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

Transcription

1

2 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 of acetic acid in benzene will be : (K f for benzene = 5. K kg mol ) [Ans. ()] () 9.6% () 6.6% () 80.% 7.6%. On treatment of 00 ml of 0. M solution of ol.6h O with excess AgNO ;. 0 ions are precipitated. The complex is : [Ans. ()] () [o(h O) 5 l]l.h O () [o(h O) l ]l.h O () [o(h O) l ].H O [o(h O) 6 ]l. Which of the following compounds will form significant amount of meta product during mononitration reaction? [Ans. ] () () (). The products obtained when chlorine gas reacts with cold and dilute aqueous NaOH are : [Ans. ] () l and lo () lo and lo () lo and lo l and lo 5. Both lithium and magnesium display several similar properties due to the diagonal relationship; however, fee one which is incorrect, is : [Ans. ()] () 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 [Ans. ] 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? [Ans. ()] () Terylene () Nylon 6 () Bakelite Nylon 6, 6 8. The Tyndall effect is observed only when following conditions are satisfied : [Ans. ()] (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)

3 JEE(Main) pk a of a weak acid (HA) and pk b of a weak base (BOH) are. and., respectively. The ph of their salt (AB) solution is : [Ans. ()] ().0 () 7. () The major product obtained in the following reaction is : [Ans. ()] () () (). Which of the following compounds will behave as a reducing sugar in an aqueous KOH solution? [Ans. ()] () () (). The correct sequence of reagents for the following conversion will be : [Ans. ()] () [Ag(NH ) ] + OH, H MgBr, H + /H OH () [Ag(NH ) ] + OH, H + /H OH, H MgBr () H MgBr, H + /H OH, [Ag(NH ) ] + OH H MgBr, [Ag(NH ) ] + OH, H + /H OH. Which of the following species is not paramagnetic? [Ans. ()] () B () NO () O O. Which of the following, upon treatment with treatment with tert-buona followed by addition of bromine water, fails to decolourize the colour of bromine? [Ans. ()] () () ()

4 JEE(Main) Which of the following reactions is an example of a redox reaction? [Ans. ()] () XeF 6 + H O XeO F + HF () XeF + O F XeF 6 + O () XeF + PF 5 [XeF] + PF 6 XeF 6 + H O XeOF + HF 6. U is equal to : [Ans. ] () Isothermal work () Isochoric work () Isobaric work Adiabatic work 7. Which of the following molecules is least resonance stabilized? [Ans. ()] () () () 8. The increasing order of the reactivity of the following halides for the S N reaction is : [Ans. ()] () (II) < (III) < (I) () (III) < (II) < (I) () (II) < (I) < (III) (I) < (III) < (II) 9. gram of a carbonate (M O ) on treatment with excess Hl produces mole of O. The molar mass of M O in g mol is : [Ans. ()] ().86 () 86 () Sodium salt of an organic acid 'X' produces effervescence with cone. H SO. 'X' reacts with the acidified aqueous al solution to give a white precipitate which decolourises acidic solution of KMnO. 'X' is : [Ans. ()] () Na O () 6 H 5 OONa () HOONa H OONa. The most abundant elements by mass in the body of a healthy human adult are : Oxygen (6.%); arbon (.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 : [Ans. ] () 0 kg () 5 kg () 7.5 kg 7.5 kg. The major product obtained in the following reaction is : [Ans. ()] () ( ) 6 H 5 H(O t Bu)H 6 H 5 () ( ) 6 H 5 H(O t Bu)H 6 H 5 () 6 H 5 H = H 6 H 5 (+) 6 H 5 H(O t Bu)H 6 H 5. Given [Ans. ] O g O g ; H 9.5kJ mol graphite r H g O g HO l ; rh 85.8kJ mol O g H O l H g ; O g ; H 890.kJ mol r Based on the above thermochemical equations, the value of (graphite) + H (g) H (g) will be : r H at 98 K for the reaction ().0 kj mol () +7.8 kjmol () +.0 kj mol 7.8 kj mol

