Jee Advanced

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ALL INDIA AAKASH TEST SERIES for JEE (Advanced)-2014

Test - 1 (Paper- II)

Topics covered :

Physics : Motion in a Straight Line, Motion in a Plane, Laws of Motion.

Chemistry : Some Basic Concepts of Chemistry, Structure of Atom, Classification of Elements and Periodicity in Properties, Chemical Bonding and Molecular Structure.

Mathematics : Complex Numbers and Quadratic Equations, Binomial Theorem.

Time : 3 hrs.

Max. Marks: 186

Online AIATS P-II

13/10/2013

INSTRUCTIONS

Pattern of the questions are as under:

(i) The question paper consists of 3 parts (Physics, Chemistry and Mathematics). Each part has 5 sections. (ii) Section 1 contains 6 multiple choice questions which have only one correct answer. Each question carries

+2 marks each for correct answer(s). There are no negative marks in this section.

(iii) Section 2 contains 5 multiple choice questions which have one or more answers are correct. Each question carries +4 marks each for correct answer and –1 mark for each wrong answer.

(iv) Section 3 contains 2 paragraphs. Based upon each paragraph 2 multiple choice questions have to be answered. Each question has only one correct answer and carries +3 marks for correct answer and –1 mark for wrong answer.

(v) Section 4 contains 2 matching column type questions which have only one correct answer. Each question carries +3 marks each for correct answer and –1 mark for each wrong answer.

(vi) Section 5 contains 3 integer value correct type questions which have only one correct answer. Each question carries +4 marks each for correct answer and –1 mark for each wrong answer.

Regd. Office : Aakash Tower, Plot No.-4, Sec-11, MLU, Dwarka, New Delhi-110075 Ph.: 011-47623456 Fax : 011-47623472

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PART - I : PHYSICS

SECTION - 1

Single Correct Answer Type

This section contains 6 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

1. Two bodies A and B move in a straight line toward each other at initial velocities v_A and v_B and with constant accelerations a_A and a_B directed against the corresponding velocities at the initial instant. The maximum initial separation l_max between the bodies for which they meet during the motion is

(A) 3 ( ) 3( ) A B A B v v a a (B) 2 ( ) 2( ) A B A B v v a a (C) 3 ( ) 3( ) A B A B v v a a ! ! (D) 2 A B A B v v a a

2. A man walking with a speed v constant in magnitude and direction passes under a lantern hanging at a height H above the ground. The velocity with which the edge of shadow of the man's head moves over the ground with it, if his height is h is

(A) Hv H!h (B) hv H!h (C) Hv H h (D) hv H h

3. Time taken by a freely falling body, starting from rest to pass the nth_{meter of its path is} (A) 2( n 1 n) g ! (B) 2( n 1 n) g (C) 2_g( n! 1 n) (D) 2_g( n! n!1)

TEST - 1 (Paper - II)_Online

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4. A man row the boat to reach point B on the opposite bank of the river from the point A as shown in figure. The distance BC = and width of river AC = !. Minimum speed relative to water should the man row the boat to reach point B, if current velocity is v₀, is

A B C " # (A) 2 0 2 v " " # (B) 2 0 2 v # " # (C) 2 0 2 v "# " # (D) 2 02 v "# " #

5. A hinged construction consists of three rhombus with the ratio of sides 5 : 3 : 1. If vertex P₃ moves in the horizontal direction at a velocity v₀, velocity of vertex P₁ is

P0 P1 P2 P3 v0 (A) 0 2 7v (B) 0 2 5v (C) 0 4 5v (D) 0 5 9v

6. Two smooth cylindrical bars of mass m each lie next to each other in contact. A third similar cylinder is placed over the two bars as shown in figure. Neglecting friction at all contacts, the minimum horizontal force on each lower bar necessary to keep them together is

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(A) 2 mg (B) mg (C) 3 mg (D) 2 3 mg SECTION - 2

Multiple Correct Answers Type

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

7. River is flowing with velocity v_r $5 m/siˆ . A boat is moving with a velocity of v_br $ ! ( 2iˆ 3 ) m/sjˆ relative to water. The river width is 90 m along y-direction. Choose the correct alternative(s)

(A) The boat will cross the river in 30 s

(B) Absolute velocity of boat with respect to ground is 3 2 m/s (C) Drift of the boat along the river flow is 45 m

(D) Absolute velocity of boat makes an angle 45° with river stream velocity

8. The position time (x-t) graphs for two students M and N returning from their school O to their homes R and S respectively are shown in figure. Choose the correct answer(s).

