PART A MATHEMATICS (SET-D)

Transcription

1 JEE MAIN-07 (PAPER & SOLUTIONS) PART A MATHEMATICS (SET-D) ALL THE GRAPHS GIVEN ARE SCHEMATIC AND NOT DRAWN TO SCALE. 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 0 has no solution, then S is: () an empty set () an infinite set () a finite set containing two or more elements (4) a singleton a (a ) a b By putting a =, we get x y z x y z x by z 0 Now, if b =, then there cannot be any solution of the system because x + y + z cannot be equal to both 0 and simultaneously.. The following statement (p q) [ ~ p q q] is: () a tautology () equivalent to ~ p q () equivalent to p ~ q (4) a fallacy p q ~ p (~ p q) q p q (~ p q) q p q ~ p q If () 5(tan x cos x) cos x 9, then the value of cos 4x is: () 5 () 9 (4) 7 9 5( cos x) 5cos x 4cos x 7 cos x 4 9 cos x cos x 5 0 cos x or 5

2 JEE MAIN-07 (PAPER & SOLUTIONS) cos 4x cos x 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) = 4 6. Then the probability at least one of the events occurs, is: () 7 () 7 () 7 (4) Solution: () P A B C = P(Exactly one of A or B) + P(Exactly one of B or C) + P(Exactly one of C or A) + P (All of A, B & C) P A B C P A B C 6 5. Let be a complex number such that z where z. If k is equal to: () z () z () (4) i As k ( ) k ( ) k = z k 7, then 6. Let k be an integer such that the triangle with vertices (k, k), (5, k) and ( k, ) has area 8 sq. units. Then the orthocentre of this triangle is at the point: (), (), (), 4 (4), 4 k k 5 k 8 5k k 46 0 k k or k 5 Points are (, 6), (5, ), (, ), Let orthocentre be (x, y)

3 JEE MAIN-07 (PAPER & SOLUTIONS) y 6 x x 5 y 6 y x x 5 7. 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 () 5 (4) 0 Solution: () (0 r) r r 0 r Area = r r (0 r) For maximum r = 0 r r = 5 Area = 5 8. The area (in sq. units) of the region {(x, y): x 0, x + y, x 4y and y + x } is: () 59 () () 7 (4) 5 x x 5 Area = x dx x dx If the image of the point P(,, ) in the plane, x + y 4z + = 0 measured parallel to the line, x y z is Q, then PQ is equal to: 4 5 () 5 () 4 () 4 (4) 6 5 Solution: () Parametric equation of line PQ is, 4, 5 Mid point of PQ lie on the given plane Now distance PQ = ( ) (6 ) ( ) 4

4 0. If for 9 () 9x JEE MAIN-07 (PAPER & SOLUTIONS) 4 x 0, 4, the derivative of 6x x tan is 9x x x () 9x x () 9x x. g(x), then g(x) equals: (4) 9x 6x x = x y tan tan 9x dy.. 9 dx 9x 9 g(x) 9x dy. If ( sin x) (y ) cos x 0 and y(0) =, then y is equal to: dx () () () (4) 4 dy sin x y cos x 0 dx d sin x y 0 dx sin x y c ; c = 4 as y(0) = y. 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: () 6 7 () 4 () 9 (4) 4 9 Solution: () tan, tan 4 tan tan tan tan tan 9. If A 4, then adj (A + A) is equal to: () 6 5 () 84 7 () 6 7 (4)

5 JEE MAIN-07 (PAPER & SOLUTIONS) 5 Solution: () Adj(A A) = For any three positive real numbers a, b and c, 9 (5a + b ) + 5(c ac) = 5b(a + c). Then: () b, c and a are in G.P. () b, c and a are in A.P. () a, b and c are in A.P. (4) a, b and c are in G.P. Solution: () 9(5a b ) 5(c ac) 5b(a c) 9(5a b) (b 5c) 5(c a) 0 5a = b, b = 5c, c = a a b c 5 b, c, a are in A.P. 5. The distance of the point (,, 7) from the plane passing through the point (,, ), having normal perpendicular to both the lines x y z 4 and x y z 7, is: () () () (4) Solution: () 6. Let Equation of plane = x y z 0 5x + 7y +z + 5 = Distance = n In tan x dx,(n ). If 5 5 I4 I6 a tan x bx C then the ordered pair (a, b) is equal to: (), (),0 5 (), 5 5 Solution: () n n tan x In tan x sec x dx In C n Put n = 6 5 tan x I6 I4 C 5 a, b 0 5, where C is a constant of integration, (4),0 5

