Jee advanced by S.Dharmaraj

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All India Aakash Test Series for JEE (Advanced)-2014 Online AIATS P-II

13/10/2013

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

ALL INDIA AAKASH TEST SERIES for JEE (Advanced)-2014 Test - 1 (Paper- II)

Time : 3 hrs.

Max. Marks: 186

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.

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.

–1–

All India Aakash Test Series for JEE (Advanced)-2014

Time : 3 Hrs.

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TEST - 1 (Paper - II)_Online

MM : 186

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 vA and vB and with constant accelerations aA and aB directed against the corresponding velocities at the initial instant. The maximum initial separation lmax between the bodies for which they meet during the motion is (A)

(v A v B )3 3(aA aB )

(v A v B )2 (B) 2(aA aB ) (v A ! v B )3 (C) 3(aA ! aB )

(D) 2.

2v Av B aA aB

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

Time taken by a freely falling body, starting from rest to pass the nth meter of its path is (A)

2 ( n g

1! n)

(B)

2 ( n g

(C)

2 ( n !1 g

(D)

2 ( n ! n ! 1) g

â&#x20AC;&#x201C;2â&#x20AC;&#x201C;

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All India Aakash Test Series for JEE (Advanced)-2014

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

(A)

(B)

"v 0 "2

#v 0 "2

"#v 0

(C)

(D)

"#v 0 " 2 #2

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

(A)

2 v0 7

(B)

2 v0 5

(C)

4 v0 5

(D)

5 v0 9

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

â&#x20AC;&#x201C;3â&#x20AC;&#x201C;

All India Aakash Test Series for JEE (Advanced)-2014 (A)

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mg 2

(B) mg (C)

(D)

mg 3 mg 2 3 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 $ 5iˆ m/s . A boat is moving with a velocity of v br $ ( !2iˆ 3 jˆ) m/s 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

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).

x S R M

(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 (D) Direction of v must be parallel or antiparallel to a –4–

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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 cosec & g 'u +g

(D) Time when particle is at B is )

( * sec & ,

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.

String

53° 12. The frictional force on the block is (A) 80 N (B) 100 N (C) 120 N (D) 150 N –5–

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13. The normal reaction of inclined plane is (A) 100 N (B) 150 N (C) 200 N (D) 250 N Paragraph for Question Nos. 14 to 15 At the moment t = 0, a stationary particle of mass m experiences a time dependent force F =

F0 t (t0 ! t ) , where F0 t02

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)

F0 t0 3

(B)

F0 t0 4

(C)

F0 t0 6

(D)

F0 t0 8

15. The displacement of particle till the force acted (A)

F0 t 02 12m

(B)

F0 t02 6m

(C)

F0 t02 4m

(D)

F0 t02 2m

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 v

(1) O

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

â&#x20AC;&#x201C;6â&#x20AC;&#x201C;

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All India Aakash Test Series for JEE (Advanced)-2014 v

(Q) u = –ve and a = +ve

(2)

t v

O (R) u = +ve and a = –ve

(3)

(S) u = –ve and a = –ve

(4)

Codes : P

(A) 2

(B) 3

(D) 1

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 an = 9t2. Column I

Column II

(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 one second (in watt)

(4) 6

Codes : P

(A) 2

(B) 4

(D) 4

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 :

–7–

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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

M1 so that beam has no tendency to rotate just M2

after release of masses.

19. In the shown arrangement, block of mass m does not slip over the triangular wedge. All surfaces are frictionless,

' 1( string and pulley are ideal. If m = 1 kg, M1 = 3 kg, " = tan–1 ) * . What must be the value of M2 in kg? +3,

m M2 M1

K , where 2x 2 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.

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

PART - II : CHEMISTRY 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. 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? 1 4 2 3 CH2 = CH – CH 2 – C - C – CH3

(A) 1 (B) 2 (C) 3 (D) 4 –8–

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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) 1s22s22p63p1 (B) $1s2$*1s2$2s2$*2s2$2pz2%2p2x%2p1y %*2px2%*2p1y (C) 1s22s22p63s23p63d54s1 (D) 1s22s13p3 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 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. 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 â&#x20AC;&#x201C;9â&#x20AC;&#x201C;

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29. Out of following polar molecule is/are (A) O3

OH (B)

Cl (C)

H C=C=C

(D)

30. A following wave function is written for an orbital 3

! Zr

' Z ( 2 ' Zr ( 2a0 .$ * ) *e 1 ) a a (24)2 + 0 , + 0 , 1

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 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. 32 to 33 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. – 10 –

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32. Which of the following lead to form gerade bonding orbital? +

–

(B)

–

(A)

+ +

(C)

–

– +

(D)

–

33. Number of nodal surface in %*2px is (A) 1 (B) 2 (C) 3 (D) Zero Paragraph for Question Nos. 34 to 35 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 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.

