JEE MAIN 2017 Test Paper Code C Questions with Solutions

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1 Disclaimer: These solutions are provided by the academic team of BASE. These solutions may be different from those to be provided by the Central Board of Secondary Education (CBSE) due to difference in assumptions taken in support of the solutions. In such case solution as provided by CBSE will be deemed as final. Every effort is made to provide accurate and complete information on this website. However, BASE cannot guarantee that there will be no errors. With respect to information on this website, neither BASE, nor their employees, representatives or Board members make any warranty, expressed or implied, with respect to information available from this website. Additionally, BASE assumes no legal liability for the accuracy, completeness or usefulness of any information disclosed herein. JEE MAIN 7 Test Paper Code C Questions with Solutions CHEMISTRY. The freezing point of benzene decreases by.5 C when. g of acetic acid is added to g of benzene. If acetic acid is 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% () 8.% () 7.6% Ans () i kf w Tf M w Tf i M w k w f.56 i CH CH (CH CH) Number of particles after association i Number of particles before association.57 =.96 % of association = 9.6. n treatment of ml of. M solution of CoCl 6H with excess AgN ;. ions are precipitated. The complex is () [Co(H ) 5 Cl]Cl.H () [Co(H ) Cl ]Cl.H () [Co(H ) Cl ].H () [Co(H ) 6 ]Cl Ans ()

2 Number of moles of CoCl.6H = M V(L) =.. = Number of moles of Cl in the complex = = Number of moles of Cl. precipitated =. 6. Number of moles of Cl remaining unprecipitated = = Since ions precipitate is twice the moles of compound, Cl atoms should be outside co-ordination sphere. Formula of compound is [Co(H ) 5 Cl]Cl.H. Which of the following compounds will form significant amount of meta product during mono-nitration reaction? NHCCH H CCH NH () () () () Aniline will form anilinium ion in the presence of nitrating mixture, which is meta directing. + NH NH NH + conc. HN N conc. H S Anilinium ion (meta directing). The products obtained when chlorine gas reacts with cold and dilute aqueous NaH are () Cl and Cl () Cl and Cl () Cl and Cl () Cl and Cl NaH Cl NaCl NaCl H cold & dilute 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 N and on heating () both form basic carbonates () both form soluble bicarbonates () both form nitrides Ans () Magnesium forms basic carbonate while lithium does not form. 6. A water sample has ppm level concentration of following anions F ; S ; N 5 The anion/anions that make/makes the water sample unsuitable for drinking is/ are () only S () only N () both S and N () only F nly F maximum limit of F is ppm. N JEE-MAIN 7

3 7. The formation of which of the following polymers involves hydrolysis reaction? () Terylene () Nylon 6 () Bakelite () Nylon 6, 6 Ans () NH H 8. The Tyndall effect is observed only when following conditions are satisfied H N (a) The diameter of the dispersed particles is much smaller than the wavelength of the light used (b) The diameter of the dispersed particle is not much smaller than the wavelength of the light used. (c) The refractive indices of the dispersed phase and dispersion medium are almost similar in magnitude. (d) 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) Ans () Each conceptual. 9. pk a of a weak acid (HA) and pk b of a weak base (BH) are. and., respectively. The ph of their salt (AB) solution is: (). () 7. () 6.9 () 7. Ans () ph 7 (pka pk b ) 7 (..) = 7. = 6.9. The major product obtained in the following reaction is DIBAL H N-6 N H n CH H () CH () CH CH H () CH CH () CH Ans () CH CH

4 . Which of the following compounds will behave as a reducing sugar in an aqueous KH solution? HH C HH CH CH C CH H () H () H H CCH H H () HH C Ans () H CH H H () HH C CH H H CCH H KH(aq) HH C H HH C. The correct sequence of reagents for the following conversion will be H CH H CH H CH H H CH H H -D-fructofuranose (reducing sugar) CH H CH CH () [Ag(NH ) ] + H, CH MgBr, H + /CH H () [Ag(NH ) ] + H, H + /CH H, CH MgBr () CH MgBr, H + /CH H, [Ag(NH ) ] + H () CH MgBr, [Ag(NH ) ] + H, H + /CH H Ans () H [Ag(NH ) ]H CH H/H + heat. Which of the following species is not paramagnetic? heat X CH MgBr excess H () B () N () C () Ans () No paired electron in C. Which of the following, upon treatment with tert-buna followed by addition of bromine water, fails to decolourize the colour of bromine? () Br () Br H H () Br C 6 H 5 () Br JEE-MAIN 7

