium position ?

P V T, , 2 , 2 , P V T

I II

(A) The pressure in the two compartments are equal and has the value 5

3

P

(B) Volume of compartment I is 3

5

V

(C) Volume of compartment II is 12

5

V

(D) Change in internal energy of gas in compartment I is zero

2. A uniform square plate of mass m is supported with its plane vertical as shown in figure. Assume centre of mass

is on horizontal line passing through A. If the cable breaks at B, then just after breaking of the cable,

B

A

bb

C

Y

X

(A) Angular acceleration of the plate is � 3

2 2

gk

b (B) Angular acceleration of the plate is

� 3

2

gk

b

(C) Acceleration of corner C is 3

2

gj� (D) The hinge reaction at A is

4

mgj�

TEST - 7A (Paper - 11111)

Time : 3 Hrs. MM : 183


All India Aakash Test Series for JEE (Advanced)-2018 Test - 7A (Paper-1) (Code A)

2/17

3. A ball strikes a wall with a velocity v at an angle 30° with the normal to the wall surface and rebounds from it at

angle 30° with the surface. Then

(A) If wall is smooth, coefficient of restitution = 1

3(B) If wall is smooth, coefficient of restitution =

1

3

(C) If wall is rough, coefficient of restitution 1

3 (D) If wall is rough, coefficient of restitution >

1

3

4. A charged particle having specific charge moves as a conical pendulum of length � making an angle with the

vertical and maintaining a constant angular velocity , in the presence of a uniform magnetic field B is directed

vertically downward as shown in figure, then

B

(A) Magnitude of magnetic field is 1

cos

g⎛ ⎞⎜ ⎟ ⎝ ⎠�

(B) Magnitude of angular momentum of the particle about the point of suspension remains constant

(C) Magnitude of magnetic field is 1

cos

g⎛ ⎞⎜ ⎟ ⎝ ⎠�

(D) Rate of change of angular momentum of the particle about the axis of rotation is not a constant vector

5. Following operations can be performed on a parallel plate capacitor

X Connect the capacitor to a battery of emf

Y Disconnect the battery

Z Reconnect the battery with polarity reversed

W Insert a dielectric slab in the capacitor

(A) In XYZ (Perform X, then Y and then Z), the stored electrical energy remains unchanged and thermal energy

developed is 5 times the stored electrical energy

(B) The electric field inside capacitor is greater after the action XWY than that after the action XYW

(C) The charge on the capacitor is greater after the action WXY than that after the action XYW

(D) The charge on the capacitor after the action XW is same as that after WX



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6. A converging lens of focal length 20 cm and refractive index 3

2 is coaxially placed in front of a convex mirror of

focal length 5 cm. Their separation is d. A parallel beam of light incident on the lens returns as a parallel beam

from the arrangement. Select the correct option(s)

(A) The beam diameters of the incident and reflected beams must be the same

(B) Value of d can be 10 cm

(C) Value of d can be 20 cm

(D) If the entire arrangement is immersed in water of refractive index 4

3, then the path followed by incident beam

remains unaltered

7. A square frame ABCD is made of insulating wires. There is a short dipole, having dipole moment p, fixed in the

plane of the figure lying at the center of the square, making an angle as shown in figure. Four point charges

are placed at the four corners of the square as shown in the figure. Select the correct alternative(s)

D q(– ) C q(+ )

B q(– )A q(+ )

p

Y

X

(A) Magnitude of electrostatic force on the system of four charges due to dipole is independent of orientation of

dipole

(B) Magnitude of electrostatic force on the system of four charges due to dipole is dependent on orientation of

dipole

(C) Net torque on the system of four charges about the centre of the square due to dipole is zero

(D) Net force on the system of four charges due to dipole is in positive Y direction if = 45°

SECTION - 2

This section contains FIVE questions. The answer to each question is a SINGLE DIGIT INTEGER ranging from 0 to

9, both inclusive.

8. A moving neutron strikes a stationary H-atom. After the collision, velocities of both neutron and the H-atom make

an angle of 30° with the initial direction of motion of neutron. Also, the H-atom is found to get excited to first

excited state. The initial kinetic energy of neutron is p times first excitation energy of H-atom. Find the value

of p. [Assume mass of neutron = mass of H - atom]



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9. The figure shows an arrangement of an equiconvex lens made of glass of refractive index, 2 = 1.5 and a concave

mirror. Medium to the left of the lens has refractive index 1 = 1.2 and that to the right of the lens has refractive

index 3 = 2.0. A point object O is placed on the principal axis at a distance of 40 cm from the lens such that

the final image is formed at the position of the object itself. The focal length of the concave mirror is 40 cm and

the focal length of lens in air is 20 cm. Find the value of 6

d (in cm).

