JEE MAIN 2017 (QUESTION WITH ANSWER)

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singleton. The following statement Ans. (p q) [(p q) q] is: a tautology () equivalent to p q equivalent to p q a fallacy. If (tan x cos x) = cos x + 9, then the value of cos x is Ans.

1 ( M P C ) JEE MAIN 0 (QUESTION WITH ANSWER) MATHEMATICS. If S is the set of distinct values of 'b' for Ans. 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 a singleton. The following statement Ans. (p q) [(p q) q] is: a tautology () equivalent to p q equivalent to p q a fallacy. If (tan x cos x) = cos x + 9, then the value of cos x is Ans. () 9 9 = 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: 6 () 6 6. Let be a complex number such that + = z where z. If k, Ans. z () z then k is equal to: 6. let k be an integer such that the triangle with vertices (k, k), (, k) and ( k, ) has area 8 sq. units. Then the orthocentre of this triangle is at the point: Ans.,, (),,. For three events A, B and C, P(Exactly one of A or B occurs) Campus Patiala : SCF 99-0, Chotti Barandari. Tel , 000, Campus Chandigarh : SCO No.-0--, Sector A, Tel , Campus Panchkula : SCO-6, nd Floor, Sector-, Tel , 0008

2 ( C M P ). Twenty meters of wire is available for Ans. fencing off a flower-bed in the form of a circular sector. Then the maximum area (in sq. m) of the flower-bed, is:. () The are (in sq. units) of the region {(x, y) : x > 0, x + y <, x < y and y < + Ans. 9 x } is: 9. If the image of the point P(,, ) in the () plane, x + y z + = 0 measured parallel to the line, is equal to : 0. If for Ans. 6x x tan 9x is 9 9x x 9x. If ( + sin x) dy dx x y z () 6 is Q then PQ x 0,, the derivative of x.g(x), then g(x) equals: x x () 9x 9x + (y + ) cos x = 0 and y(0) =, then y is equal to: Ans. (). 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: Ans.. If 6 9 A, equal to: () 9 then adj (A + A) is () For any three positive real numbers a, b and c, 9(a + b ) + (c ac) = b (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 a, b and c are in G.P. The distance of the point (,, ) from the plane passing through the point (,, ), having normal perpendicular to both the lines x y z and x y z, is: 0 8 () Campus Patiala : SCF 99-0, Chotti Barandari. Tel , 000, Campus Chandigarh : SCO No.-0--, Sector A, Tel , Campus Panchkula : SCO-6, nd Floor, Sector-, Tel , 0008

3 ( C M P ) 6. Let n In tan xdx,(n ). If I + I 6 = a tan x + bx + C, where C is a constant of integration, then the ordered pair (a, b) is equal to:,, (),0,0. 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: y x = () x y = x + y = x + y = 8. A hyperbola passes through the point P(, ) and has foci at (±, 0). Then the tangent to this hyperbola at P also passes through the point:, (),,, 9. The function Ans. 0. x f x, is: x invertible () injective but not surjective surjective but not injective f : R, defined as neither injective nor surjective. cot x cos x lim x 8 x equals: () 6. 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 Then a.c is equal to 8 () and a b 8 be 0.. The normal to the curve y(x ) (x )= x+6 at the point where the curve intersects the y-axis passes through the point:,, (),,. 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, Ans. 6 (). A man X has friends, of them are ladies Ans. and are men. His wife Y also has 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 : 8 () Campus Patiala : SCF 99-0, Chotti Barandari. Tel , 000, Campus Chandigarh : SCO No.-0--, Sector A, Tel , Campus Panchkula : SCO-6, nd Floor, Sector-, Tel , 0008

