Joint Entrance Exam/IITJEE-2017 Paper Code - C

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Joint Entrance Exam/IITJEE-07 Paper Code - C nd April 07 9.0 AM.0 PM Important Instructions: CHMISTRY, MATHEMATICS & PHYSICS.

1 Joint Entrance Exam/IITJEE-07 Paper Code - C nd April AM.0 PM Important Instructions: CHMISTRY, MATHEMATICS & PHYSICS. Immediately fill in the particulars on this page of Test Booklet with only Blue / Black Ball Point Pen provided in the examination hall.. The Answer Sheet is kept inside this Test Booklet. When you are directed to open the Test Booklet, take out the Answer Sheet and fill in the particulars carefully.. The test is of hours duration.. The Test Booklet consists of 90 questions. The maximum marks are There are three parts in the question paper A, B, C, consisting of Chemistry, Mathematics and Physics having 0 questions in each part of equal weightage. Each question is allotted (four) marks for each correct response. 6. Candidates will be awarded, marks as stated above in instruction No. 5 for correct response of each question. ¼ (one fourth) marks of the total marks allotted to the question (i.e. mark) will be deducted for indicating incorrect response for each question. No deduction from the total score will be made if no response is indicated for an item in the answer sheet. 7. There is only one correct response for each question. Filling up more than one response in each question will be treated as wrong response and marks for wrong response will be deducted accordingly as per instruction 6 above. 8. For writing particulars/marking responses on Side - and Side- of the Answer Sheet use only Black Ball Point Pen provided in the examination hall. 9. 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 room/hall. 0. Rough work is not to be done on the space provided for this purpose in the Test Booklet only. This space is given at the bottom of each page and in four pages (Pages 0-) at the end of the booklet.. 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.. The CODE for this booklet is C. Make sure that the CODE printed on Side of the Answer Sheet and also tally the serial number of the Test Booklet and Answer Sheet are the same as that on this booklet. In case of discrepancy, the candidate should immediately report the matter to the Invigilator for replacement of both the Test Booklet and the Answer Sheet.. Do not fold or make any stray mark on the Answer Sheet. VMC/IIT JEE-07 JEE Entrance Examination

2 Joint Entrance Exam/IITJEE-07 CHMISTRY, MATHEMATICS & Physics PART-A CHEMISTRY. The freezing point of benzene decreases by 0.5 C when 0. g of acetic acid is added to 0 g of benzene. If acetic acid associates to form a dimer in benzene, percentage association of acetic acid in benzene will be : (K f for benzene = 5. K kg mol ) 9.6 % () 6.6 % () 80.% 7.6%. On treatment of 00 ml of 0. M solution of CoCl.6HO with excess AgNO ; precipitated. The complex is: [Co(HO) 5Cl]Cl.HO () [Co(HO) Cl ]Cl.H O () [Co(HO) Cl ].H O [Co(HO) 6]Cl. 0 ions are. Which of the following compounds will form significant amount of meta product during mono-nitration reaction? () (). The products obtained when chlorine gas reacts with cold and dilute aqueous NaOH are: Cl and ClO () ClO and ClO () ClO and ClO Cl and ClO 5. Both lithium and magnesium display several similar properties due to the diagonal relationship; however, the one which is incorrect, is: nitrates of both Li and Mg yield NO and O on heating () both form basic carbonates () both form soluble bicarbonates both form nitrides 6. A water sample has ppm level concentration of following anions F 0; SO 00; NO 50 The anion/anions that make/makes the water sample unsuitable for drinking is/are: Only () Both SO () Only NO SO and NO Only F 7. The formation of which of the following polymers involves hydrolysis reaction? Terylene () Nylon 6 () Bakelite Nylon 6, 6 VMC/IIT JEE-07 JEE Entrance Examination