5 Ans () Br (no - proton) 5 tert-buna 5. Which of the following reactions is an example of a redox reaction? alkene () XeF 6 + H Xe F + HF () XeF + F XeF 6 + () XeF + PF 5 [XeF] + PF 6 () XeF 6 + H XeF + HF Ans () 6 XeF F XeF 6 6. U is equal to () Isothermal work () Isochoric work () Isobaric work () Adiabatic work First equation for adiabatic change becomes U = q + w U = + w Thus, U = w 7. Which of the following molecules is least resonance stabilized? () Ans () () () () N The compound given as option () is a dienone which is non-aromatic, whereas rest of the compounds are aromatic. Hence, dienone is least resonance stabilized. 8. The increasing order of the reactivity of the following halides for the S N reaction is CH CHCH CH CH CH CH Cl p H C C 6 H CH Cl Cl (I) (II) (III) () (II) < (III) < (I) () (III) < (II) < (I) () (II) < (I) < (III) () (I) < (III) < (II) Ans () Greater the stability of carbocation higher is the reactivity towards S N reaction. Carbocations (I) and (II) are stabilized by hyperconjugation, whereas carbocation (III) is stabilised by resonance. 9. gram ot a carbonate (M C ) on treatment with excess HC produces.86 mole of C. The molar mass of M C in g mol is ().86 () 86 () 8. () 8.6 Ans () M C HCl MCl C H g.86 mol.86 M Molecular Mass = 8. g mol.86

6 . Sodium salt of an organic acid X produces effervescence with conc. H S. X reacts with the acidified aqueous CaC solution to give a white precipitate which decolourises acidic solution of KMn. X is () Na C () C 6 H 5 CNa () HCNa () CH CNa Ans () Na C H S Na S H C (X) effervescence CaCl NaCl + CaC (s) white ppt (calcium oxalate) decolourization 5C Mn 8H C Mn H. The most abundant elements by mass in the body of a healthy human adult are: xygen (6.%); Carbon (.9%), Hydrogen (.%); and Nitrogen (.6%). The weight which a 75 kg person would gain if all H atoms are replaced by H atoms is () kg () 5 kg () 7.5 kg () 7.5 kg Mass of H Kg Mass of D, if replaced = 7.5 = 5 kg Mass gained = = 7.5 kg. The major product obtained in the following reaction is Br C 6 H 5 C (+) H C 6 H 5 t BuK () ()C 6 H 5 CH( t Bu)CH C 6 H 5 () ()C 6 H 5 CH( t Bu)CH C 6 H 5 () C 6 H 5 CH = CHC 6 H 5 () (+)C 6 H 5 CH( t Bu)CH C 6 H 5 Ans () Base t BuK being bulky, it will abstract proton and -elimination takes place. Br C 6 H 5 (+). Given C (graphite) + (g) C (g); r H = 9.5 kj mol H (g) + (g) H (l); r H = 85.8 kj mol H heat t BuK C 6 H 5 C heat 6 H 5 CH = CHC 6 H 5 C (g) + H (l) CH (g) + (g); r H = +89. kj mol Based on the above thermochemical equations, the value of r H at 98 K for the reaction C (graphite) + H (g) CH (g) Will be (). kj mol () +7.8 kj mol () +. kj mol () 7.8 kj mol C C H 9.5 kj / mol () JEE-MAIN 7 6

