TEST - 7 (Paper - II)

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3 Test - 7 (Paper-II) All India Aakash Test Series for JEE (Advanced)-014 Time : Hrs. MM : 186 TEST - 7 (Paper - II) PART - I : PHYSICS SECTIN - 1 nly ne ption Correct Type This section contains 6 multiple choice questions. Each question has 4 choices,, and out of which NLY NE is correct. 1. In the given graph K α line is drawn for square root of frequency and atomic number. Then choose the K β line graph in figure shown. v ( a) K α ( b) () c ( d) a c z b d. The angle of incidence i for an equilateral prism of refractive index so that the ray suffers minimum deviation is Either 0 or 60. A vessel is half filled with a liquid of refractive index μ. The other half of the vessel is filled with immiscible liquid of refractive index 1.5 μ. The apparent depth of the vessel is 50% of the actual depth, then μ is Monochromatic light strikes normally on two thin different films, which are in air as shown. If t denotes the film thickness and λ denotes the wavelength of light in the film, which film(s) will produce constructive interference as seen by observer? eye I only t t II only I and II both None of these μt = 5 λ 4 (I) μt = λ (II) eye 1/19

4 All India Aakash Test Series for JEE (Advanced)-014 Test - 7 (Paper-II) 5. In YDSE, one of the slits is wider than the other, so that, the amplitude of the light from one slit is double that from the other slit. If I m be the maximum intensity, the resultant intensity when they interfere at a phase difference φ is given by Im φ 1+ cos Im φ 1+ 4cos 5 Im φ 1+ 8cos 9 Im φ 8+ cos 9 6. The ratio of time period of revolution of nd orbit electron in He + ion and rd excited state electron in Le ++ is SECTIN - ne or More ptions Correct Type This section contains 5 multiple choice questions. Each question has 4 choices,, and out of which NE R MRE are correct. 7. A equi-biconvex length of focal length 10 cm is silvered as shown in figure. Refractive index of glass is equal to. Focal length of mirror would be equal to 5 cm Focal length of mirror would be equal to.5 cm An object is placed at point on axis such that its image is also formed at same point, the distance of that point from lens would be 10 cm An object is placed at point on axis such that its image is also formed at same point, the distance of that point from lens would be 5 cm /19

5 Test - 7 (Paper-II) All India Aakash Test Series for JEE (Advanced) A beam of white light incident on a combination of thin prisms with equal angles. In the outgoing beam, the rainbow colours are observed as shown. μ stands for refractive index and θ for angle of dispersion. Then μ White light R Y μ 1 V μ 1 < μ μ = μ 1 μ 1 > μ θ 1 > θ 9. Two coherent monochromatic sources A and B emit light of wavelength λ. The distance between A and B is integral multiple of λ. If a light detector is moved along a line CD, parallel to AB, from to +, 8 minimas are observed. Choose the correct options. A Y D B x = 0 C X The distance between AB is 4λ If the detector is moved along X-axis from B to, then 5 maximas will be observed At a distance of At a distance of 15λ x = first minima will be observed 4 15λ x = first minima will be observed 8 /19

6 All India Aakash Test Series for JEE (Advanced)-014 Test - 7 (Paper-II) 10. ABC is a right angled prism having other angles of 0 and 60 as shown. Two rays 1, are incident on prism such that ray 1 just suffers TIR on second face. Ray is incident on one face and emerges perpendicular to the other face. If light incident has same wavelength, choose correct options. A 0 1 B 60 C Refractive index of the prism is Deviation suffered by ray is 60 Angle of deviation suffered by ray is 0 The refractive index of the prism is 11. A gas of hydrogen like atoms has some atoms in the lowest ground energy level A and some atoms in a particular upper excited energy level B and there are no atoms in any other energy level. The atoms of gas make transition to higher energy level by absorbing monochromatic light of photon energy.7 ev. Subsequently the atoms emit radiation of only six different energy photons. Some of the emitted photons have an energy.7 ev, some have more and some less than.7 ev. The principal quantum number of initially excited level B is The ionisation energy of gas atoms is 14.4 ev Maximum emitted energy of photon is 1.5 ev Minimum emitted photon has energy 0.7 ev SECTIN - Paragraph Type This section contains 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,, and. Paragraph for Question Nos. 1 to 1 Consider a neutron and an electron bound to each other due to gravitational force. Assume that the electron orbits around the neutron in circular path. Bohr's quantization rule for angular momentum is applicable in this case. Take mass of neutron as m 1 and mass of electron as m. (assume m 1 >>>m ) 4/19