3 8. The Tyndall effect is observed only when following conditions are satisfied : (a) (b) (c) (d) The diameter of the dispersed particles is much smaller than the wavelength of the light used. The diameter of the dispersed particle is not much smaller than the wavelength of the light used. The refractive indices of the dispersed phase and dispersion medium are almost similar in magnitude. The refractive indices of the dispersed phase and dispersion medium differ greatly in magnitude. (b) and (c) () (a) and (d) () (b) and (d) (a) and (c) 9. pk a of weak acid (HA) and salt (AB) solution is: pk b of a weak base (BOH) are. and., respectively. The ph of their.0 () 7. () The major product obtained in the following reaction is : () (). Which of the following compounds will behave as a reducing sugar in an aqueous KOH solution. () (). The correct sequence of reagents for the following conversion will be Ag NH () Ag NH OH,CH MgBr, H / CH OH OH, H / CH OH, CH MgBr () CH MgBr, H / CH OH, Ag NH CH MgBr, Ag NH OH OH, H / CH OH VMC/IIT JEE-07 JEE Entrance Examination

4 . Which of the following species is not paramagnetic? B () NO () CO O. Which of the following, upon treatment with tert-buona followed by addition of bromine water, fails to decolourize the colour of bromine? () () 5. Which of the following reactions is an example of a redox reaction? XeF6 HO XeOF HF () XeF OF XeF6 O 5 6 XeF PF XeF PF XeF6 HO XeOF HF () 6. U is equal to: Isothermal work () Isochoric work () Isobaric work Adiabatic work 7. Which of the following molecules is least resonance stabilized? () () 8. The increasing order of the reactivity of the following halides for the S N reaction is: I. CH C HCHCH Cl II. CHCHCHCl III. 6 (II) < (III) < (I) () (III) < (II) < (I) () (II) < (I) < (III) (I) < (III) < (II) p H CO C H CH Cl 9. gram of a carbonate (M CO ) on treatment with excess HCl produces mole of CO. The molar mass of M CO in g mol is:.86 () 86 () Sodium salt of an organic acid X produces effervescence with conc. H SO. X reacts with the acidified aqueous CaCl solution to give a white precipitate which decolourises acidic solution of KMnO. X is : Na C O () C 6 H 5 COONa () HCOONa CH COONa. The most abundant elements by mass in the body of a healthy human adult are: Oxygen (6.%); Carbon (.9%), Hydrogen (0.0%); and Nitrogen (.6%). The weight which a 75 kg person would gain if all H atoms are replaced by H atoms is: 0 kg () 5 kg () 7.5 kg 7.5 kg VMC/IIT JEE-07 JEE Entrance Examination

5 . The major product obtained in the following reaction is : 6 5 t t C H CH O BuCHC6H 5 () t () C6H5CH CHC6H5 C H CH O Bu CH C H C H CH O Bu CH C H Given : C O (g) CO (g); H 9.5 kj mol (graphite) r H (g) O (g) HO(l); rh 85.8 kj mol CO (g) H O(l) CH (g) O (g); H 890. kj mol r Based on the above thermochemical equations, the value of C(graphite) H (g) CH (g) will be:.0 kj () +.0 kj r H mol () +7.8 kj at 98 K for the reaction mol mol 7.8 kj mol. In the following reactions, ZnO is respectively acting as a/an: (a) ZnO NaO NaZnO (b) ZnO CO ZnCO acid and base () base and acid () base and base acid and acid 5. The radius of the second Bohr orbit for hydrogen atom is: (Planck's Const. electron = kg; charge of electron kg m A ) 9 h Js; mass of e C; permittivity of vacuum. Å ().65 Å ().76 Å 0.59 Å 6. Two reactions R and R have identical pre-exponential factors. Activation energy of R exceeds that of R by 0 kj mol. If k and k are rate constants for reactions R and R respectively at 00 K, then ln(k /k ) is equal to : R 8. J mol K () 8 () 6 7. A metal crystallizes in a face centred cubic structure. If the edge length of its unit cell is a, the closest approach between two atoms in metallic crystal will be: a 8. The group having isoelectronic species is: O, F, Na,Mg () O, F, Na, Mg () a () a a () O O, F, Na, Mg, F, Na, Mg VMC/IIT JEE-07 5 JEE Entrance Examination