40 cm

d

2 = 1.50

O 3 =2.0

1 = 1.2

2

10. In the circuit shown, the switch S is shifted to position 2 from position 1 at t = 0, having been in position 1 for

a long time. The current in the circuit as a function of time is I = a – be–ct, where a, b and c are constants.

Find value of a (in SI units).

5 H

10

40 V

10 H

1

2

S

11. Heat flows radially outward through a cylindrical insulator of outer radius 16 cm surrounding a steam pipe of radius

4 cm. The temperature of the inner surface of the insulator is 100°C and that of outer surface is 50°C.

At what distance (in cm) from the centre of the pipe, the temperature is equal to 75°C ?

12. One end of an elastic string of natural length l0 and force constant k N/m is fixed to a point on a smooth horizontal

surface and the other end is attached to a particle of mass m lying on the surface. The particle is pulled to a

distance 2l0 from the fixed point and then released from rest. Time period (in s) for complete oscillation of the

particle will be n. Find the value of n. 1 kg, 4 2m k

SECTION - 3

This section contains SIX questions of matching type related to TWO tables (each having 3 columns and 4 rows).

Each question has four options. Only one of these four options is correct.

Answer Q.13, Q.14 and Q.15 by appropriately matching the information given in the three columns of

the following table.



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In column 1, various circuits are shown with different types of combinations of circuit elements : capacitor, resistor

and inductor. In column 2, phase relationship between voltage and total current through the circuit are listed.

In column 3, values of current amplitude (in A) are given. All the equations and plots in table have standard

notations.

Column 1 Column 2 Column 3

(I)

I

C R = 100

L

V t = 220 sin

R = 100 (i) Current (I) leads voltage (V) by 4

(P) 2.2 2

XL = X

c = 100

(II)

I

L

C

V t = 220 sin

C

R/2

R/2

(ii) Current (I) lags voltage (V) by 4

(Q) 2.2

XL = X

c = R = 100

(III)

I

L

V t = 220 sin

R = 100 (iii) Current (I) lags voltage (V) by 3

(R) 1.1

XL = 100

(IV)

I L C

(iv) Current (I) and voltage (V) are in same (S)2.2

2

V = 220 sint phase

XL = 100 3 1 XC = 100

13. Which of following is the correct combination for the case in which current amplitude is maximum ?

(A) (III) (ii) (P) (B) (III) (i) (P)

(C) (II) (ii) (P) (D) (II) (i) (P)



6/17

14. For which of the combination current will lag the voltage always even if frequency of source is changed?

(A) (II) (i) (R) (B) (III) (i) (P)

(C) (III) (ii) (P) (D) (II) (i) (S)

15. Combination for which current is in phase with applied voltage?

(A) (III) (iv) (R) (B) (I) (iv) (Q)

(C) (I) (iv) (P) (D) (IV) (iv) (Q)



In column 1, set-up for Young’s double slit experiment with different combinations are indicated with slits S1 and

S2. Assume that S1 and S2 are equally wide and intensity from each slit is I0. Distance of screen from the slits

is D while separation between slits S1 and S2 is d (D >> d). In column 2, distance of nearest maxima from O is

indicated. In column 3, intensity at point O is given. Take proper assumption if required. is wavelength of light

in air. f is focal length of converging lens.


(I)

O

S1

S2

S

fD

(i)4

D

d

(P) 2I0

(II)

O

S1

S2

S

D

t

f

(ii)3

D

d

(Q) 4I0

t = 3

, = 1.5

(III) O

D

f

2f3d

S1

S2

S

(iii) 0 (R) 3I0

(IV)

O

D

= 1.5

= /6 d

S1

S2 (iv)

6

D

d

(S) I0



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16. In which of the combination, distances of two nearest maxima from O are in ratio of 3 : 1 ?

(A) (IV) (i) (Q) (B) (IV) (i) (P)

(C) (III) (ii) (R) (D) (III) (iii) (S)

17. In which of the combination, change in intensity at O will be maximum if one of slits is covered by opaque

sheet ?

(A) (I) (iii) (Q) (B) (I) (iii) (R)

(C) (IV) (iii) (R) (D) (III) (iv) (S)

18. Which of the following is a correct combination?

(A) (II) (iv) (S) (B) (III) (ii) (P)

(C) (II) (iv) (R) (D) (IV) (i) (Q)

PART - II : CHEMISTRY

SECTION - 1



19. The manufacturing of photoelectric cell (solar cell) depend upon the concept of photoelectric effect. Choose the

correct options among the following.