5 JEE(Main) 07. In the following reactions, ZnO is respectively acting as a/an : [Ans. ()] (a) ZnO + Na O Na ZnO (b) ZnO + O ZnO () acid and base () base and acid () base and base acid and acid 5. The radius of the second Bohr orbit for hydrogen atom is : [Ans. ()] (Planck's onst, h = Js; mass of electron = kg; charge of electron e = ; permittivity of vacuum 0 = kg m A ) (). 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 : [Ans. ()] (R = 8. J mol K ) () () 8 () 6 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 : [Ans. ()] () a () a () a a 8. The group having isoelectronic species is : [Ans. ()] () O, F, Na, Mg () O, F, Na, Mg () O O, F, Na, Mg, F, Na, Mg 9. Given [Ans. ()] E.6 V, E 0.7 V l / l r / r E.V, E.5V ro 7 / l MnO / Mn Among the following, the strongest reducing agent is : () l () r () Mn + r Methyl-pent--ene on reaction with HBr in presence of peroxide forms an addition product. The number of possible stereoisomers for the product is : [Ans. ()] () Four () Six () Zero Two

6 JEE(Main) 07. The integral dx cos x MATHEMATIS PART B is equal to : [Ans. ] () () () n. Let I x dx n n tan,. If I I a x bx where is a constant of integration, then tan, the ordered pair (a, b) is equal to : [Ans. ] (), 5 (), 0 5. The area (in sq. units) of the region () 7 () 5 (), 5 x, y : x 0, x y, x y and y x, 0 5 is : [Ans. ()] () 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 : [Ans. ()] () () dy If ( + sin x) y cos x 0 dx and () () () 5 6 y 0, then y is equal to : [Ans. ()] () 6. Let be a complex number such that z where z. If equal to : k, then k is 7 [Ans. ()] () () () z z 7. Let a iˆ ˆj kˆ and b iˆ ˆ. j Let c be a vector such that c a, a b c and the angle between c and a b be 0. Then a c is equal to : [Ans. ] () 5 () 8 () The radius of a circle, having minimum area, which touches the curve is : y x and the lines, y x () () () [Ans. ()] 9. If for x 0,, the derivative of tan 6x x 9x is x g x, then g(x) equals : [Ans. ()] x () 9x x () 9x 9 () 9x x x 9x 5

7 JEE(Main) 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 : [Ans. ()]. () 5 cot x cos x lim equals : x () 8 x. The value of () () 7 55 ( 0 ) + ( 0 ) + ( 0 ) + ( 0 ) ( ) is : () () () 0 9 () 0 0 () 0. For three events A, B and, P(Exactly one of A or B occurs) = P(Exactly one of B or occurs) = P(Exactly one of 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 () [Ans. ] [Ans. ()] [Ans. ]. Let a vertical tower AB have its end A on the level ground. Let be the mid-point of AB and P be a point on the ground such that AP = AB. If BP, then tan is equal to : [Ans. ()] () 9 () 9 () 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 : [Ans. ] () 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... 0 has two consecutive integral solutions, then n is equal to : [Ans. ()] () 0 () () 9 7. The following statement ~ () equivalent to p ~ q p q p q q is : [Ans. ()] () a fallacy () a tautology equivalent to ~ p q 8. The normal to the curve passes through the point : (), y x x x 6 at the point where the curve intersects the y-axis (), (),, [Ans. ] 6

8 JEE(Main) For any three positive real number, a b and 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. [Ans. ] 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 : [Ans. ] 5 () () 6 5 () 5 5. If 5 tan x cos x cos x 9, then the value of cos x is : [Ans. ()] () 9 5. Let a, b, c R. If f(x) = () f x y f x f y xy, x, y R, then 0 f n is equal to : n 7 () 9 5 ax bx c is such that a + b + c = and [Ans. ()] () 90 () 55 () The distance of the point (,, 7) from plane passing through the point (,, ), having normal perpendicular to both the lines x y z and x y z 7, is : [Ans. ] () 5 8 () If S is the set of distinct values of 'b' for which the following system of linear equations [Ans. ()] x y z 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 55. If A, then adj A A is equal to : [Ans. ] () () A hyperbola passes through the point, () () P and has foci at, Then the tangent to this hyperbola at P also passes through the point : [Ans. ] (), (), (),, 7