7 H H H 85.8 kj / mol () C H CH H 89. () Eq() Eq() Eq() gives C H CH H 9.5 ( 85.8) kj / mol. In the following reactions, Zn is respectively acting as a/an: (a) Zn + Na Na Zn (b) Zn + C ZnC () acid and base () base and acid () baseandbase () acid and acid Ans () Zn Na Na Zn Acidic oxide Basic oxide Basic oxide Zn C ZnC Acidic oxide 5. The radius of the second Bohr orbit for hydrogen atom is: (Planck s Const. h = 6.66 Js; mass of electron = 9.9 kg; charge of electron e =.6 9 C; permittivity of vacuum = kg m A ) (). Å ().65 Å ().76 Å ().59 Å Ans () Radius of n th Bohr orbit, r n = a n Radius of nd orbit r =.5 =. Å 6. Two reactions R and R have identical pre-exponential factors. Activation energy of R exceeds that of R by kj mol. If k and k are rate constants for reactions R and R respectively at K, then ln(k /k ) is equal to: (R = 8. J mol K ) () () 8 () () 6 Ans () k k Ae Ae Ea RT Ea RT RT k k e ln k k 8. k ln k 7. A metal crystallises 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 () () a () a () a Ans () r a a a r Closest approach between two atoms rs, r a r 7

8 8. The group having isoelectronic species is (), F, Na +, Mg + (), F, Na +, Mg + (), F, Na, Mg (), F, Na, Mg + Ans (),F,Na,Mg 6 all have s s p 9. Given E.6 V, E.7 V ; E. V, E.5 V. Among the Cl /Cl Cr /Cr Cr 7 /Cr Mn/Mn following, the strongest reducing agent is () Cl () Cr () Mn + () Cr + Ans () The one with low reduction potential is a good oxidising agent. E.7 V has lowest reduction potential. Cr /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 Ans () HBr Peroxide Br * * Number of optically active compounds = =. The integral dx is equal to cosx MATHEMATICS () () () () Given integral cos JEE-MAIN 7 8 x dx x tan x sec dx x tan tan tan 8 8 cot tan =

9 . Let n In tan x dx, (n ) ordered pair (a, b) is equal to (), (), 5 5 In n Tan x dx. If I + I 6 = a tan 5 x + bx 5 + C, where C is a constant of integration, then the (), 5 (), 5 n Tan x (sec x ) dx n tan x sec x dx I n n In In t dt n n t tan x n n If n = 6 5 tan x I6 I C 5 a ; b 5 (a,b), 5. The area (in sq. units) of the region (x, y) : x, x y, x y and y x () 7 () 5 Ans () Required area = A + A x A x dx x x x x x x x 8 9 A x A x dx x is () () 59 () 9

10 x x x.. 6 (, ) y (, ) A A (, ) x = y y x x x + y = 6 6 A Required Area = A + A = 9 5. A box contains 5 green and yellow balls. If balls are randomly drawn, one-by-one, with replacement, then the variance of the number of green balls drawn is () () 6 5 () 5 Ans () n =, p,q variance npq = dy 5. If ( sin x) (y ) cos x and y() =, then y is equal to dx () () () Ans () dy cos x (y ) dx sin x dy cosx cosx y dx sin x sin x cosxdx sin x log(sin x) I.F e e sin x y( sin x) sin x c x =, y = c = x, y( ) y 6. Let be a complex number such that + = z where z. If equal to () 6 () () () () z () z k 7, then k is JEE-MAIN 7

11 Ans () K R R R K K R R R K ( ) K ( ) K ( ) K ( z) K K = z 7. Let a i ˆ ˆj kˆ and b ˆi ˆj. Let c be a vector such that c a between c and a b be. Then a c is equal to () 5 () () a b c a b c sin i j k a b i( ) j( ) k( ) i j k a b c, a c a c a a.c 9 9 a.c 9 a.c a b c, () and the angle

12 8. The radius of a circle, having minimum area, which touches the curve y = x and the lines, y = x is () () () () Ans () Circle be x + (y k) = r k r k k k k k or k k k k r or or k k k or r ; Since r r r 9. If for x,, the derivative of 6x x tan is 9x x () 9x Ans () Let x x tan tan tan tan tan (tan ) tan (x x ) () 9x x g(x), then g(x) equals 9 () 9x x x () 9x 9x 9 x x 9x 9 So g(x) 9x. If two different numbers are taken from the set {,,,,..., } ; then the probability that their sum as well as absolute difference are both multiple of, is () () 7 () Ans () n(s) C 55 Let A = sum as well as absolute difference of the number is multiple of {(,),(,8),(,),(,6),(,8),(6,)} n(a) 6 n(a) 6 P(A) n(s) 55 y = x Y (, ) (, k) () 55 y = x JEE-MAIN 7