(A) No photoelectric effect occurs if energy of incident photon is less than the threshold energy of metal

(B) Kinetic energy of photoelectrons increases linearly with the increase in energy of incident photons, (energy

of individual photon is less than work function)

(C) The number of photoelectrons increases if the intensity of incident radiation increases (energy of incident

radiation is greater than threshold energy)

(D) Stopping potential increases linearly with increase of kinetic energy of photoelectron

20. A cell is made up of electrodes having area of cross-section 3 cm2 and are separated by distance 2 cm. The

resistance of 0.5 M solution of a given electrolyte is 50 . Identify the correct options.

(A) Cell constant is 0.67 cm–1

(B) Specific conductance is 0.0133 S m–1

(C) Molar conductance is 2.66 × 10–3 S m2 mol–1

(D) On adding water to solution, molar conductance increases



8/17

21. Non terminal alkynes gives varieties of reaction depending upon the reagent used in the reaction

Et C C Et

1

4

C CEt

HH

Et

C CEt

HEt

H

C CH2 –EtEt

O

COOH2Et

3

2

Identify the correct choices of reagent for the above conversions.

(A) Reagent used in reaction 1 is Ni/H2 (excess)

(B) Reagent used for the reaction 3 can be H2SO4/HgSO4, H2O

(C) Reagent of the reaction 2 is Lindlar catalyst

(D) Reagent of reaction 4 could be KMnO4/H+/

22. A is the oxyacid of sulphur, which cannot act as an reducing agent. A can be prepared by Contact process. It

gives following series of reactions. Select the correct options.

2 mole of A

SO3

–H O2

–H O2

+O

H O2

B

A

E

C

F

D

(A) A, B, F, D are the diprotic acids

(B) A, B, C, D, E, F contains at least one p – d bond

(C) A and F are same

(D) E contain oxygen of –1 oxidation number

23. In an ionic compound A is present at lattice sites forming FCC lattice, C are present in all tetrahedral voids and

B are present in all octahedral voids. Mark the correct statements.

(A) If all particles touch each other in ideal manner then length of body diagonal = 2rA + 2rB(B) Formula of compound is ABC2(C) Number of particles of C that are nearest to B is 8

(D) Number of particles of B that are nearest to A is six



9/17

24. Consider the following sequence of reaction

OH

H , +

A(i) NBS

B(ii) alc. KOH,

(i) NBSC

(ii) , alc. KOH

O3

DH O2 2

Choose the correct options

(A) D on heating give CO2 and two neutral oxides

(B) C can undergo electrophilic substitution reaction

(C) D can be oxidised using KMnO4/H+ on heating

(D) Double bond equivalence of B is 2

25. The rate of chemical reaction can be increased by increasing temperature or by using positive catalyst. Select

the correct options.

(A)

Fra

ction o

f m

ole

cule

s

Kinetic energy

t

( + 10)t

This areashows fractionof moleculesreacting at t

Molecules havingenergy of activation

This area showsfraction of additionalmolecules whichreact at ( + 10)t

(B)

E1

E2

Energy

E - Threshold energy without catalyst

E - Threshold energy with positive catalyst

1

2

Fra

ctio

n o

f m

ole

cu

les

(C) Increasing temperature or using positive catalyst lead to increase in number of effective collision

(D)Ea/RT

k=Ae

, in this equation A (frequency factor) is the maximum value of rate constant that can be attained

at infinite high temperature



10/17

SECTION - 2


9, both inclusive.

26. The denticity of EDTA–4 in the compound [Cr(EDTA)(NH3)]–1 is

27. Glucose on treatment with conc. HNO3 finally give compound (X). Degree of unsaturation in X is

28. A solution is saturated with respect to both AgCl and AgBr. The concentration of Cl– is 0.5 M. The concentration

of Br– in the solution can be represented as 10–x. What is the value of ‘x’? Ksp(AgCl) = 2 × 10–10,

Ksp(AgBr) = 4 × 10–13

29. Consider the following acidic dehydration reaction of alcohols, identify only those reactants which provide the alkene

through rearrangement.

OH

,

CH3

C

CH3

CH3

CH OH

CH3

,

OH

, OH ,

OH

,

OH

,

OH

,

OH

,

OH

30. Consider the following factors and predict how many factors may change the value of equilibrium constant.

(Assume only one factor is changed at a time)

(i) Changing temperature of the reaction

(ii) Changing pressure of reaction

(iii) Changing concentration of reactant

(iv) Changing the volume of the container

(v) Changing the medium of reaction

(vi) Addition of inert gas

(vii) Use of positive catalyst

(viii) Changing the way of representation of the balanced chemical equation.