7 Test - 7 (Paper-II) All India Aakash Test Series for JEE (Advanced) Radius of orbit of electron for n th quantum number is nh π Gm m 1 nh π Gm m 1 nh πgm m 1 nh 4π Gm m 1 1. Speed of electron in n th orbit is πgm m nh 1 πgm m nh 1 Gm1m nh 4πGm m nh 1 Paragraph for Question Nos. 14 to 15 A cylinder of height h and radius R is kept in the path of a parallel beam of light of large aperture. If beam carries an intensity I. 14. If surface of cylinder is perfectly reflecting, the force on cylinder would be 8IhR C πihr C IhR C IhR C 15. Let the surface of cylinder has reflection co-efficient 0.8, then force on cylinder would be 8IhR C 8 IRh 15 C IhR 15C 64 IRh 15 C 5/19

8 All India Aakash Test Series for JEE (Advanced)-014 Test - 7 (Paper-II) SECTIN - 4 Matching Column Type This section contains multiple choice questions. Each question has matching Columns. The codes for the Columns have choices,, and out of which NLY NE is correct. 16. In YDSE as shown in figure, θ is the angular position of any point on screen. Both the slabs are of same thickness = 10 μm. Match column-i with column-ii in the codes given below the columns. slab1 μ 1 α θ μ slab Screen Column I Column II (P) Central maxima must be above (1) If α > 7 and μ 1 μ (Q) Central maxima must be below () If α = 7, μ 1 = 1.5, μ = 1.5 (R) Central maxima must be at () If α = 0 and μ 1 = μ (S) Central maxima may be below (4) If α = 0 and μ 1 < μ Codes : P Q R S /19

9 Test - 7 (Paper-II) All India Aakash Test Series for JEE (Advanced) An electron is orbiting around the nucleus in n th orbit, of a hydrogen like atom. Assuming Bohr's model to be true, match the physical quantities given in column-i with their dependence on the principal quantum number in column-ii, in the codes given below the columns. Column I Column II (P) Magnetic field at the site of nucleus (1) 1 4 n (Q) Magnetic dipole moment 1 () 5 n (R) de-broglie wavelength () n (S) Centripetal acceleration (4) n Codes : P Q R S SECTIN - 5 Integer Value Correct Type This section contains 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 RS 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 : X Y Z A radioactive sample contains two radioactive nuclides A and B having decay constant λ hr 1 and λ hr 1. Initially 5% of total decay comes from A. How long (in hr) will it take before 75% of total decay comes from A? [Take λ = ln ] 19. A light of wavelength λ is incident on a metal sheet of work function ev. The wavelength varies with time as λ = t, where λ is in Å and t is in second. The time (second) after which the photoelectric emission will stop to the nearest integer is 16n, find n. [Take hc = 1400 ev Å] 0. To measure the volume of the blood of an animal, the following experiment was done. A 10 ml sample of solution containing radioactive element (t 1/ = 40 min) with an activity of 450 dps was injected into the animals blood stream. 0 min required for complete circulatory mixing. After 80 min, a 4.0 ml sample was withdrawn and found to have an activity of 5 dps. If the volume of the blood in animal is 10 n (in ml), then find n. 7/19

10 All India Aakash Test Series for JEE (Advanced)-014 PART - II : CHEMISTRY Test - 7 (Paper-II) SECTIN - 1 nly ne ption Correct Type This section contains 6 multiple choice questions. Each question has 4 choices,, and out of which NLY NE is correct. 1. Which of the following statement is incorrect? Cyclopentanone undergoes faster nucleophilic addition reaction than cyclohexanone In water, HCH exists majorly as geminal diol In CH Cl, aldehydes and ketone can never form diol hence are not oxidized by PCC in CH Cl Chloral majorly exists in form of dihydrate. In the reaction sequence NH P 5 Δ P (i) CH MgBr (Dry ether) + (ii) H Q I Ca(H) R + yellow ppt 'R' is taken out from solution and dry heated which produces 'S'. P and S respectively are NH and NH N and NH and C N and NH. A B C D (M = 11 g/mol) NaN HCl yellow oily liquid Which of the following is incorrect for above reaction? "D" is having molecular formula C 7 H 15 N Reagent "C" can be H /Ni or LiAlH 4 "B" has a characteristic smell Reagent "A" is present in acidic medium 8/19