4 ( C M P ). The value of C 0 0 C C C 0 0 Ans. C C C C... C C is: () A box contains 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. () 6 6. 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 0 f(n) is equal to: n Ans. 0 () The radius of a circle, having minimum Ans. area, which touches the curve y = x and the lines, y = x is: () 9. If, for a positive integer n, the quadratic Ans. equation, x(x + ) + (x + ) (x + )+.+(x+ n ) (x+n)=0n has two consecutive integral solutions, then n is equal to: () The integral dx cos x () PHYSICS is equal to:. 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. T t () log. T log t log. log. t T t = T log (.) log. The following observations were taken for determining surface tension T of water by capillary method: diameter of capillary, D =. 0 m rise of water, h =. 0 m. Using g = 9.80 m/s and the simplified relation rhg T 0 N/m, the possible error in surface tension is closest to: 0% () 0.%.%.% Ans. Campus Patiala : SCF 99-0, Chotti Barandari. Tel , 000, Campus Chandigarh : SCO No.-0--, Sector A, Tel , Campus Panchkula : SCO-6, nd Floor, Sector-, Tel , 0008

5 ( C M P ). 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 :. 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 cos g sin () g sin g cos. 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? () 6. C p and C v are specific heats at constant Ans. 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 = 8 b () a b a = b a = b. A copper ball of mass 00 gm is at a Ans. temperature T. It is dropped in a copper calorimeter of mass 00 gm, filled with 0 gm of water at room temperature. Subsequently, the temperature of the system is found to be C. T is given by : (Given : room temperature = 0 C, specific heat of copper = 0. cal/gm C) 8 C () 800 C 88 C 0 C Campus Patiala : SCF 99-0, Chotti Barandari. Tel , 000, Campus Chandigarh : SCO No.-0--, Sector A, Tel , Campus Panchkula : SCO-6, nd Floor, Sector-, Tel , 0008

6 6 ( C M P ) 8. 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 m + c 9. The temperature of an open room of volume Ans. 0 m increases from C to C due to the sunshine. The atmospheric pressure in the room remains 0 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 :. 0 () In a Young's double slit experiment, slits Ans. are separated by 0. mm, and the screen is placed 0 cm away. A beam of light consisting of two wavelengths, 60 nm and 0 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 :.6 mm ().6 mm.8 mm 9. mm. 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 wavelength A to B after the collision is : Ans. A B A B () A B A B. A magnetic needle of magnetic moment 6. 0 Am and moment of inertia. 0 6 kg m is performing simple harmonic oscillations in a magnetic field of 0.0 T. Time taken for 0 complete oscillations is : 8.6 s () 6.6 s 8.89 s 6.98 s. An electric dipole has a fixed dipole moment p, which makes angle with respect to x-axis. When subjected to an electric field E Eˆi, 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 () 0 60 Ans.. 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 : Wb () 0 Wb Wb 0 Wb Ans.. 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 : 8 J (). J J 9 J Campus Patiala : SCF 99-0, Chotti Barandari. Tel , 000, Campus Chandigarh : SCO No.-0--, Sector A, Tel , Campus Panchkula : SCO-6, nd Floor, Sector-, Tel , 0008

7 ( C M P ) 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 In the above circuit the current in each resistance is : 0 A () A 0. A 0. A Ans. 8. A body is thrown vertically upwards. Which one of the following graphs correctly represent the velocity vs time? Ans. 9. 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 Ans. 0. 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 r r () CE r CE r r r CE r r () Ans.. In a common emitter amplifier circuit using Ans. an n p n transistor, the phase difference between the input and the output voltages will be : 80 () 90 Campus Patiala : SCF 99-0, Chotti Barandari. Tel , 000, Campus Chandigarh : SCO No.-0--, Sector A, Tel , Campus Panchkula : SCO-6, nd Floor, Sector-, Tel , 0008