SECTION - 3





11/17



The following graphs represent the different types of acid base titration curve, corresponding conductometric curves

and formulae used for the pH measurement.


(I) pH at equivalence (i)

conductance

VNaOH

(P)pH

7

VNaOH

point = w

pK

2

(II) pH at half equivalence (ii) conductance

VNH OH4

(Q)

pH

VNaOH

point = pKa

(III) Bromothymol blue (pH (iii)

conductance

VNaOH

(R)

pH

VNaOH

range = 6 to 7.5) can be

the choice of suitable

indicator to detect the

equivalence point

(IV) pH at first equivalence (iv)

VNaOH

conductance

(S)

7

VNH OH4

pH

point = 1 2

2

a apK pK



12/17

31. Which is correct for the titration of CH3COOH with NH4OH?

(A) (III) (i) (S) (B) (IV) (iii) (S)

(C) (III) (ii) (S) (D) (I) (iii) (P)

32. Which set of code represent the solution that can form acidic buffer?

(A) (I) (ii) (P) (B) (III) (iii) (Q)

(C) (II) (ii) (P) (D) (II) (iv) (R)

33. Select the option which is not correctly matched.

(A) (I) (iii) (P) (B) (II) (iv) (R)

(C) (III) (iii) (S) (D) (III) (ii) (S)



Column 1 (Reactions) Column 2 (Name of Column 3 (Property of reaction

Reactions) or product)

(I)

ONa

+ CHCl32

(i) OH

(ii) H /H O

(i) Benzil Benzilic reaction (P) Order of reaction = 4

(II)

O

CHO (ii) Cannizzaro reaction (Q) Alcoholic or phenolic group is present

3 2

2

CH CO O, AcONa,

H O/H ,

(III)

O

O

(1) OH –

(2) H +

(iii) Perkin reaction (R) Carboxylic acid or derivative is present

(IV) H C H + Ph C H

O O

(1) high conc.OH

(2) H

(iv) Reimer Tiemann reaction (S) Carbon-carbon double is present

outside the aromatic ring



13/17

34. Identify the correct match.

(A) (I) (iv) (R) (B) (III) (i) (S)

(C) (IV) (ii) (P) (D) (II) (iii) (Q)

35. Which combination in column 1, 2, 3 of table can provide same product as following reaction ?

OH

(i) SnCl /HCl2

(ii) H O2

CN

(A) (I) (iv) (Q) (B) (II) (ii) (P)

(C) (I) (iii) (Q) (D) (III) (i) (S)

36. Identify the incorrect match.

(A) (I) (iv) (Q) (B) (II) (i) (S)

(C) (IV) (ii) (Q) (D) (III) (i) (Q)

PART - III : MATHEMATICS

SECTION - 1



37. The length of tangents from A, B and C to the incircle of triangle ABC are 4, 6 and 8 cm respectively, then the

(A) Area of triangle ABC is 12 15 sq. cm

(B) Ex-radii r1, r2, r3 with respect to triangle ABC are in H.P.

(C) Length of sides of triangle ABC, a, b, c are in A.P.

(D) Inradius of triangle ABC is 4 6

3 cm

38. Let f (x) = 2 + | x – 1 | and g(x) = min (f (t)), where x t x2 + x + 1, then

(A) Number of points of discontinuity of g(x) is 3

(B) Number of points of non-differentiability of g(x) is 3

(C) Range of g(x) is [2, )

(D) Range of g(x) is R



14/17

39. Four identical dice are rolled once, then the probability that

(A) All four outcomes are different is 5

42

(B) All four outcomes are identical is 2

21

(C) All four outcomes are prime numbers is 5

42

(D) All four outcomes are prime numbers is 1

7

40. The sixth term in the expansion of

1

2

1

2

7

log 9 7

1log (3 1)

5

12

2

x

x

⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦

is equal to 84. Then the number of values of x

is equal to

(A) The remainder when (2100 + 1) is divided by 3

(B) The remainder when 2100 is divided by 3

(C) The number of rational terms in expansion of (23/7 + 32/7)7

(D) The number of rational terms in expansion of 253 2

7 72 3

41. Let f : R R is a function satisfying f (2 – x) = f (2 + x) and f (20 – x ) = f (x) x R, then

(A) Period of f (x) is 16

(B) If f (0) = 5, then the number of all possible values of x for which f (x) = 5 for x [0, 170] is 21