11 Test - 7 (Paper-II) All India Aakash Test Series for JEE (Advanced)-014 CH 0 H 4. 1 CH NaD D/THF When the above reaction takes place several hydrogens are readily exchanged by deuterium. The readily exchangeable hydrogens are on atoms numbered and 0 only, 4 and 17 only, 4 and 0 only 1,, 17 and 0 5. Cl + NH The major product in above reaction is Cl NHCH CH NHCH CH NHCH CH NH Cl 6. Which of the following reactions would not be an acceptable method for the preparation of methyl benzoate? C Cl CH H C CH C Na CH I C CH C Na CHH C CH C C CH H C CH 9/19

12 All India Aakash Test Series for JEE (Advanced)-014 Test - 7 (Paper-II) SECTIN - ne or More ptions Correct Type This section contains 5 multiple choice questions. Each question has 4 choices,, and out of which NE R MRE are correct. 7. Which of the following give single organic product on treatment with KH? PhCCPh HCCH HC(CH ) 5 CH 8. Which is true about the following reaction sequence? (C H ) N : + : CCl A C H + B 5 4 Δ C H/H CH.. CCl is acting as nucleophile Compound "B" is N CHCl "A" to "B" is effective in polar aprotic solvent Compound "C" is N CH 9. The type of possible interaction/s in Nylon-6, 6 is/are Hydrogen bonding van der Waal interaction Diple-dipole interaction Induced dipole - Induced dipole interaction 0. C CuCl, HCl AlCl A (major product) HCH conc. KH B + C (major products) Which of following is true for above reaction sequence? B = CK C = CH H C = CH H B = HCK 10/19

13 Test - 7 (Paper-II) All India Aakash Test Series for JEE (Advanced) In which of the following reaction/s cyclic intermediate / transition state is involved? Perkin reaction Decomposition of β -keto acid Wittig reaction Heating of α-hydroxy acid SECTIN - Paragraph Type This section contains 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,, and. Paragraph for Question Nos. to An ordinary D-(+)-glucose has melting point 146ºC and specific rotation [α] = ne another form of D - (+)- glucose has melting point 150 C and specific rotation [α] = The form of low melting point for glucose is known as α form and other form as β-form. When any of the pure form is allowed to stand in acidic solution then optical rotation changes till reaches to fix value 5.7. This change in optical rotation towards an equilibrium value is called mutarotation.. Mutarotation is the characteristic feature of Enantiomer Epimer Anomer Ring chain isomers. What percentage of β- (+) glucopyranose is found at equilibrium in aqueous solution? 50% 74% 6% 64% Paragraph for Question Nos. 4 to 5 A well known aromatic compound is put up in following sequence of reaction A H/Pd (i) Br C F (Major product) B (C H ) NaC, Δ hν (mono bromination) (i) aq.kh E (C H ) ZnCl (i) (i) DMS D ( H ) 4. What is the double bond equivalence of "F"? /19

14 All India Aakash Test Series for JEE (Advanced)-014 Test - 7 (Paper-II) 5. If "F" is put up in reductive ozonolysis then formed product is SECTIN - 4 Matching Column Type This section contains multiple choice questions. Each question has matching Columns. The codes for the Columns have choices,, and out of which NLY NE is correct. 6. In column (I) acids are given their respective acidic strength order is given from right to left in column (II). Column I (P) CH F CH, Cl CH CH, Cl CCH Column II (1) Increases, Increases (Q) + Me NCH CH, NCH CH, NCCH CH () Decreases, Decreases (R) m-hydroxy benzoic acid, o-hydroxy benzoic acid, p-hydroxy benzoic acid (S) xalic acid, Succinic acid, Propanedioic acid () Decreases, Increases (4) Increases, Decreases Codes : P Q R S /19