13 cot x cosx. lim equals x ( x) () 8 cot x cosx lt ( x) x () Put x h cot h cos h lt h ( h) tanh sinh lt h 8 h () () 6 sinh lt h 8 h cosh sinh h lt sin h 8 cosh h h sin tanh lt h 8 h h 8 6 C C C C C C C C... C C is. The value of () 9 () () () Ans () ( C + C + + C ) ( C + C + + C ) S = C + C + + C S = C + C C S = C + C + + C S = S = ( C + C + + C ) = ( C + C + + C ) ( C + C + + C ) = + =. 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). Then 6 the probability that at least one of the events occurs, is () 7 () () P(A) P(B) P(A B) () () 7 6

14 P(B) P(C) P(B C) () P(C) P(A) P(C A) () P(A B C) () 6 Adding (), (), () [P(A) P(B) P(C) P(A B) P(B C) P(C A)] P(A) P(B) P(C) P(A B) P(C A) 8 7 P(A B C) 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 () Ans () h tan h h tan( ) h tan tan tan tan tan tan tan tan 9 tan tan 9 5. The eccentricity of an ellipse whose centre is at the origin is. If one of its directrices is x =, then the equation of the normal to it at, is () x + y = 7 () x + y = () y x = () x y = a Given e ; x a a e Now b a ( e ) x y Equation to the ellipse is JEE-MAIN 7 P h B h C h A

15 Then x dy x = slope of the tangent at dx y, y 6,,, Equation of the normal at, is y (x ) i.e., x y i.e., x y = 6. If, for a positive integer n, the quadratic equation, x(x ) (x )(x )... x n (x n) n has two consecutive integral solutions, then n is equal to () () () () 9 Ans () nx + ( n ) x + [. + + n(n )] = n n(n )(n ) nx n x n (n )(n ) x nx For n = x + x + = (x + 5) (x + 6) = x = 5, x = 6 7. The following statement (p q) [(~ p q) q] is () equivalent to p ~ q () a fallacy () a tautology () equivalent to ~ p q Ans () p q p q ~p ~p q (~p q) q (p q) [(~p ~q) q] T T T F T T T T F F F T F T F T T T T T T F F T T F T T 8. The normal to the curve y (x ) (x ) = x + 6 at the point where the curve intersects the y-axis passes through the point (), y(x ) (x ) = x + 6 put x = y = P(, ) Differentiate y (x ) (x ) + y (x 5) = x =, y = y = (), (), (), 5

16 Slope of the normal = m' y' N : (y ) = (x ) x + y =, lies on the normal x + y = 9. For any three positive real numbers a, b and c, 9(5a + b ) + 5(c ac) = 5b(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. 5a + 9b + 5c 75ac 5ab 5bc = (5a) (b) (5c) (75)ac (5)ab (5)bc (5a b) + (b 5c) + (5a 5c) = 5a = b, b = 5c, 5a = 5c b = 5a, b = 5c, a = c If a = k, b = 5k, c = k b, c, a are in A.P. 5. If the image of the point P (,, ) in the plane, x y z measured parallel to the line, 5. If x y z is Q, then PQ is equal to: 5 () () 6 5 () 5 () Equation of line through P(,, ) and parallel to given line x y z 5 Point on line be ( +,, 5 + ) It lies on the plane x + y z + = = M (,, 8) PQ PM 5 5(tan x cos x) cos x 9, then the value of cos x is: () 9 Ans () () 5 (tan x cos x) = cos x tan x 5 cos x = (cos x ) tan x = 9 cos x sin x = 9 cos x + 7 cos x 5 5 cos x = 9 cos x + 7 cos x 9 cos x + cos x 5 = 9 cos x + 5 cos x cos x 5 = cos x ( cos x + 5) ( cos x + 5) = 7 () 9 () 5 JEE-MAIN 7 6