(C) y = f (x) is symmetrical about line x = 10

(D) y = f (x) is symmetrical about line x = 4

42. For a complex number z; z2 + 2z + 1 = 0; is a parameter which can take any real value, then the roots of

this equation are such that

(A) They lie on a certain circle in argand plane if –1 < < 1

(B) One root lies inside a unit circle centred at origin and other outside of it if > 1

(C) They lie on a certain circle in argand plane if > 1

(D) They lie on a straight line for every R



15/17

43. The equation(s) of normal(s) to the curve y = 2

1

x

x at the point(s) where tangent makes an angle of

4

with

positive direction of x-axis is/are

(A) x + y = 0 (B) x + y = 3

2

(C) x + y = 2 2 (D) x + y = 3

2

SECTION - 2


9, both inclusive.

44. If ,a b

� �

and c

�

are vectors such that | | 3,| | 4a b � ��

and | | 5c �

and a b� �

is perpendicular to ,c b c� � �

is

perpendicular to a

�

and c a� ��

is perpendicular to b�

, then the value of 1

| |2

a b c � � �

is equal to

45. The solution of differential equation 2

2 2

16

dyx ydx

x

x y

is

1sin

y

x

⎛ ⎞⎜ ⎟⎝ ⎠

= mx2 + c, where c is constant. The value

of m is

46. Let f : [0, 4] R be a differentiable function, then there exist real numbers a, b belonging to (0, 4) such that

(f (4))2 – (f (0))2 = Kf (a).f (b), where K is equal to

47. The number of ways in which three objects can be selected from 100 objects fixed along a circle, so that no two

of them are adjacent is N, then sum of digits of N is

48. The sum of the roots of the equation 233x – 2 + 211x + 2 = 222x + 1 + 1 is p

q, where p and q are coprime integers,

then | p – q | is equal to

SECTION - 3





16/17



Column 1 contains functions, column 2 contains exhaustive domains of functions. Column 3 contains monotomic

behaviour of functions corresponding to set A.


(I) f(x) = 1 2cos 2 1x x

(i)3 3,

2 2

⎡ ⎞ ⎟⎢⎣ ⎠

(P) Strictly increasing in A

(II) f(x) = 1 2cot 3x x

(ii)1

,2

⎛ ⎤ ⎜ ⎥⎝ ⎦

[1, ) (Q) Strictly decreasing in A

(III) f(x) = 3 | | 2x x (iii) (– , – 3] [ 0, ) (R) Constant in given interval in A

(IV) f(x) = 1 1

sin2

x ⎡ ⎤⎢ ⎥⎣ ⎦

, (iv) [– 2, 0] (S) Neither increasing nor

where [.] represents decreasing in its domain in A

greatest integer function

49. If A = (–7, – 4), then the correct combination is

(A) (I) (iv) (R) (B) (IV) (ii) (R)

(C) (II) (iii) (P) (D) (III) (ii) (P)

50. If 3 1, ,

2 2A

⎛ ⎞ ⎜ ⎟⎝ ⎠

then the correct combination is

(A) (I) (iv) (Q) (B) (II) (iii) (R)

(C) (III) (ii) (Q) (D) (IV) (i) (P)

51. If 1 3, ,

2 2A

⎛ ⎞ ⎜ ⎟⎝ ⎠

then the only correct combination is

(A) (IV) (i) (Q) (B) (II) (iii) (P)

(C) (I) (iv) (S) (D) (IV) (i) (R)



17/17

� � �



Column 1 contains number and nature of dice thrown together and column 2 contains number of sample points

and column 3 contains the probability that outcomes be same number on each die.


(I) 2 different dice (i) 216 (P)1

6

(II) 2 identical dice (ii) 21 (Q)2

7

(III) 3 different dice (iii) 36 (R)1

36

(IV) 4 different dice (iv) 1296 (S)1

216

52. Which of the following options is the only CORRECT combination?

(A) (IV) (iv) (R) (B) (II) (iii) (P)

(C) (II) (ii) (Q) (D) (I) (iii) (Q)

53. Which of the following options is the only CORRECT combination?

(A) (III) (i) (P) (B) (III) (i) (R)

(C) (II) (iii) (Q) (D) (I) (ii) (Q)

54. Which of the following options is the only INCORRECT combination?

(A) (II) (ii) (Q) (B) (III) (i) (R)

(C) (I) (iii) (P) (D) (II) (iii) (P)

Test - 7A (Paper - 1) (Code-A) (Answers & Hints) All India Aakash Test Series for JEE (Advanced)-2018

1/8

1. (A, B, C, D)

2. (A, C, D)

3. (A, C)

4. (A, B)

5. (A, B, C, D)