6 JEE MAIN-07 (PAPER & SOLUTIONS) 6 7. The eccentricity of an ellipse whose centre is at the origin is. If one of its directrices is x = 4, then the equation of the normal to it at, is: () y x () 4x y () 4x y 7 (4) x y 4 Solution: () e, ae 4 a = b e b x y = is the ellipse a 4 normal at, is 4x y = 8. A hyperbola passes through the point this hyperbola at P also passes through the point: P, and has foci at,0 (), (), (), (4),. Then the tangent to Solution: () ae = 4, a = PS PS = x y 4 Now tangent at, is It passes through, y x 9. x The function f : R, defined as f (x) x, is: () invertible. () injective but not surjective. () surjective but not injective. (4) neither injective nor surjective. Solution: () x x f (x) ; f '(x) x ( x ) not injective Range =, Hence, surjective 0. cot x cos x lim equals: ( x) x () 4 Solution: () cot x cos x lim ( x) x () 6 () 8 Let x h tan h sin h tan h cos h lim lim. 8h h h 8 6 h0 h (4) 4

7 JEE MAIN-07 (PAPER & SOLUTIONS) 7. Let a i ˆ ˆj kˆ and b ˆi ˆj. Let c be a vector such that c a, a b c and the angle between c and a b be 0 o. Then a.c is equal to: () 5 () () 5 (4) 8 8 Solution: () a b c o a b. c.sin 0 as a b c c a c a a. c 9 a. c. The normal to the curve y(x )(x ) = x + 6 at the point where the curve intersects the y-axis passes through the point: (), (), (), (4), Solution: () x 6 y Point on y-axis is (0, ) (x )(x ) dy dx x 0 Normal is x + y = It passes through,. 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 4, is: () 6 55 () 55 () 4 45 (4) 7 55 a + b = 4m, a b 4n both should be even and are of same type either 4k or 4k + type C C 6 C A man X has 7 friends, 4 of them are ladies and are men. His wife Y also has 7 friends, of them are ladies and 4 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: () 485 () 468 () 469 (4) 484

8 JEE MAIN-07 (PAPER & SOLUTIONS) 8 X 4 ladies, men Y ladies, 4 men as 4 cases are possible therefore C C C C C C C C C Co Co C No. of ways = X Y X Y X Y 4 4 Co C C Co X Y 5. The value of C 0 C C 0 C C 0 C C 0 C... C 0 C is: () () 0 () 0 9 (4) 0 0 C 0 C C 0 C... C 0 C 0 0 C C... C 0 C 0 C... 0 C 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: 485 () 5 () 6 () 4 (4) 6 5 Variance = n. p. q Here n = 0, p = Variance = 5 5, q = 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, yr, then 0 f (n) is equal to: n () 0 () 65 () 90 (4) 55 f (x y) f(x) f(y) xy x, y R f (0 0) 0 c 0 f (x h) f(x) f (h) f '(x) lim x lim h0 h h0 h f '(x) x f '(0) ax b x b 5 a, b, as a + b + c = 0 0 n 5n f (n) 0 n n

9 JEE MAIN-07 (PAPER & SOLUTIONS) 9 8. The radius of a circle, having minimum area, which touches the curve y = 4 x and the lines, y = x is: Solution: () () Equating radii, Radius = () () 4 (4) 4 a 4 a a = 4 9. 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: () () 9 () 0 (4) Let the solutions are m and m +, 5... n m m n n n k(k ) 0 n k m(m ) n Eliminating m from both the equations n = 0. The integral Solution: () 4 4 dx is equal to; cos x n () () () 4 (4) I 4 4 dx cos x 4 I cosec x dx 4 I 4 4 dx cos x cos x