17 ( cos x + 5) ( cos x ) = cos x = 5 cos x = (not possible) cos x cos x = cos x [cos x ] 5. Let a,b,c R. If f (x) ax bx c is such that a b c and f (x y) f (x) f (y) xy, x,y R then n f (n) is equal to: () 9 () 55 () () 65 Ans () f(x + y) = f(x) + f(y) + xy x, y R f() = putting x =, y = f() = f() + = 7 putting x = y = f() = f() + f() + = n f (n) Aliter f() = a + b + c = f(x + y) = f(x) + f(y) + xy Differentiate partially w.r.t. x, f (x y) f ( ) y Now put x =, then y = x f (x) f () x f (x) x k x f (x) k put x = f () k 5 k 7

18 x 5 f (x) x 5 f (x) 5 f (x) (x ) x x The distance of the point (,, 7) from the plane passing through the point (,, ), having normal perpendicular to both the lines x y z and x y z 7, is: 5 () () () () The normal vector to the plane ˆi ˆj kˆ n 5i ˆ 7ˆj kˆ Equation to the plane is 5(x ) + 7 (y + ) + (z + ) = i.e., 5x + 7y + z + 5 = Distance of the point from (,, 7) to the above plane is If S is the set of distinct values of b for which the following system of linear equations x y z x ay z ax by z has no solution, then S is: () a finite set containing two or more elements () a singleton () an empty set () an infinite set Ans () No solution If A = (adj A) B a a b (a b) ( a) + (b a ) = a a + = a = The system of equations becomes x + y + z = JEE-MAIN 7 8

19 x + by + z = This system has no solution if b = 55. If A, then adj (A A) is equal to: (A) 6 7 (B) 8 5 (C) A 6 9 A 8 7 A A A A adj[a A] (D) A hyperbola passes through the point P(, ) and has foci at (, ). Then the tangent to this hyperbola at P also passes through the point: () (, ) () (, ) () (, ) () (, ) Foci ( ae, ) = (, ) ae = b = a (e ) a + b = (or) b = a The equation to the hyperbola is x y a a This passes through P, a 9a 8 a a (a 8) (a ) = a = ( a 8) Now the equation to the hyperbola is x y Equation of tangent at P, is y x is x y Which is satisfied only by, 9

20 57. Let k be an integer such that the triangle with vertices (k, k), (5,k) and ( k, ) has area 8 sq. units. Then the orthocenter of this triangle is at the point: (), (), Ans () k k 5 k 8 k k(k ) + k(5 + k) + ( + k ) = 56 5k + k 6 = k = A is perpendicular to BC h = Also B is perpendicular to AC k 8 h 5 k h 5 k orthocenter is, JEE-MAIN 7 (), (), 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 () ().5 () Ans () Perimeter P r r r r A r r r r r( r) (r) ( r) r r A attain for r r 5 Max area.5( ).5. 5 B (5, ) A (, 6) (h, k) C (, )

21 59. The function f : R, defined as x f (x), is: x () surjective but not injective () neither injective nor surjective () invertible () injective but not surjective. Ans () f : R, x f (x) x ( x ) x(x) x f (x) ( x ) ( x ) f (x) is both + ve and ve. Hence function is not injective. x x y x y x y x y x y y y y, Function is surjective. 6. 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 this party, is: () 69 () 8 () 85 () 68 Ans () X Y M L M L M L W H W H W H W H W H W H C. C. C. C C. C. C. C = = = 85 C. C C. C

22 PHYSICS ALL THE GRAPHS/DIAGRAMS GIVEN ARE SCHEMATIC AND NT DRAWN T SCALE. 6. An observer is moving with half the speed of light towards a stationary microwave source emitting waves at frequency GHz. What is the frequency of the microwave measured by the observer? (speed of light = 8 ms ) (). GHz () 7. GHz () 5. GHz (). GHz Ans () The observed frequency, f f v where.5 c f f 7. GHz s s 6. The following observations were taken for determining surface tension T of water by capillary method: diameter of capillary, D =.5 m rise of water, h =.5 m. Using g = 9.8 m/s rhg and the simplified relation T N / m, the possible error in surface tension is closest to: ().5% ().% () % ().5% Ans () T The fractional error in surface tension is given by T T r h g D h g T r h g D h g T.5 T T (%).5% T 6. Some energy levels of a molecule are shown in the figure. The ratio of the wavelengths r = /, is given by: () r () r () Ans () The energy of the photon of wave length is given by hc E E E () The energy of photon of wavelength is given by JEE-MAIN 7 r () r