6. (A, B, C)

7. (A, C, D)

8. (3)

9. (5)

10. (4)

11. (8)

12. (1)

13. (A)

14. (C)

15. (B)

16. (B)

17. (A)

18. (C)

19. (A, C, D)

20. (A, C, D)

21. (B, D)

22. (A, B, C, D)

23. (B, C, D)

24. (A, B, C)

25. (A, B, C, D)

26. (5)

27. (2)

28. (3)

29. (8)

30. (3)

31. (C)

32. (D)

33. (C)

34. (C)

35. (A)

36. (B)

37. (B, C, D)

38. (B, C)

39. (A, C)

40. (A, C)

41. (A, C)

42. (A, B)

43. (A, B, D)

44. (5)

45. (8)

46. (8)

47. (8)

48. (9)

49. (C)

50. (C)

51. (D)

52. (C)

53. (B)

54. (D)

PHYSICS CHEMISTRY MATHEMATICS

Test Date : 14/05/2018

ANSWERS

TEST - 7A (Paper-1) - Code-A

All India Aakash Test Series for JEE (Advanced)-2018

All India Aakash Test Series for JEE (Advanced)-2018 Test - 7A (Paper - 1) (Code-A) (Answers & Hints)

2/8

PART - I (PHYSICS)

ANSWERS & HINTS

1. Answer (A, B, C, D)

4 3PV PV P V

RT RT RT

P = 5

3

P

4PV = P V

V = 12

5

V

2. Answer (A, C, D)

2

bMg =

22

3Mb

= 3

2 2

g

b

ac = 2b

= 3

2

g

mg – N = ma

mg – N = 3

4

mg

N = 4

mg

3. Answer (A, C)

tan

tane

1

3

If surface is rough, line of impact will not be normal.

4. Answer (A, B)

T cos = mg

T sin + q� sin B = m2�sin

B = 1

cos

g⎛ ⎞⎜ ⎟ ⎝ ⎠�


6. Answer (A, B, C)

For image to be formed on same place ray should

retrace its path.

f1

Case I

f1

f2

C

f1

2f2

Case II

f1

f2

7. Answer (A, C, D)

Y

X

– q

2

sin

kp

r 3

Kp cosr 3

Kp

sin

r3

pcos

psin

r3

2Kp cos

Fy

= 3

3 sin2

Kpq

r

Fx

= 3

3cos 2

Kpq

r

F = 2 2

3

6x y

KpqF F

r

Net torque will be zero since force perpendicular to

diagonal ends are equal.

8. Answer (3)

u

+n H-atom

n

v1

H

v2

30°

30°

v1

= v2

u = 2v cos30°

v = 3

u

Loss in K.E =

221 1 2

2 2 3

mumu

⎛ ⎞⎜ ⎟⎜ ⎟

⎝ ⎠


3/8

9. Answer (5)

After refraction through lens image should be at

centre of curvature of mirror.

1

1

1.5 1.2 1.5 1.2100 cm

40 20v

v

⇒

1

2.0 1.5 2.0 1.5

20

v v

Solving, d = 80 + v = 30 cm

10. Answer (4)

120

diiR L

dt

at t = 0, i = 4A

3

2

38

43

t

i e

11. Answer (8)

Q

= – 2 xl dT

dx

4 1002

x T

Q dxdT

l x

∫ ∫

ln 1002 4

Q xT

l

⎛ ⎞ ⎜ ⎟ ⎝ ⎠

Solving, 16

4

x

x

x = 8 cm

12. Answer (1)

Motion will be combination of SHM + Uniform motion

T = 0

max

42

alm

K v

vmax

= l0

13. Answer (A)

14. Answer (C)

15. Answer (B)

16. Answer (B)

17. Answer (A)

18. Answer (C)

PART - II (CHEMISTRY)

19. Answer (A, C, D)

B is false because no electrons are ejected if energy

of photons < threshold energy.

20. Answer (A, C, D)

R = 50

C = 1

50 s

Cell constant = l / a

2

3 cm–1

= 66.67 m–1

Specific conductance, K kappa = 66.67 1

50

= 1.33 Sm–1

Concentration = 0.5 mol/lit = 0.5 mol/dm3

= 500 mol/m3

Molar conductivity = K 1.33

C 500

= 2.66 10–3 S m2 mol–1

21. Answer (B, D)

Reaction 1 - Lindlar catalyst

Reaction 2 - Na/liq. NH3

Reaction 3 - H2O, H

2SO

4/HgSO

4

Reaction 4 - KMnO4/H+/ or O

3/HOAc

(without zinc)


Oleum

H SO2 4

H SO2 5

H S O2 2 7

H SO2 4

SO3

2 mole of A

SO3

–H O2

–H O2

O

H O2

H O S O OH

O

O–1 –1


4/8

23. Answer (B, C, D)

A - Lattice points of FCC

B - Octahedral void

C - Tetrahedral void

No. of particles in a unit cell = A4 B

4 C

8

= A B C2

B at body center is surrounded by the 8 particles of

‘C’. A at corner is surrounded by 6 particles of ‘B’ at

edge center.