S R M N x t O

(A) M lives closer to the school than N (B) M starts from the school at earlier than N (C) M moves faster than N

(D) M and N reach homes at same time

9. Let _v and a denote the velocity and acceleration of a particle. Select the correct statements. (A) a can be non-zero when v $0

(B) a must be zero when v $0 (C) a may be zero when v %0

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10. A particle is projected from a point A with a velocity u at an angle " with the horizontal. At a certain point B it moves at right angles to its initial direction then

(A) Velocity of particle at B is u cosec " (B) Velocity of particle at B is u cot "

(C) Time when particle is at B is u_gcosec &

(D) Time when particle is at B is u sec

g

' ( & ) * + ,

11. Two blocks having masses m and M are connected by thread and are placed on an inclined plane with thread loose as shown in figure. When the blocks are released

m

M

&

(A) Thread will remain loose if m < M and # is same for both the blocks (B) Thread will remain loose if plane is smooth

(C) Thread will remain loose if m is smooth and M is rough (D) Thread will remain loose if m is rough and M is smooth SECTION - 3 Paragraph Type

This section contains 2 paragraphs. Each describing theory, experiment, data etc. Four questions relate to two paragraphs with two questions on each paragraph. Each question of a paragraph has only one correct answer among the four choices (A), (B), (C) and (D).

Paragraph for Question Nos. 12 to 13

A triangular prism weighing 200 N, is lying at rest on an inclined plane whose inclination with horizontal is shown in figure. The block is tied up by a horizontal string, which has a tension of 100 N.

53° String

12. The frictional force on the block is (A) 80 N

(B) 100 N (C) 120 N (D) 150 N

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13. The normal reaction of inclined plane is (A) 100 N

(B) 150 N (C) 200 N (D) 250 N

At the moment t = 0, a stationary particle of mass m experiences a time dependent force F = 0 0 2 0 ( ) F t t t t ! , where F0

is a constant, t₀ is the time for which the force acts.

14. The momentum of the particle when the action of the force stopped

(A) 0 0 3 F t (B) 0 0 4 F t (C) 0 0 6 F t (D) 0 0 8 F t

15. The displacement of particle till the force acted

(A) 2 0 0 12 F t m (B) 2 0 0 6 F t m (C) 2 0 0 4 F t m (D) 2 0 0 2 F t m SECTION - 4 Matching Column Type

This section contains 2 multiple choice questions. Each question has matching Columns. The codes for the Columns have choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

16. A particle is going along a straight line with acceleration a, having initial velocity u. Then match the columns

Column I Column II

(P) u = +ve and a = +ve (1) O

t v

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(Q) u = –ve and a = +ve (2)

O _t

v

(R) u = +ve and a = –ve (3)

O

t v

(S) u = –ve and a = –ve (4)

O _t v Codes : P Q R S (A) 2 1 4 3 (B) 3 4 1 2 (C) 2 3 4 1 (D) 1 4 2 3

17. A particle of mass 500 g moves along horizontal circle of radius 16 m such that normal acceleration of particle varies with time as a_n = 9t2_.

(P) Tangential force on particle at t = 1 s (in newton) (1) 72 (Q) Total force on particle at t = 1 s (in newton) (2) 36 (R) Power delivered by total force at t = 1 s (in watt) (3) 7.5 (S) Average power developed by total force over first (4) 6

one second (in watt) Codes : P Q R S (A) 2 1 3 4 (B) 4 3 1 2 (C) 3 1 2 4 (D) 4 1 2 3 SECTION - 5

Integer Answer Type

This section contains 3 questions. The answer to each of the question is a single digit integer, ranging from 0 to 9. The appropriate bubbles corresponding to the respective question numbers in the ORS have to be darkened. For example, if the correct answers to question numbers X, Y and Z (say) are 6, 0 and 9, respectively, then the correct darkening of bubbles will look like the following :

0 X Y Z 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9

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18. A pivoted beam of negligible mass has, "Atwood's machine" suspended from one end and a mass M₁ suspended from the other end as shown in figure. Given M₂ = 3M₃ and l₂ = 3l₁. The pulley is frictionless, massless and negligible dimension, gravity is acted downward. Find the ratio 1

2

M

M so that beam has no tendency to rotate just

after release of masses.