10 JEE MAIN-07 (PAPER & SOLUTIONS) 0 PART B PHYSICS (SET-D) ALL THE GRAPHS GIVEN ARE SCHEMATIC AND NOT DRAWN TO SCALE. A radioactive nucleus A with a half-life T, decays into a nucleus B. At t = 0 there is no nucleus B. At some time t, the ratio of the number of B to that of A is 0. Then, t is given by: T T log log. () t () t () t T (4) t T log(.) log. log. log Solution: () A B No t = 0 N N0 N ---- t = t No N 0. N t/t N o N o. T log(.) t log() N N o.. The following observations were taken for determining surface tension T of water by capillary method: Diameter of capillary, D =.5 0 m rise of water, h =.45 0 m Using g = 9.80 m/s rhg and the simplified relation T 0 N/m, the possible error in surface tension is closest to () 0% () 0.5% ().5% (4).4% Solution: () dhg T = 0 4 T d h T d h =.5 %. 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 () () () (4)

11 JEE MAIN-07 (PAPER & SOLUTIONS) Solution: () min hc e hc log( min ) log log V e 4. 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? () () () (4) Solution: () I MR ML 4 Volume = R L V Hence, R L So, I= M V ML 4 L di MV ML 0 dl 4 L L V R L 6 4 L 4 L R L R L L R 5. 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 g () () cos sin g g () (4) sin cos Solution: () L Mg sin

12 JEE MAIN-07 (PAPER & SOLUTIONS) I MgL sin ML g sin L 6. Cp and Cv are specific heats at constant pressure and constant volume respectively. It is observed that Cp Cv = a for hydrogen gas Cp Cv = b for nitrogen gas The correct relation between a and b is: () a = 8 b () a = b () a = b (4) a = 4 b 4 R Cp C v a MH Cp Cv R b MN Hence a = 4 b 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) () 85oC () 800oC () 885oC (4) 50oC Solution: () 00gm 0. T T = 88.5oC 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 () m () c (4) m c Solution: () Signal contains 8. c m, c, c m 9. The temperature of an open room of volume 0 m increases from 7oC to 7oC due to the sunshine. The atmospheric pressure in the room remains 05. Pa. If ni and nf are the number of molecules in the room before and after heating, then nf ni will be: ().5 05 ().6 0 ().8 0 (4).5 05

13 n f PV ni R Tf Ti JEE MAIN-07 (PAPER & SOLUTIONS) 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: () 5.6 mm ().56 mm () 7.8 mm (4) 9.75 mm Solution: () n 650 m 50 n 4 m y mm 4. A particle A of mass m and initial velocity v collies 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 () B Solution: () m mv mva v vb v va v v v v B A A v, v 4v B A B B m 4v. m v m v v m. B A A B A () B A ().(i).(ii) B A (4) B 4. A magnetic needle of magnetic moment Am and moment of inertia kg m is performing simple harmonic oscillation in a magnetic field of 0.0 T. Time taken for 0 complete oscillation is: () 8.76 s () 6.65 s () 8.89 s (4) 6.98s

14 Solution: () I T sec B t 0T 6.65sec JEE MAIN-07 (PAPER & SOLUTIONS) 4 4. An electric dipole has a fixed dipole moment p, which makes angle with respect to x-axis. When subjected to an electric E ˆ E i, 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 : () 90 o () 0 o () 45 o (4) 60 o pcos ˆi psin ˆj Ei ˆ PE sin kˆ pcos ˆi psin ˆj Ej ˆ PE sin PE cos kˆ PE cos o tan 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: () 75 Wb () 00 Wb () 5 Wb (4) 50 Wb q Area under the curve R Wb 45. A times 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 : () 8 J () 4.5 J () J (4) 9 J Solution: () F a 6t m dv 6t dt 6t v t m / sec W KE = 4.5 J.