24. Answer (A, B, C)

OH+

H

–H O2

Ring

expansion

+

(A)

(i) NBS

(ii) OH , –

NBSOH ,

–

(B)

O3

C

C

OH

OHO

O

(C)(D)

+

H O + CO + CO2 2


26. Answer (5)

The maximum denticity of EDTA is 6.

Cr+ shows 6 Co. No.

So it must be attached with one donating site of

NH3 and 5 donating sites of EDTA.

27. Answer (2)

X is HOOC –(CHOH)4–COOH

28. Answer (3)

[Ag+] [Cl–] = 2 10–10

[Ag+] (0.5) = 2 10–10

[Ag+] = 4 10–10 M

[Ag+] [Br–] = 4 10–13

[4 10–10] [Br–] = 4 10–13

[Br–]

13

10

4 10

4 10

= 10–3 M

29. Answer (8)

(i)+Ring

expansion+

+

H

(ii) CH C CH3

CH3

CH3

CH3CH

3

+Methyl

shiftC CH

CH3

CH3

CH3

CH3

C C

CH3

CH3

CH3

+

(iii)

+

(iv) +

Ring

contraction+

+

(v)+

Ring

expansion

+

(vi)Ring

contraction+

+

(vii)

Ring

expansion

+

+

(viii)

Ring

expansion +

+


5/8

30. Answer (3)

Only (i), (v) and (viii) can change the value of

equilibrium constant.

31. Answer (C)

32. Answer (D)

33. Answer (C)

Solution of Q.no. 31 to 33

Correct matches are the

I - iii - P Titration of HCl with NaOH

II - iv - R Titration of CH3COOH with NaOH

III - ii - S Titration of CH3COOH with NH

4OH

34. Answer (C)

35. Answer (A)

36. Answer (B)

Solutions of Q.no. 34 to 36

Products of reaction

(I)

OH

CHO

(II)

O

CH CH COOH

(III)

COOH

OH

(IV)

O

H C OH + Ph CH OH2

PART - III (MATHEMATICS)

37. Answer (B, C, D)

A

B C

4 4

8

8

6

6

a = 14 cm, b = 12 cm

adc = 10 cm

S = 2

a b c = 18

= 18. 4. 6. 8

= 24 6 sq. c.m.

∵ a, b, c are in A.P

then , ,

S a S b S c

are in H.P.

r1, r

2, r

3 are in H.P.

Inradius = r = 24 6

18S

= 4 6

3 cm

38. Answer (B, C)

∵ f(x) = 2 + | x – 1 | =

3 , 1

1, 1

x x

x x

⎧⎨ ⎩

f(t) =

3 , 1

1, 1

t t

t t

⎧⎨ ⎩

g(x) = min (f(t)) =

2 [ 1, 0)3 ( 1),

, 1 (0,1]2,

1, [1, )

xx x

x x

⎧ ⎪ ⎨⎪ ⎩

Graph of g(x) is

y

x

g x( ) = 2g x( ) = 2 g x( ) = x+1

–1 10

y

x


6/8

39. Answer (A, C)

The different type of outcomes are possible

as: aaaa, aaab, aabb, abcc or abcd.

i.e n(S) = 6C1

+ 2. 6C

2 + 3. 6C

3 + 6C

4

= 126

Probability that all four outcomes are different

= 15 5

126 42

Probability that all four outcomes are alike

= 6 1

126 21

Number of ways when outcomes are prime

n(E) = 3C1 + 2. 3C

2 + 3C

2 + 3. 3C

3

= 15

Probability that all four outcomes are prime

numbers

= 15 5

126 42

40. Answer (A, C)

1

2log 9 7 1

2 9 7

x

x

1

2

1 1log (3 1)

15 52 3 1

x

x

Sixth term = 7C5 21

1

19 7 . 84

3 1

x

x

3x–1 = 1, 3 x = 1, 2

2100 +1 = 1 + 450 = 1 + (3 + 1)50

= 2 + 50C1. 3 + 50C

2. 32 + ...