M1

M3

M2

l1 l2

19. In the shown arrangement, block of mass m does not slip over the triangular wedge. All surfaces are frictionless, string and pulley are ideal. If m = 1 kg, M₁ = 3 kg, " = tan–1 1

3 ' ( ) *

+ ,. What must be the value of M2 in kg?

M2

M1 &

m

20. A body of mass 10 g is moving along the positive x-axis under the influence of a force ( ) 2 2

K F x

x

$ ! , where K = 10–2_N/m2_{. At time t = 0, it is at x = 1 m and starts from rest. Find the velocity of body in m/s when it reaches} to x = 0.5 m.

PART - II : CHEMISTRY

SECTION - 1

21. One of the hydrides of an element has 25% hydrogen and has formula MH₄ and other hydride of the same element has 20% hydrogen. The empirical formula of that hydride is

(A) MH₂ (B) MH₃ (C) M₃H₈ (D) M₄H₁₀

22. Which one of the labelled carbon atoms has the highest electronegativity?

CH = CH – CH – C C – CH 2 2 - 3 1 ₂ ₃ ₄ (A) 1 (B) 2 (C) 3 (D) 4

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23. 20 gram impure MgSO₄ on strong heating produces 0.56 litre of O₂ at STP then % purity of MgSO₄ in that sample is (A) 50% (B) 40% (C) 30% (D) 25%

24. Which of the following electronic configuration represents ground state of an element / compound? (A) 1s2_2s2_2p6_3p1 (B) $1s2_$*1s2_$2s2_$*2s2_$2p z 2_%2p x 2_%2p y 1_%*2p x 2_%*2p y 1 (C) 1s2_2s2_2p6_3s2_3p6_3d5_4s1 (D) 1s2_2s1_3p3

25. Correct pair regarding electron gain enthalpy is (A) Cl > F

(B) Cl > S (C) N > O (D) Li > Be

26. Correct sequence of IE, for carbon family (A) C > Si > Ge > Sn < Pb

(B) C > Si > Ge > Sn > Pb (C) C > Si > Ge < Sn > Pb (D) C > Pb > Si > Ge > Sn

SECTION - 2

27. In a sample of hydrogen, electron jumps from 5th shell to ground state and we observe no spectral lines in Paschen series then correct statement(s) is/are

(A) Total no. of spectral lines observed is 7

(B) No. of spectral lines observed in Balmer series is 2 (C) No. of spectral lines observed in Lyman series is 4 (D) No. of spectral lines in Bracket series will be 1 28. Which of the following contain same no. of O atoms?

(A) 9 ml at 277 K H₂O (B) 15 gram of glucose (C) 11 gram of CO₂ gas (D) 11.5 gram of NO₂ gas

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29. Out of following polar molecule is/are (A) O₃ (B) OH OH (C) Cl Cl (D) C = C = C H H Cl Cl

30. A following wave function is written for an orbital

0 3 Zr 2 2a 1 0 0 2 1 Z Zr e a a (24) ! ' ( ' ( . $ ₎ _{* )} _* + , + ,

where a₀ is Bohr radius and r is distance from nucleus then, correct regarding this is (A) This is for the 2s orbital

(B) This is for 2p orbital

(C) No. of radial node in this is zero (D) No. of radial node is 1

31. Correct pair regarding bond angle is (A) OCl₂ < ClO₂

(B) PF₃ > PH₃

(C) O(CH₃)₂ < O(SiH₃)₂ (D) NO₂ > NO₂–

SECTION - 3 Paragraph Type

When atomic orbitals overlap they form molecular orbital. Number of molecular orbital is equal to no. of overlapping atomic orbital. The molecular orbitals are of two types bonding molecular orbital and antibonding molecular orbital. Bonding molecular orbitals are represented by $, %, and & while antiboding are represented by $*,'%*. We consider z as internuclear axis.