9 JEE(Main) 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 : [Ans. ()] (), (), (),, 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 : [Ans. ()] () 5 () 0 () The function f : R, defined as f x, x x is : [Ans. ()] () surjective but not injective () neither injective nor 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 this party, is : [Ans. ()] () 69 () 8 ()

10 JEE(Main) 07 PHYSIS PART 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 observe? (speed of light = 0 8 ms ) [Ans. ()] (). GHz () 7. GHz () 5. GHz 0. GHz 6. 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 =.5 0 m. Using g = 9.80 m/s and the rhg simplified relation T 0 N / m, the possible error in surface tension is closest to: [Ans. ()] ().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 : [Ans. ()] () r () r () r r 6. A body of mass m = 0 kg is moving in a medium and experiences a frictional force F= kv. Its initial speed is v 0 = 0 ms. If, after 0 s, its energy is mv 0, the value of k will be : [Ans. ()] 8 () 0 kg s () 0 kg m () 0 kg m s 0 kg m 65. p and v are specific heats at constant pressure and constant volume respectively. It is observed that p v = a for hydrogen gas p v = b for nitrogen gas The correct relation between a and b is : () a = b () a = b () a = 8 b a [Ans. ()] 66. The moment of inertia of a uniform cylinder of length l and radius R about its perpendicular bisector is I. ratio l/r such that the moment of inertia is minimum? [Ans. ] () () () 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 : [Ans. ()] () log. t T () t T log(.) () log T t log(.) T log t log. 68. Which of the following statements is false? [Ans. ()] () 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. 9

11 JEE(Main) A capacitance of µf is required in an electrical circuit across a potential difference of.0 kv. A large number of u.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 : [Ans. ()] () 6 () () 70. In the given circuit diagram when the current reaches steady state in the circuit, the charge on the capacitor of capacitance will be : [Ans. ()] r r r () E () E () E (r r) (r + r) (r r) E 7. [Ans. ()] In the above circuit the current in each resistance is : () 0.5 A () 0.5 A () 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? [Ans. ] () 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 : [Ans. ()] () 90 () 5 () 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 75. T is given by : [Ans. ()] (Given : room temperature = 0, specific heat of copper = 0. cal/ gm ) () 885 () 50 () 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 : [Ans. ()] () 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 E Eˆ j it experiences a torque T T. The angle is: [Ans. ()] () 5 () 60 () 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 : [Ans. ] () g sinθ l () g cosθ l () g cosθ l g sinθ l 0

12 JEE(Main) An external pressure P is applied on a cube at 0 so that it is equally compressed from all sides. K is the bulk modulus of the material of the cube and a 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: [Ans. ] () P K () PK () PK P K 79. A diverging lens with magnitude of focal length 5cm is placed at a distance of 5 an from a converging lens of magnitude of focal length 0 cm. A beam of parallel falls on the diverging lens. The final image formed is : [Ans. ] () 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. 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 is the smallest possible wavelength of X-ray in the spectrum, the variation of log min min with log V is correctly represented: [Ans. ] () () () 8. The temperature of an open room of volume 0 m increases from 7 to 7 due to the sunshine. The atmospheric pressure in the room remains 0 5 Pa. If n and n are the number of molecules in the room before and after heating, then n f n i will be : [Ans. ()] ().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 [Ans. ()] () 5 Wb () 50 Wb () 75 Wb 00 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 0 0 V is : [Ans. ] ().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 : [Ans. ] () J () 9 J () 8 J.5 J i f

13 JEE(Main) 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: [Ans. ] () 8.89 s () 6.98 s () 8.76 s 6.65 s 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. ()] () () () 87. A body is thrown vertically upwards. Which one of the following graphs correctly represent the velocity vs time? [Ans. ()] () () () 88. 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 is: A () B A () B A () B A to A B after the collision [Ans. ()] 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 [Ans. ()] B () () () 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: [Ans. ] () 9 () 8 () 8 9

14