– 11 –

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36. Match the following Column I

Column II

(P) CH2 = C = CH2 (Q)

(1) Planar (# = 0)

NO2–

(2) Non-planar (# = 0)

(R) PCl3Br2

(3) Planar (#'( 0)

(S) XeF4

(4) Non-planar (#'( 0)

Codes : P

(A) 2

(B) 2

(D) 1

37. Match the following Column I

Column II

(P) 2s

(1) Non-directional

(Q) 4d x 2 ! y 2

(2) Probability is maximum along y axis

(R) 3dxy

(3) 3 radial node

(S) 5pz

(4) yz nodal plane

Codes : P

(A) 1

(B) 1

(D) 4

3 SECTION - 5

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 PCl5 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

(7) Fe

(8) Ni – 12 –

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PART - III : MATHEMATICS 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. 41. If the range of

8 – xP 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 1 !1 i 3 20 $ !1 and / $ then x x 2

43. If x

(A)

1 x19

may have the value

2 /

(B) 2 (C) –1 (D)

1 2

44. The equation

9x 2

$ (3 5)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 – 13 –

All India Aakash Test Series for JEE (Advanced)-2014 46. If zz $ 2 and z

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z $ zz , then sum of all the values of z is

(A) 1 (B) 0 (C) 4i (D) 2 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. 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 8iz 3

48. If , !, *'are the roots of the equation (A)

x! 2 2

x! 3 3

2 x! 2

3 x! 3

4z 2 ! 10z ! 125i $ 0

then

'!'*'= 0

(B) There are two irrational roots of the equation (C) All roots are positive (D) If 'is rational and, !'and *'are irrational then "9

02 = 30 24

49. Which of the following statements are true ? (A) nCr is always divisible by 'n' when 'n' is a prime number (r + n)

(B) (1 + x)3/2

3 x = 1 2

3'3 ( ) ! 1* 2+2 , 2 x 2!

3 ' 3 (' 3 ( ) ! 1*) ! 2 * 2 + 2 ,+ 2 , x3 3!

....1 2 x 3 R

(C) (x + y)n = nC0xny0 + 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 – w2 = 0 – 14 –

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41 5 51. Number of values of x satisfying |x – 1| + |x – 2| = b, where b 3 6 , 3 7 , may be 87 9 (A) 0 (B) 2 (C) Infinite (D) Exactly 3 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. 52 to 53 Consider the expansion of (1 + x)2014 =

2014

C2 x 2

C1x

2014

C3 x 3

and give the answers of the following questions 52.

2014

C10

22014 ' 2015 : (A) ) 1 cos 5 + 5

53.

2014

C15

cos2015

2: 5

(B)

22014 5

(C)

22014 ' 2015 : )1 ! cos 5 + 5

(D)

22014 5

2: ' 2015 : ! cos2015 )1 cos 5 5 +

2014

..... equals to cos2015

3: 5

cos2015

4: ( * 5 ,

2: 3: 4: ( ' 2015 : ! cos2015 ! cos 2015 ! cos2015 )1 ! cos * 5 5 5 5 , +

4 :5 (A) 6 sin 7 8 89

; 2014 C1 <

cos2015

2: 3: ! cos2015 5 5 cos2015

cos 2015

3: 4: ( ! cos 2015 * 5 5 ,

2 ; 2014 C2 < 2 2 ; 2014 C3 < .... 21007

2014

: 4 (B) 6 sin 8 8

:5 cos 7 89

4: ( * 5 ,

2014

: 8 (C) : sin2014 8 cos2014

: 8 (D) 2014 : cos 8 sin2014

– 15 –

; 2014 C2014 < equals to

2014

C4 x 4

.....

2014

C2014 x 2014

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Paragraph for Question Nos. 54 to 55

1 ( ' Consider the equation ) 1 * x ! 1, +

1 ( ' )1 ! * $ a(a ! 1) and give the answers of the following questions. x 1, +

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 =a=! 2 2

(D) Only a > 2 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. 56. Match Column I with Column II and select the correct answer using the code given below in the Columns. Column I

Column II

(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 x5

(S) Number of solutions of

2 ! x 2 $ 5 is

(4) 0

Codes : P

(A) 2

(B) 1

(D) 1

3 – 16 –

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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

'z!3( : ; (Q) arg ) * $ , z % 5< +z!5, 3

(2) Parabola

(R) |z – i| + |z – 3 – 5i| = |4 + 3i|

(3) Circle

(S) (Im(z))2 = 4Re(z)

(4) Hyperbola

Codes : P

(A) 1

(B) 4

(D) 4

2 SECTION - 5

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

:( , then the value of tan " tan # tan 0 tan > is ______. 3 *,

59. Number of roots of ix5 + x4 – ix3 – x2 + ix + 1 = 0, where x is a complex number lying on real axis or imaginary axis is ______.

4 60. In the expansion of 6 3/4 8x

x !1 x1/2

x1/4

x1/3

5 17 9

, the coefficient of term containing x7 is

all digits in n is ______.

– 17 –

24C n

then sum of