23 hc E E E () 6. A body of mass m = kg is moving in a medium and experiences a frictional force F = kv. Its initial speed is v = ms. If, after s, its energy is mv, value of k will be: 8 () kg s () kg m () kg m s () kg m Ans () F dv kv a m dt m v dv k dt v m v t [ energy becomes v kt v m v kt v v m kt v m m k kg m v t () dv m kv dt v dv k v m vb v v dt k v m k k v v m v v m vm v m kv v m E m mv (m kv ) 8 m (m kv ) m m kv m kv m k kg m v mv 8 R v, speed becomes ]

24 65. C p and C v are specific heats at constant pressure and constant volume respectively. It is observed that C p C v = a for hydrogen gas C p C v = b for nitrogen gas The correct relation between a and b is: () a = b () a = b () a = 8 b () a b Ans () Considering specific heat in terms of mass m 5 Q mcpt RT W M m 5 mcvt R T M m m(cp C V) T R T M R Hence CP CV M R R From question CP CV a and b 8 or a = b Note: The problem doesn't states molar specific heat otherwise C P C V = R for all ideal gases a = b (There is ambiguity since generally capital symbols are used for molar specific heat) 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? () () () R l constant RldR R dl RldR R dl dr R dl l I mr ml di dr mr ml dl dl 6 R dr l dl 6 R l l 6 l 6 R l R () JEE-MAIN 7

25 67. A radioactive nucleus A with a half life T, decays into a nucleus B. At t =, there is no nucleus B. At sometime t, the ratio of the number of B to that of A is.. Then, t is given by: log. T () t T () t T log (.) () t () log log(.) Ans () After n half lives the number of nuclei left N N n t Here, n and N =.7 N T N R.7N n n 7 nlog = log. log. t T log 68. Which of the following statement is false? T log t log. () 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 Ans () magnitude. n changing the cell and the galvanometer the null point does not change. 69. A capacitance of F is required in an electrical circuit across a potential difference of. kv. A large number of F capacitors are available which can withstand a potential difference of not more than V. The minimum number of capacitors required to achieve this is () 6 () () () Ans () Let say there are n capacitors are connected in series and m number of such rows are connected as shown. The potential difference across each capacitor should be less than or equal to V 5

26 Hence n() n or n Also m F F or m = 8 Hence total capacitors required = 8 = 7. In the given circuit diagram when the current reaches steady state in the circuit, the on the capacitor of capacitance C will be: r r r () CE () CE () CE (r r) (r r ) (r r) Ans () () CE When steady state is reached, the current through capacitor is zero. Hence current through resistance r is E i r r Er The potential difference across capacitor and resistance r is same and it is V ir r r CEr Hence Q = CV r r 7. In the above circuit the current in each resistance is: ().5 A ().5 A () A () A Ans () By allotting V at terminals A and B, it is clearly seen that points C, D; E, F ; G, H are equipotential points, hence no current flows through branch AB, CD or EF. Current through each resistance = A. JEE-MAIN 7 6

27 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 The variation of amplitude modulated (AM) wave with frequency () is given as: Hence, m is not contained in modulated wave. 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: () 9 () 5 () 8 () 5 Ans () In a common emitter amplifier, the input diode (emitter base junction) is forward biased and the output diode (collector base junction) is reverse biased. Hence positive half cycle of input signal is converted into large negative half cycle at the output. Hence the phase difference between input and output is A copper ball of mass gm is at a temperature T. It is dropped in a copper calorimeter of mass gm, filled with 7 gm of water at room temperature. Subsequently, the temperature of the system is found to be 75 C. T is given by: (Given: room temperature = C, specific heat of copper =. cal/gm C) () 885 C () 5 C () 85 C () 8 C Ans () Heat lost by hot body = Heat gained by cold body Heat lost by copper ball = heat gained by copper calorimeter + heat gained by water m s (t 75) m s (75 ) m s (75 ) ball ball calori calori water water. (t 75) t 885 C 75. In a Young s double slit experiment, slits are separated by.5 mm, and the screen is placed 5 cm away. A beam of light consisting of two wavelengths, 65 nm and 5 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 Ans () nd nd d d n 5 n 65 5 th bright fringe corresponding to 65 nm coincides with 5 th bright fridge corresponding to 5 nm. 7