6 Cl / Cl Cr / Cr 9. Given E.6 V, E 0.7V CrO7 / Cr MnO / Mn E. V, E.5V Among the following, the strongest reducing agent is: Cl () Cr () Mn + Cr Methyl-pent--ene on reaction with HBr in presence of peroxide forms an addition product. The number of possible stereoisomers for the product is: Four () Six () Zero Two PART-B MATHEMATICS. The integral dx is equal to : cos x () () n tan x dx, n. If ordered pair (a, b) is equal to : n. Let I I I atan x bx C, where C is a constant of integration, then the 5, () 0 5,. The area (in sq. units) of the region () 5, 0 5, x,y : x 0, x y, x y and y x is : 7 () 5 () 59. A box contains 5 green and 0 yellow balls. If 0 balls are randomly drawn, one-by-one, with replacement, then the variance of the number of green balls drawn is : () 6 5 dy 5. If ( sin x) ( y ) cos x 0 and y(0), then dx () () () 5 y is equal to : 6. Let be a complex number such that z where z. If k, then k is equal to : 7 6 () () z z VMC/IIT JEE-07 6 JEE Entrance Examination

7 7. Let a i j k and b i ˆ ˆ j. Let c be a vector such that c a angle between c and a b 5 () be 0. Then a c is equal to : 8 8. The radius of a circle, having minimum area, which touches the curve y x is : () 5 8, a b c and the y x and the lines () () 9. If for x 0,, the derivative of 6 tan x x is x g( x), then g( x ) equals : 9x x 9x () 9x () 9 9x x x 9x 0. If two different numbers are taken from the set {0,,,,., 0} ; then the probability that their sum as well as absolute difference are both multiple of, is : 5 () 7 55 () cot x cos x lim x x 8 equals : () () 6. The value of C C C C C C C C... C0 C0, is : 0 9 () 0 0 () 0. For three events A, B and C, P(Exactly one of A or B occurs) = P (Exactly one of B or C occurs) = P (Exactly one of C or A occurs) = and P (All the three events occur simultaneously) = 6. Then the probability that at least one of the events occurs, is : 7 6 () 6 () Let a vertical tower AB have its end A on the level ground. Let C be the mid point of AB and P be a point on the ground such that AP AB. If BPC, then tan is equal to : 9 () 9 () 6 7 VMC/IIT JEE-07 7 JEE Entrance Examination

8 5. The eccentricity of an ellipse whose centre is at the origin is. the equation of the normal to it at, is : If one of its directrices is x, then x y 7 () x y () y x x y 6. If, for a positive integer n, the quadratic equation, x x x x... x n x n 0n has two consecutive integral solutions, then n is equal to : 0 () () 9 7. The following statement p q p q q is : equivalent to p q () a fallacy () a tautology equivalent to p q 8. The normal to the curve through the point :, y x x x 6 at the point where the curve intersects the y-axis, passes (), 9. For any three positive real numbers, and, (),, a b c a b c ac b a c Then : a, b and c are in A.P. () a, b and c are in G.P. () b, c and a are in G.P. b, c and a are in A.P. 50. If the image of the point P(,,) in the plane, x y z 0 measured parallel to the line, x y z is Q, then PQ is equal to : 5 () 6 5 () 5 5. If 5(tan x cos x) cos x 9, then the value of cos x is : 9 () 7 () Let a, b, c R. If is such that a + b + c = and f ( x y) f ( x) f ( y) xy, f ( x) ax bx c 0 x, y R, then f ( n) is equal to : n 90 () 55 () 0 65 VMC/IIT JEE-07 8 JEE Entrance Examination

9 5. The distance of the point (,, 7) from the plane passing through the point (,, ), having normal 7 perpendicular to both the lines x y z and x y z is : () () If S is the set of distinct values of 'b' for which the following system of linear equations x y z 55. If x ay z ax by z has no solution, then S is : 0 a finite set containing two or more elements () a singleton () an empty set an infinite set A, then adj A A () is equal to : A hyperbola passes through the point hyperbola at P also passes through the point : () P, and has foci at, Then the tangent to this, (), (),, 57. Let k be an integer such that the triangle with vertices k, k, 5, k and k, units. Then the orthocentre of this triangle is at the point :, (), (), has area 8 sq., 58. Twenty meters of wire is available for fencing off a flower-bed in the form of a circular sector. Then the maximum area (in sq. m) of the flower-bed, is : 5 () 0 () The function f : R, x is : defined as f x x, Surjective but not injective () Neither injective not surjective () Invertible Injective but not surjective 60. A man X has 7 friends, of them are ladies and are men. His wife Y also has 7 friends, of them are ladies and are men. Assume X and Y have no common friends. Then the total number of ways in which X and Y together can throw a party inviting ladies and men, so that friends of each of X and Y are in the party, is : 69 () 8 () VMC/IIT JEE-07 9 JEE Entrance Examination