Remainder = 2

41. Answer (A, C)

f (2 – x) = f (2 + x) ...(i)

Replace x by (2 – x) : f (x) = f(4 – x) ...(ii)

given that f(20 – x) = f(x) ...(iii)

for (ii) and (iii) : f (4 – x) = f(20 – x) ...(iv)

Replace x by 4 – x : f (x) = f (x + 16) ...(v)

In eq. (iii) Replace x by (10 – x) : f (10 + x)

= f (10 – x).

f(x) is symmetrical about line x = 10.

42. Answer (A, B)

z2 + 2z + 1 = 0

z = – ± 21

z = – ± i 21 if –1 < < 1

or z = – ± Ki, where 21 0K

z + = Ki or, z = – Ki

(z + ) z = K2

|z + | = K

z lies on a circle with centre – and radius K.

if > 1, we have

z = – + 21 or, – – 2

1

z = – + K1. or, z = – – K

1

where K1

2 = 2 – 1

z = – ± K1

if z1 and z

2 are roots then, |z

1| = |– + K

1|

and |z2| = | + K

1|

|z1| |z

2| = |K

1

2 – 2| = 1

|z1| < 1 then |z

2| > 1

If one root inside circle then other is outside.

Alternative solution of Q. No. 42 :

(z + )2 = 2 – 1

21z

21 | |z

and

2| | 1z


7/8

43. Answer (A, B, D)

The slopes of tangent is 1, we have

2

22

11

1

dy x

dxx

x = 0, ± 3

The points are (0, 0), 3

3,2

⎛ ⎞⎜ ⎟⎜ ⎟

⎝ ⎠ and

33,

2

⎛ ⎞⎜ ⎟⎜ ⎟

⎝ ⎠

Equation of normal at (0, 0) is x + y = 0

Equation of normal at 3

3,2

⎛ ⎞⎜ ⎟⎜ ⎟

⎝ ⎠ is x + y =

3

2

Equation of normal at 3

3,2

⎛ ⎞⎜ ⎟⎜ ⎟

⎝ ⎠ is x + y = – 3

2

44. Answer (5)

. 0a b c � � �

. . 0a c b c � � � �

. 0b c a � � �

. . 0b a c a � � � �

. 0c a b � � �

. . 0]c b a b � � � �

. . . 0a b b c c a � � � � � �

2 2 2 2| | | | | | | | 2a b c a b c

� � � � � �

. . .a b b c c a � � � � � �

| |a b c � � �

= 5 2

45. Answer (8)

dyx ydx

= 16x2 2 2x y

Let y = vx then

v + x dv

dx – v = 16x2 2 2 2

x v x

dvxdx

= 16x2 21 v

2

1

dv

v = 16x dx

On integrating we get:

1sin

y

x

⎛ ⎞⎜ ⎟⎝ ⎠

= 8x2 + C

46. Answer (8)

By LMVT, there exist a (0, 4) such that

(4) (0)

4 0

f f = f´(a)

f (4) – f (0) = 4f´(a) ...(i)

(4) (0)

2

f flies between f(0) and f(4) , by the

intermediate value theorem of continuous function,

there exist b (0, 4) such that f(4) + f(0) = 2f(b)

...(ii)

From equation (i) and (ii) ,

(f(4))2 – (f(0))2 = 8f´(a) f (b).

47. Answer (8)

Let the 100 things are A1, A

2 ... A

100 fixed on circle.

If A1 is selected then A

2 and A

100 cannot any two

non - adjacent of A1 he selected from A

3 to A

99. This

can be done by 97C2 – 96 = 4560 ways. Similarly for

other two letters also.

Total number of selections = 4560 × 100

= 456000, but here every thing is counted three

times.

N = 1

4560003 = 152000.

48. Answer (9)

Let t = 211x

3

4

t + 4t = 2t2 + 1

t3 – 8t2 + 16t – 4 = 0

t1.t

2.t

3 = 4

1 2 311 11 112

x x x = 4

x1 + x

2 + x

3 =

2

11

|p – q | = |2 – 11| = 9


8/8

49. Answer (C)

The graph of f (x) = 1 2cot 3x x

is

y

x

y

x –3 0

50. Answer (C)

The graph of f(x) = 3 | | 2x x is

(–1/2,0) (1, 0)

51. Answer (D)

Graph of f(x) = 1 1

sin2

x ⎡ ⎤⎢ ⎥⎣ ⎦

is

–

–2 –3/2

–1

–1/2 ½ 1 3/2

c

c

52. Answer (C)

53. Answer (B)

54. Answer (D)

� � �

test - 7a (paper - 1)1 · space for rough work all india aakash test series for jee (advanced)-2018...

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