15 Test - 7 (Paper-II) All India Aakash Test Series for JEE (Advanced) Compounds given in column (I) are treated with CH MgBr (excess) in dry ether followed by addition of H and qualitative test on formed products are given in column II. Column I (P) CH C Cl (Q) CH C N Column II (1) Positive DNP () Gas is insoluble in H (R) CH C NH (S) H C CH Codes : P Q R S () Blue colour in Victor Meyer test (4) Instantaneous white turbidity with Lucas reagent SECTIN - 5 Integer Value Correct Type This section contains 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 RS 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 : X Y Z Succinaldehyde on reaction with P 5 produces organic compound 'X'. How many π electrons are there in 'X' in π electron cloud? 9. Phthalic anhydride is treated with phenol in acidic medium. How many aromatic rings are there in one molecule of product? 40. How many functionality are present in monomer of Nylon-6? 1/19

16 All India Aakash Test Series for JEE (Advanced)-014 PART - III : MATHEMATICS Test - 7 (Paper-II) SECTIN - 1 nly ne ption Correct Type This section contains 6 multiple choice questions. Each question has 4 choices,, and out of which NLY NE is correct. 41. If xdy = y(dx + ydy), y 0, y(1) = 1 and y(β) =, then 'β' is equal to A term is selected from the expansion of (x + y + z) 10 at random. The probability that two variables out of x, y and z have the same power is Let r = ( a b)sin x + ( b c)cosy + ( c a), where abc,, are non-zero and non-coplanar vectors. If r is orthogonal x + y to a+ b+ c, then find the minimum value of π 4 π π π 44. Two urns contains, respectively m 1 and m white balls and n 1 and n black balls. ne ball is drawn at random from each urn and then from the two drawn balls one is taken at random. The probability that the drawn ball is white 1 mn 1 1 mn + m1 n1 m n m1 m + m1 n1 m n mn 1 mn 1 + m1 n1 m1 n n1 m1 + m1 n1 m1 n /19

17 Test - 7 (Paper-II) a = λ log ˆ ˆ ˆ x i + j + k b = log x iˆ+ ( λlog x) ˆj kˆ 45. Let ( ) ( ) All India Aakash Test Series for JEE (Advanced)-014 Given angle between a and b π lies in the range, π for every x (0, ). Then λ belongs to [0, 1] [ 1, 0] [ 1, 1] [0, ] 46. If uvw,, are non-zero and non-coplanar vectors, then find the number of ordered pairs (p, q) so that [ u pv pw] [ pv w qu] [ w qv qu] = 0 p, q, R 1 More than SECTIN - ne or More ptions Correct Type This section contains 5 multiple choice questions. Each question has 4 choices,, and out of which NE R MRE are correct. 47. Which of the following statement(s) is/are true for any two events A and B? Suppose that P(A/B) = P(B/A), P(A B) = 1 and P(A B) > 0 then P > 1 If P(B C ) = 1 4 and P(A/B) = 1 then maximum value of P = 5 8 If P = 1 and P = 1, then P(AC B C ) C + P(A C B C ) C = If A is subset of B, then P(B/A) is 1, where P Let first and second row vectors of matrix A be r 1 = [1 1 ] and r = [ 1 1] and let the third row vector be in the plane of r 1 and r and perpendicular to r with magnitude 5, then which of the following is /are true? T r = Volume of parallelopiped formed by r, r and r r equals 0 Row vectors are linearly dependent r r r r r r = [ ] /19

18 All India Aakash Test Series for JEE (Advanced)-014 Test - 7 (Paper-II) 49. If g(x) be a function defined on [ 1, 1]. If the area of the equilateral triangle with two of its vertices at (0, 0) and (x, g(x)) is 4, then the function is gx ( ) = x 1 gx ( ) = 1 x gx ( ) = 1 x gx ( ) = x The chance of occurrence of an event A is the square of the chance of occurrence of event B but the odds against the event A are the cube of the odds against the event B. The chances of the events are 1 9 P( A ) = ( ) 1 P A = P( B ) = ( ) dy ax + h 51. The solution of = represents a parabola when dx by + k P B = a = 0, b 0 a 0, b 0 b = 0, a a = 0, b R SECTIN - Paragraph Type This section contains 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,, and. Let L : r = ( iˆ+ ˆj kˆ) +λ( iˆ ˆj + kˆ) 1 Paragraph for Question Nos. 5 to 5 8iˆ and L ˆ ˆ ˆ ˆ ˆ : r = j + k +μ( i j + k) where λ and μ R be two lines in space. A line L from origin meets the line L 1 and L at P and Q respectively. 5. The equation of the plane passing through the points P and Q and perpendicular to the plane r.( iˆ jˆ+ kˆ) + 1 = 0 is r.(iˆ ˆj) = 0 r.( iˆ jˆ) = 0 r.(iˆ+ ˆj) = 0 r.( iˆ+ jˆ) = 0 16/19