10 PART-C PHYSICS 6. An observer is moving with half the speed of light towards a stationary microwave source emitting waves at frequency 0 GHz. What is the frequency of the microwave measured by the observer? (speed of light = 0 8 ms ). GHz () 7. GHz () 5. GHz 0. GHz 6. The following observations waver taken for determining surface tension T of water by capillary method: Diameter of capillary, D.5 0 m rise of water, h.5 0 m. Using is closest to: g 9.80 m /s and the simplified relation rhg T 0 N / m, the possible error in surface tension.5% ().% () 0% 0.5% 6. Some energy levels of a molecule are shown in the figure. The ratio of the wavelengths r / is given by: () r () r r r 6. A body of mass m 0 kg is moving in a medium and experiences a frictional force speed is v0 0 ms. If, after 0 s, its energy is 0 kg s () 0 kg m mv 0, the value of k will be: 8 () 0 kg m s F k v. Its initial 0 kg m 65. C and C are specific heats at constant pressure and constant volume respectively. It is observed that p v C C a for hydrogen gas p p v C C b for nitrogen gas v The correct relation between a and b is: a b () a b () a 8 b a b 66. The moment of inertia of a uniform cylinder of length l and radius R about its perpendicular bisector is I. What is the ratio l/r such that the moment of inertia is minimum? () () 67. A radioactive nucleus A with a half life T, decays into a nucleus B. At t = 0, there is no nucleus B. At sometime t, the ratio of the number of B to that of A is 0.. Then, t is given by: t log. T log () t T log. () T t log. T log t log. 68. Which of the following statements is false? VMC/IIT JEE-07 0 JEE Entrance Examination

11 In a balanced Wheatstone bridge if the cell and the galvanometer are exchanged, the null point is disturbed. () A rheostat can be used as a potential divider () Kirchhoff s second law represents energy conservation Wheatstone bridge is the most sensitive when all the four resistances are of the same order of magnitude 69. A capacitance of µf is required in an electrical circuit across a potential difference of.0 kv. A large number of µf capacitors are available which can withstand a potential difference of not more than 00 V. The minimum number of capacitors required to achieve this is: 6 () () 70. In the given circuit diagram when the current reaches steady state in the circuit, the charge on the capacitor of capacitance C will be : r r CE () CE ( r r ) ( r r ) r () CE CE ( r r ) 7. In the above circuit the current in each resistance is: 0.5 A () 0.5A () 0 A A 7. In amplitude modulation, sinusoidal carrier frequency used is denoted by c and the signal frequency is denoted by m. The bandwidth ( m) of the signal is such that m c. Which of the following frequencies is not contained in the modulated wave? c () m c () c m m 7. In a common emitter amplifier circuit using an n-p-n transistor, the phase difference between the input and the output voltages will be: 90º () 5º () 80º 5º 7. A copper ball of mass 00 gm is at a temperature T. It is dropped in a copper calorimeter of mass 00 gm, filled with 70 gm of water at room temperature. Subsequently, the temperature of the system is found to be 75ºC. T is given by: (Given : room temperature = 0ºC, specific heat of copper = 0. cal/gmºc) 885ºC () 50ºC () 85ºC 800ºC VMC/IIT JEE-07 JEE Entrance Examination