15 JEE MAIN-07 (PAPER & SOLUTIONS) Some energy levels of a molecule are shown in the figure. The ratio of the wavelengths r = /, is given by () r = / () r = 4/ () r = / (4) r = /4 hc E hc E 47. In the above circuit the current in each resistance is: () 0 A () A () 0.5 A (4) 0.5 A Each resistance has zero potential difference across it. 48. A body is through vertically upwards. Which one of the following graphs correctly represent the velocity vs time () () () (4) V V gt A capacitance of F is required in an electrical circuit across a potential difference of.0 kv. A large number of F 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 (4) 4

16 JEE MAIN-07 (PAPER & SOLUTIONS) 6 V 000V C F 4 capacitors in series then 8 such branches in parallel 50. 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 () CE () CE r r () r CE (4) r r In steady state. E I r r Er VA VB Ir r r Q C V V. A B r CE r r 5. In a common emitter amplifier circuit using an n-p-n transistor, the phase difference between the input and the output voltage will be: () 80 o () 45 o () 90 o (4) 5 o Input and output voltages have a phase difference of. 5. Which of the following statements is false? () Kirchhoff s second law represents energy conservation. () Wheatstone bridge is the most sensitive when all the four resistance s are of the same order of magnitude () In a balanced Wheatstone bridge is the cell and the galvanometer are exchanged, the null point is disturbed. (4) A rheostat can be used as a potential divider. Solution: () The circuit remains unchanged if we interchange battery and galvanometer. 5. 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: () () () (4)

17 JEE MAIN-07 (PAPER & SOLUTIONS) 7 KE oscillates with a period of T/. 54. 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 m/s) () 5. GHz () 0. GHz (). GHz (4) 7..GHz app v act c v c GHz A man grown 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 () /8 () 9 () /9 (4) 8 Solution: () Stress = 9 weight Mg 9 times. Area A 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 0 0 V is () () () (4).55 0 Solution: () V 0 R G 5 i 5 0 g The variation of acceleration due to gravity g with distance d form centre of the earth is best represented by (R = Earth s radius) : () () () (4) GM r e g,r R e R e GMe g,r R r e

18 JEE MAIN-07 (PAPER & SOLUTIONS) 8 An external pressure P is applied on a cube at 0oC so that it is equally compressed from all sides. K is the bulk modules 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 P () PK () () (4) K K PK Solution: () dp K dv / v 58. K p T T p K 59. A diverging lens with magnitude of focal length 5 cm is placed at a distance of 5 cm form 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: () real and at a distance of 6 cm from the convergent lens. () real and at a distance of 40 cm from convergent lens. () virtual and at a distance of 40 cm from convergent lens. (4) real and at a distance of 40 cm form the divergent lens. Solution: () For convex lens u 40 cm f 0 cm V 40 cm V A body of mass m = 0 kg moving in medium and experiences a fractional force F = kv. Its initial speed is v0 = 0 ms. If, after 0 s, its energy is /8 mv 0, the value of k will be: () 0 kg m s () 0 kg m () 0 kg s F kv kv dv a dt 0 v0 / v0 0 dv k dt v 0 0 k 0 v0 v0 k 0 4 (4) 0 4 kg m

19 JEE MAIN-07 (PAPER & SOLUTIONS) 9 PART C CHEMISTRY (SET-D) 6. gram of a carbonate (MCO) on treatment with excess HCl produces mole of CO. The molar mass of MCO in g mol is : () 84. () 8.6 ().86 (4) 86 Solution:() M CO HCl MCl H O CO gm mole So = M = 84. M 6. Given C(graphite) + O(g) CO(g) ; rh = 9.5 kj mol H(g) + O(g) HO(l); rh = 85.8 kj mol CO(g) + HO(l) CH4(g) + O(g) ; rh = kj mol Based on the above thermochemical equations, the value of rh at 98 K for the reaction. C(graphite) + H(g) CH4(g) will be : () kj mol () 74.8 kj mol () 44.0 kj mol (4) kj mol Solution:() H H H H O 890. fch f 4 CO f H 890. ( 9.5) ( 85.8 ) f CH4 H 74.8 kj / mole fch 4 6. The freezing point of benzene decreases by 0.45 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 : (Kf for benzene = 5. K kg mol ) () 80.4% () 74.6% () 94.6% (4) 64.6% Solution:() Tf = ikf m 0.45 = ( /) 5. = 94.6% The most abundant elements by mass in the body of a healthy human adult are : Oxygen (6.4%); 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 : () 7.5 kg () 7.5 kg () 0 kg (4) 5 kg Solution:() Amount of H = = 7.5 kg Increase in mass = 7.5 kg 65. U is equal to : () Isobaric work () Adiabatic work () Isothermal work (4) Isochoric work