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32. Which of the following lead to form gerade bonding orbital? (A) – + + + – (B) – + + – + (C) + – + + – (D) + – + – +

33. Number of nodal surface in %*2p_x is (A) 1

(B) 2 (C) 3 (D) Zero

Quantum numbers are the set of four numbers which give complete information about an electron in an isolated atom. (1) Principal quantum number (n)

(2) Azimuthal quantum number (l) (3) Magnetic quantum number (m) (4) Spin quantum number (s)

34. Which of the quantum number associate with size? (A) n, s only

(B) l, m only (C) n, l only (D) m, s only

35. For a set of degenerate orbitals in hydrogen like species which quantum number must have same value? (A) n only

(B) l only (C) (n + l) (D) (n + l + m)

SECTION - 4 Matching Column Type

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36. Match the following Column I Column II (P) CH₂ = C = CH₂ (1) Planar (# = 0) (Q) NO₂– _{(2) Non-planar (# = 0)} (R) PCl₃Br₂ (3) Planar (#'( 0) (S) XeF₄ (4) Non-planar (#'( 0) Codes : P Q R S (A) 2 4 1 3 (B) 2 3 4 1 (C) 1 3 2 4 (D) 1 2 3 4

37. Match the following

(P) 2s (1) Non-directional

(Q) 4d_x2_!_y2 (2) Probability is maximum along y axis

(R) 3d_xy (3) 3 radial node (S) 5p_z (4) yz nodal plane Codes : P Q R S (A) 1 2 4 3 (B) 1 3 4 2 (C) 1 2 3 4 (D) 4 2 1 3 SECTION - 5

Integer Answer Type

0 X Y Z 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9

38. How many stable resonating structure possible for XeO₆–4 ? 39. Sum of n + l + m for d e–_{which take part in hybridisation in PCl}

5 in excited state is x. The value of x may be. 40. Out of following how many species have no. of exchanges ) 10 in ultimate and penultimate shell (ns and (n – 1)d)

only?

(1) Cr (2) Fe+2

(3) Co+2 _{(4) Mn}

(5) Zn (6) Cu+2

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PART - III : MATHEMATICS

SECTION - 1

41. If the range of 8 – x_P

x – 3 contains elements then '=

(A) 3 (B) 4 (C) 5

(D) More than 5

42. Sum of real solution(s) of |x!1| 1! = |5 – x| is

(A) 7 2 (B) 6 (C) 8 (D) 4 43. If x 1 1 x $ ! and 1 3 2 i ! / $ then x20 1₁₉

x may have the value

(A) _/2 (B) 2 (C) –1 (D) 1 2 44. The equation 5 9 (3 5) 2 x x x $ has (A) No solution (B) One solution (C) Two solutions (D) Three solutions

45. If locus of z satisfying |z –7 – 5i | + |z –4 –i | = k is an ellipse then the least integral value of k is (A) 5

(B) 4 (C) 6 (D) 7

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46. If zz $2 and z $z zz, then sum of all the values of z is (A) 1 (B) 0 (C) 4i (D) 2 SECTION - 2

47. The area of the triangle on the Argand diagram formed by complex numbers 2 + i, 2i – 1 and 1 + 3i is

(A) 25

4

(B) Area is the solution of the equation z2_{+ 25i = |z|}2_{+ i} (C) 5

2

(D) If area of the triangle is A then 'A' is the solution of the equation 8iz3 4z2!10z!125i $0

48. If , !, *'are the roots of the equation 2 3 2 3

2 3 2 3 x x x x ! ! _$ ! ! then (A) '!'*'= 0

(B) There are two irrational roots of the equation (C) All roots are positive

(D) If 'is rational and, !'and *'are irrational then

2

9 2

24 0 " # = 30 49. Which of the following statements are true ?