28 Distance of th bright fringe from central maximum D d 9 D.5m, 65 m d 5 m Distance = 7.8 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 E Eˆ j it experiences a torque T T. The angle is: () 5 () 6 () 9 () Ans () I case a PEsin ( k) II case PE cos (k) as we have tan 6 choice () is correct 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 ml l We have mg sin = I ml l But I m m l ml l mg sin gsin l () g cos l mg () g cos l () g sin l JEE-MAIN 7 8

29 78. An external pressure P is applied on a cube at 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 () () a P () PK () ak PK K PV V P K ; V V K V L But dt V L P dt K P t k 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 cm. A beam of parallel light falls on the diverging lens. The final image formed is: () virtual and at a distance of cm from convergent lens. () real and at a distance of cm from the divergent lens. () real and at a distance of 6 cm from the convergent lens. () real and at a distance of cm from convergent lens. For diverging lens u and f 5 v 5 For converging lens u 5 5 f v = 8. 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: () () () () In X-ray continuous spectrum. hc ev min 9

30 hc k min ev V say log log k log V min 8. The temperature of an open room of volume m increases from 7 C to 7 C due to the sunshine. The atmospheric pressure in the room remains Pa. If n i and n f are the number of molecules in the room before and after heating, then n f n i will be: ().8 ().5 5 ().5 5 ().6 Ans () We know that P V ni N A RT n n f PV N RT i f A P V N R 9 5 m [.5].8 =.5 5 A f ni 8. In a coil of resistance, 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: () 5 Wb () 5 Wb () 75 Wb () Wb Ans () We know that d dt d i R dt dq d dt R dt q R q = Area under the current-time graph 5 Wb 8. When a current of 5 ma 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 V is: ().5 ().55 ().5 ().985 JEE-MAIN 7

31 I = 5 ma for full scale deflection G = 5 X =? Voltmeter range = V V (5 x) 5mA x = 5 = 985 x = 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 F 6t 6t a 6t m dv 6t dt v dv 6 t dt 6 [v] [t ] v v According to work energy theorem W K mv mu mv ().5 J 85. A magnetic needle of magnetic moment 6.7 Am and moment of inertia kg m is performing simple harmonic oscillations in a magnetic field of. T. Time taken for complete oscillations is: () 8.89 s () 6.98 s () 8.76 s () 6.65 s M = 6.7 Am I = kg m B = T 6 I 7.5 Using formula T MB 6.7 = 6.65 s

32 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): () () () () Ans () If r < R, Gm g m r r G g r G r r g r If r > R, GM g r g r 87. A body is thrown vertically upwards. Which one of the following graphs correctly represent the velocity vs time? () () () () Ans () Acceleration is constant and g is downwards. Hence the graph is a straight line. 88. A particle A of mass m and initial velocity v collides with a particle B of mass m which is at rest. The collision is head on, and elastic. The ratio of the de-broglie wavelengths A to B after the collision is: A () A () A () A () B Ans () m From conservative of linear momenta, mv mv v v + v = v () v v Also v v v = v () v v Hence, v and v m v A p B B p v A m B B B JEE-MAIN 7

33 89. A particle is executing simple harmonic motion with a time period T. At time t =, it is at its position of equilibrium. The kinetic energy - time graph of the particle will look like: () () () () Ans () T T Kinetic energy is minimum and zero at t, T Kinetic energy is maximum at t,,t and kinetic energy increases non-linearly. T t Alternate method Ans () At t =, KE = max t t, KE = t t, KE = max T t, KE = T t v = t = T t v max v = T T T 9. 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 Mass = Ah M = 8 9 (Ah) A = 8A M'g 9(Ah )g New stress 9h g A' A M Ahg ld stress h g A A Stress increases 9 times T * * *