20 JEE MAIN-07 (PAPER & SOLUTIONS) 0 Solution:() U = q + w if q = 0 then U = w hence adiabatic work. NCERT XI Vol.-- [Page no.-60] 66. The formation of which of the following polymers involves hydrolysis reaction? () Bakelite () Nylon 6, 6 () Terylene (4) Nylon 6 Solution:(4) Nylon 6 is obtained by heating caprolactum with water at a high temperature. NCERT XII Vol.- [Page 4] 67. Given : E.6 V, E 0.74V Cl /Cl Cr /Cr E. V, E.5V. CrO 7 /Cr MnO 4 /Mn Among the following, the strongest reducing agent is : () Mn + () Cr + () Cl (4) Cr Solution:(4) The one having most ve standard reduction potential is strongest reducing agent. 68. The Tyndall effect is observed only when following conditions are satisfied : () 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. (4) The refractive indices of the dispersed phase and dispersion medium differ greatly in magnitude. () (b) and (d) () (a) and (c) () (b) and (c) (4) (a) and (d) Solution:() NCERT XII Vol.-- [5.4.6 (ii) Page no.-9] 69. In the following reactions, ZnO is respectively acting as a/an : (a) ZnO + NaO NaZnO (b) ZnO + CO ZnCO () base and base () acid and acid () acid and base (4) base and acid Solution:() ZnO is Amphoteric oxide when reacts with base it act as acid & vice verse.

21 JEE MAIN-07 (PAPER & SOLUTIONS) 70. Which of the following compounds will behave as a reducing sugar in an aqueous KOH solution? () () () (4) Solution:(4) on alkaline hydrolysis produces 7. The major product obtained in the following reaction is : () C6H5CH= CHC6H5 () (+)C6H5CH(O t Bu)CHC6H5 () ( ) C6H5CH(O t Bu)CHC6H5 (4) ()C6H5CH(O t Bu)CHC6H5 Solution:() It will undergo elimination 7. Which of the following species is not paramagnetic? () CO () O () B (4) NO Solution:() CO is 4 e s * s s * s px py * So no unpaired e NCERT XI Vol.-- [Page no.-6] 7. On treatment of 00 ml of 0. M solution of CoCl.6HO with excess AgNO;. 0 ions are precipitated. The complex is : () [Co(HO)Cl].HO () [Co(HO)6]Cl () [Co(HO)5Cl]Cl.HO (4) [Co(HO)4Cl]Cl.HO 74. pka of a weak acid (HA) and pkb of a weak base (BOH) are. and.4, respectively. The ph of their salt (AB) solution is : () 6.9 () 7.0 ().0 (4) 7. p Solution:().0 Number of moles of precipitate = moles of complex = = 0 So from mole complex two moles of AgCl is precipited.