(A) n_C

r is always divisible by 'n' when 'n' is a prime number (r + n)

(B) (1 + x)3/2₌ 2 3 3 3 3 3 3 1 1 2 3 2 2 2 2 2 1 .... 2x 2! x 3! x x R ' _! ( ' _! (' _! ( ) * ) *) * + , + ,+ , _{1 2 3} (C) (x + y)n₌n_C

0xny0 + nC1xn–1y1+ ... + nCnx0yn is valid for n , N and x, y can be real as well as complex

numbers.

(D) If ax2_{+ bx + c = 0 has two real roots of opposite sign, then the sufficient condition for this to happen is} a.f(0) < 0 where f(x) = ax2_{+ bx + c}

50. If z + iw = 2 and 2z + 3iw = 5 + i then (A) w = 1 + i

(B) Im(z) = –1 (C) Re(w) = 1 (D) z2_{– w}2_{= 0}

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51. Number of values of x satisfying |x – 1| + |x – 2| = b, where 1, 3 7 b3 64 5₇ 8 9, may be (A) 0 (B) 2 (C) Infinite (D) Exactly 3 SECTION - 3 Paragraph Type

Consider the expansion of (1 + x)2014₌2014 2014 2014 2 2014 3 2014 4 2014 2014

0 1 2 3 4 ... 2014

C C x C x C x C x C x

and give the answers of the following questions 52. 2014 2014 2014 2014 0 5 10 15 ... C C C C equals to (A) 2014 2015 2015 2015 2015 2 2 3 4

1 cos cos cos cos

5 5 5 5 5 : : : : ' ( ) * + , (B) 2014 2015 2015 2015 2015 2 2 3 4

1 cos cos cos cos

5 5 5 5 5 : : : : ' _! _! ( ) * + , (D) 2014 2015 2015 2015 2015 2 2 3 4

1 cos cos cos cos

5 5 5 5 5 : : : : ' _! _! ( ) * + , 53. 2014C₀ 2

;

2014C₁

< ;

2 2014C₂

<

2 2

;

2014C₃

<

.... 21007

;

2014C₂₀₁₄

<

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Consider the equation

2 2 1 1 1 1 ( 1) 1 1 a a x x ' ( ' _! ( _$ _! ) _! * ) *

+ , + , and give the answers of the following questions.

54. The equation has two real roots, then (A) 1 < a < 2

(B) a > 2 (C) a < –1 (D) a > – 1

55. The equation has four real roots if (A) 1 > a > – 1 (B) a < –1 or a > 2 (C) 1 1 2= = !a 2 (D) Only a > 2 SECTION - 4 Matching Column Type

56. Match Column I with Column II and select the correct answer using the code given below in the Columns.

(P) Number of solutions of |x|2 !5 |x| $6 0 is (1) 2

(Q) Number of roots of z2_{= z is} _{(2) 4}

(R) If we divide 52014_{by 13. Then the sum of the} _{(3) 3} digits of its remainder will be

(S) Number of solutions of x5 2!x2 $5 is (4) 0 Codes : P Q R S (A) 2 1 3 4 (B) 1 2 3 4 (C) 2 1 4 3 (D) 1 2 4 3

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57. Match Column I to Column II according to the equation in Column I and locus in Column II Column I Column II (P) |z – 3| – |z – 5| = 1 (1) Straight line (Q) arg 3 ,; 5< 5 3 z z z ! : ' (_$ _% ) _! * + , (2) Parabola

(R) |z – i| + |z – 3 – 5i| = |4 + 3i| (3) Circle

(S) (Im(z))2_{= 4Re(z)} _{(4) Hyperbola}

Codes : P Q R S (A) 1 3 4 2 (B) 4 3 1 2 (C) 1 4 3 2 (D) 4 1 3 2 SECTION - 5

Integer Answer Type

0 X Y Z 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9

58. If -'!, *, &'are the roots of tan 3x = tan

3

x :

' (

) *

+ ,, then the value of tan tan tan tan" # 0 > is ______.

59. Number of roots of ix5_{+ x}4_{– ix}3_{– x}2_{+ ix + 1 = 0, where x is a complex number lying on real axis or imaginary} axis is ______. 60. In the expansion of 24 1/3 3/ 4 1/2 1/ 4 1 1 1 x x x x x ! 4 5 6 7

8 9 , the coefficient of term containing x

7_is24_C

n then sum of

all digits in n is ______.