12 75. In a Young s double slit experiment, slits are separated by 0.5 mm, and the screen is placed 50 cm away. A beam of light consisting of two wavelengths, 650 nm and 50 nm, is used to obtain interference fringes on the screen. The least distance from the common central maximum to the point where the bright fringes due to both the wavelengths coincide is: 7.8 mm () 9.75 mm () 5.6 mm.56 mm 76. An electric dipole has a fixed dipole moment P, which makes angle with respect to x-axis. When subjected to an electric field E ˆ Ei, it experiences a torque T ˆ k. When subjected to another electric field ˆ E E j it experiences a torque T T. The angle is: 5º () 60º () 90º 0º 77. A slender uniform rod of mass M and length l is pivoted at one end so that it can rotate in a vertical plane (see figure). There is negligible friction at the pivot. The free end is held vertically above the pivot and then released. The angular acceleration of the rod when it makes an angle with the vertical is: g sin () l g cos () l g cos l g sin l 78. An external pressure P is applied on a cube at 0 C so that it is equally compressed from all sides. K is the bulk modulus of the material of the cube and is its coefficient of linear expansion. Suppose we want to bring the cube to its original size by heating. The temperature should be raised by: P K () PK () PK 79. A diverging lens with magnitude of focal length 5 cm is placed at a distance of 5 cm from a converging lens of magnitude of focal length 0 cm. A beam of parallel light falls on the diverging lens. The final image formed is: Virtual and at a distance of 0 cm from convergent lens. () Real and at a distance of 0 cm from the divergent lens. () Real and at a distance of 6 cm from the convergent lens. Real and at a distance of 0 cm from convergent lens. P K 80. An electron beam is accelerated by a potential difference V to hit a metallic target to produce X-rays. It produces continuous as well as characteristic X-rays. If min is the smallest possible wavelength of X- ray in the spectrum, the variation of log min with log V is correctly represented in: () () VMC/IIT JEE-07 JEE Entrance Examination

13 8. The temperature of an open room of volume atmospheric pressure in the room remains 0 Pa room before and after heating, then n f ni will be : 0m increases from 7 C to 7 C due to the sunshine. The 5. If n i and n f are the number of molecules in the.8 0 () () In a coil of resistance 00, a current is induced by changing the magnetic flux through it as shown in the figure. The magnitude of change in flux through the coil is: 5Wb () 50Wb () 75Wb 00Wb 8. When a current of 5mA is passed through a galvanometer having a coil of resistance 5, it shows full scale deflection. The value of the resistance to be put in series with the galvanometer to convert it into a voltmeter of range 0 0V is :.05 0 ().55 0 () A time dependent force F 6t acts on a particle of mass kg. If the particle starts from rest, the work done by the force during the first sec. will be: J () 9 J () 8 J.5 J 85. A magnetic needle of magnetic moment Am and moment of inertia kg m is performing simple harmonic oscillations in a magnetic field of 0.0 T. Time taken for 0 complete oscillations is: 8.89 s () 6.98s () 8.76 s 6.65s 86. The variation of acceleration due to gravity g with distance d from centre of the earth is best represented by (R = Earth s radius) : VMC/IIT JEE-07 JEE Entrance Examination

14 87. A body is thrown vertically upwards. Which one of the following graphs correctly represent the velocity vs time? () () 88. A particle A of mass m and initial velocity v collides with a particle B of mass The collision is head on, and elastic. The ratio of the de-broglie wavelengths is: A B () A B () A B A to m which is at rest. after the collision A B B 89. A particle is executing simple harmonic motion with a time period T. At time t = 0, it is at its position of equilibrium. The kinetic energy time graph of the particle will look like: () () 90. A man grows into a giant such that his linear dimensions increase by a factor of 9. Assuming that his density remains same, the stress in the leg will change by a factor of : 9 () 8 () 8 9 VMC/IIT JEE-07 JEE Entrance Examination

CHEMISTRY PART A (1) (2) (3) (4) 4. The products obtained when chlorine gas reacts with cold and dilute aqueous NaOH are : [Ans.

CHEMISTRY PART A (1) (2) (3) (4) 4. The products obtained when chlorine gas reacts with cold and dilute aqueous NaOH are : [Ans. JEE(Main) 07 HEMISTRY PART A. The freezing point of benzene decreases by 0.5 when 0. g of acetic acid is added to 0 g of benzene. If acetic acid associates to form a dimer in benzene, percentage association