22 JEE MAIN-07 (PAPER & SOLUTIONS) Solution:() ph = 7 + pka pkb = The increasing order of the reactivity of the following halides for the SN reaction is : CHCHCHCH CHCHCHCl p HCO C6H4 CHCl Cl (I) (II) (III) () (II) < (I) < (III) () (I) < (III) < (II) () (II) < (III) < (I) (4) (III) < (II) < (I) Solution:() Rate of SN reaction depends on stability of carbocation. So III > I > II 76. Both lithium and magnesium display several similar properties due to the diagonal relationship; however, the one which is incorrect, is : () both form soluble bicarbonates () both form nitrides () nitrates of both Li and Mg yield NO and O on heating (4) both form basic carbonates Solution:() NCERT XI vol. II. [0.. (iv) Page no.96] 77. The correct sequence of reagents for the following conversion will be : () CHMgBr, H + /CHOH, [Ag(NH)] + OH () CHMgBr, [Ag(NH)] + OH, H + /CHOH () [Ag(NH)] + OH, CHMgBr, H + /CHOH (4) [Ag(NH)] + OH, H + /CHOH, CHMgBr Solution:(4)

23 JEE MAIN-07 (PAPER & SOLUTIONS) 78. The products obtained when chlorine gas reacts with cold and dilute aqueous NaOH are : () ClO and ClO () Cl and ClO () Cl and ClO (4) ClO and ClO Solution:() Cl NaOH NaCl NaClO (cold dil) NCERT XII Vol.-, [7.9 Page no. 97] 79. Which of the following compounds will form significant amount of meta product during mononitration reaction? () () () (4) Solution:() NCERT XII Vol;.- [Page no. 05] 80. -Methyl-pent--ene on reaction with HBr in presence of peroxide forms an addition product. The number of possible stereoisomers for the product is : () Zero () Two () Four (4) Six Solution:() no. of stereo isomers = 4 8. 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 = 8.4 J mol K ) () () 6 () 4 (4) 8 Solution:() Ea ln K = ln A RT K (Ea E a ) 00 ln 4 K RT 8.00

24 JEE MAIN-07 (PAPER & SOLUTIONS) 4 8. Which one the following molecules is least resonance stabilized? () () () (D) Solution:(),, 4 are aromatic 8. The group having isoelectronic species is () O, F, Na, Mg + () O, F, Na, Mg + () O, F, Na +, Mg + (4) O, F, Na +, Mg + Solution:(4) O, F, Na + & Mg + all have 0e. NCERT XI Vol.-- [Page no.-84] 84. The radius of the second Bohr orbit for hydrogen atom is (Plank s Const. h = Js; mass of electron = kg; charge of electron e = C; permittivity of vacuum, 0 = kg m A ) () 4.76 Å () 0.59 Å (). Å (4).65 Å Solution:() H r = 0.59 Å 0.59.Å Z NCERT XI Vol.-- [Page no.-44] 85. The major product obtained in the following reaction is DIBALH () () () (4) Solution:() DIBAL H NCERT XII Vol.- [Page no. -54]

25 JEE MAIN-07 (PAPER & SOLUTIONS) Which of the following reactions is an example of a redox reaction? () XeF+ PF5[XeF] + PF 6 () XeF6+ HO XeOF4 + HF Solution:(4) () XeF6+ HO XeOF + 4HF (4) XeF4+ OF5XeF6 + O XeF O F XeF O 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 () (4) a Solution:() Closest approach between two atoms in FCC = a a NCERT XII Vol.-- [Page no.-8] 88. Sodium salt of an organic acid X produces effervescence with conc. HSO4. X reacts with the acidified aqueous CaCl solution to give a white precipitate which decolourises acidic solution of KMNO4. X is () HCOONa () CHCOONa () NaCO4 (4) C6H5COONa Solution:() NaCO4 + HSO4 CO + CO NaCO4 + CaCl CaCO 4 (White ppt) 89. A water sample has ppm level concentration of following anions F = 0; SO 4 = 00 ; NO = 50 The anion/anions that make/makes the water sample unsuitable for drinking is/are : () Both SO 4 and NO () Only F () Only SO 4 (4) Only NO Solution:() F > ppm SO4 500 pm NO 50 ppm is not suitable for drinking. NCERT XI Vol.- [Page- 407, 408] 90. Which of the following, upon treatment with tert-buona followed by addition of bromine water, fails to decolourize the colour of bromine? Solution:(4) () () () (4) does not give alkene on reaction with test BuONa