19 Test - 7 (Paper-II) All India Aakash Test Series for JEE (Advanced) The volume of the tetrahedron PAB where '' is the origin and A(0, 1, ) and B(, 0, 5) is equal to Paragraph for Question Nos. 54 to 55 The probability that a family has exactly 'n' children is αp n, n 1. All sex distributions of n children in a family have the same probability. 54. The probability that a family contains exactly 'k' boys is (where k 1) αp k (1 p) k 1 αp ( p) k αp k ( p) k 1 αp k 1 ( p) k Given that a family includes at least one boy, show that the probability that there are two or more boys is p ( p) p 1 p p ( p) p (1 p) SECTIN - 4 Matching Column Type This section contains multiple choice questions. Each question has matching Columns. The codes for the Columns have choices,, and out of which NLY NE is correct. 56. For the non-zero vectors a and b, match the following. Column I Column II (P) If ab. = ac. = c (1) Always true (Q) ab. = ac. and a b = a c = c () Always false (R) a b = a c and b c, then a is () May be true, may be false it will depends perpendicular to b c upon b and c (S) a + b = a b a. b = 0 (4) True only for unit vector b and c 17/19

20 All India Aakash Test Series for JEE (Advanced)-014 Test - 7 (Paper-II) Codes : P Q R S Match the following : Column I Column II (P) If the function y = e 4x + e x is a solution of the differential equation (1) d y dy 1 dx dx y k = k then the value of is (Q) Number of straight lines which satisfy the differential equation () 4 dy dy + x y = 0 dx dx is (R) If real value of 'm' for which the substitution, y = u m will transform () the differential equation, 4 dy 4 6 x y + y = 4x into a homogeneous dx equation then the value of m is (S) If the solution of differential equation d y dy x + x = 1y is (4) 1 dx dx y = Ax m + Bx n then number of possible non-zero values of m + n are Codes : P Q R S /19

21 Test - 7 (Paper-II) All India Aakash Test Series for JEE (Advanced)-014 SECTIN - 5 Integer Value Correct Type This section contains 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 RS 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 : X Y Z A six digit number is selected at random the probability that sum of square of its digit is 9 is of digits of k is k then sum 59. If xy dy = (x + y + 1)dx, y(1) = 0 and y(x 0 ) =, then sum of all possible values of x 0 is xa+ yb+ zc = α ( xiˆ+ yj ˆ+ zkˆ) has a non- 60. Let a = iˆ+ ˆj + 4kˆ ; b = ( iˆ+ kˆ ) and c = 4iˆ+ jˆ+ kˆ. If the equation trivial solution, then find the sum of all distinct possible values of α. 19/19

Test - 6 (Paper - II) (Answers & Hints) All India Aakash Test Series for JEE (Advanced)-014 TEST - 6 (Paper - II) ANSWERS PHYSICS 1... 4. 5. 6. 7. (A,B,C) 8. (B,C,D) 9. (A,C) 10. (B,C) 11. (A, C) 1.

24 Test - 6 (Paper - II) (Answers & Hints) All India Aakash Test Series for JEE (Advanced)-014 TEST - 6 (Paper - II) ANSWERS PHYSICS (A,B,C) 8. (B,C,D) 9. (A,C) 10. (B,C) 11. (A, C) (1) 19. () 0. (4) CHEMISTRY (A, B) 8. (B, C) 9. (A, B, C) 0. (B, C, D) 1. (A, B, D) (7) 9. (4) 40. (4) MATHEMATICS (B, D) 48. (A, B) 49. (A, B) 50. (A, B) 51. (A, C) () 59. (0) 60. () 1/10

CHEMISTRY. SECTION 1 (Maximum Marks : 28) at room temperature changes from gas to solid down the group (B) decrease in HOMO-LUMO gap down the group

CHEMISTRY. SECTION 1 (Maximum Marks : 28) at room temperature changes from gas to solid down the group (B) decrease in HOMO-LUMO gap down the group JEE ADVANCED 07_-05-7 (PAPER-I)_Code-0 [ ] This section contains SEVEN questions. CEMISTRY SECTIN (Maximum Marks : 8) Each question has FUR options (A), (B), (C) and (D). NE R MRE TAN NE of these four