8 8 ( C M P ). Which of the following statements is false? 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. In a balanced wheatstone bridge if the cell and the galvanometer are exchanged, the null point is disturbed. A rheostat can be used as potential divider. Ans.. 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 :. 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 : 8 9 () When a current of ma is passed through a galvanometer having a coil of resistance, 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 :.00 0 () 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.. 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 () 0. GHz. GHz. GHz Ans. Ans. 8. 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 : PK () P K P K PK Campus Patiala : SCF 99-0, Chotti Barandari. Tel , 000, Campus Chandigarh : SCO No.-0--, Sector A, Tel , Campus Panchkula : SCO-6, nd Floor, Sector-, Tel , 0008

9 9 ( C M P ) 9. A diverging lens with magnitude of focal length cm is placed at a distance of 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 : real and at a distance of 6 cm from the convergent lens. () real and at a distance of 0 cm from convergent lens. virtual and at a distance of 0 cm from convergent lens real and at a distance of 0 cm from the divergent lens. 60. A body of mass m = 0 kg is moving in a Ans. medium and experiences a frictional force F = kv. Its initial speed is v 0 = 0 ms. If, after 0s, its energy is k will be : mv 0, 8 0 kg m s () 0 kg m 0 kg s 0 kg m the value of CHEMISTRY 6. gram of a carbonate (M CO ) on Ans. 6. Given treatment with excess HCl produces mole of CO. The molar mass of M CO in g mol is : 8. () C (graphite) + O (g) CO (g) ; rh = 9. kj mol H g O g HO ; rh = kj mol Based on the above thermochemical equations, the value of rh at 98 K for the reaction C (graphite) + H (g) CH (g) will be : +.0 kj mol ().8 kj mol.0 kj mol +.8 kj mol 6. The freezing point of benzene decreases by 0. 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: Ans. (K f for benzene =. K kg mol ) 80.% ().6% 9.6% 6.6% 6. 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 kg person would gain if all H atoms are replaced by H atoms is :. kg (). kg 0 kg kg 6. U is equal to : Isobaric work () Adiabatic work Isothermal work Isochoric work 66. The formation of which of the following Ans. polymers involves hydrolysis reaction? Bakelite () Nylon 6, 6 Terylene Nylon 6 rh = 8.8 kj mol CO (g) + H O(l) CH (g) + O (g); Campus Patiala : SCF 99-0, Chotti Barandari. Tel , 000, Campus Chandigarh : SCO No.-0--, Sector A, Tel , Campus Panchkula : SCO-6, nd Floor, Sector-, Tel , 0008

10 0 ( C M P ) 6. Given Ans. o o Cl /Cl Cr /Cr E.6 V, E 0.V o o CrO /Cr MnO /Mn E.V, E.V. Among the following, the strongest reducing agent is : Mn + () Cr + Cl Cr 68. The Tyndall effect is observed only when Ans. following conditions are satisfied : (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 (d) () (a) and (c) (b) and (c) (a) and (d) 69. In the following reactions, ZnO is Ans. respectively acting as a/an : (a) ZnO NaO NaZnO (b) ZnO CO ZnCO base and base () acid and acid acid and base base and acid 0. Which of the following compounds will behave as a reducing sugar in an aqueous KOH solution? () Ans.. The major product obtained in the following reaction is : C H CH CHC H 6 6 () Ans. t ( )C 6HCH(O Bu)CH C6H t ( )C 6HCH(O Bu)CH C6H t ( )C 6HCH(O Bu)CH C6H. Which of the following species is not paramagnetic? CO () O Ans. B NO Campus Patiala : SCF 99-0, Chotti Barandari. Tel , 000, Campus Chandigarh : SCO No.-0--, Sector A, Tel , Campus Panchkula : SCO-6, nd Floor, Sector-, Tel , 0008

11 ( C M P ). On treatment of 00 ml of 0. M solution of CoCl.6H O with excess AgNO,. The correct sequence of reagents for the following conversion will be :. 0 ions are precipitated. The complex is : [Co(H O) Cl ].H O () [Co(H O) 6]Cl Ans. [Co(H O) Cl]Cl.H O [Co(H O) Cl ]Cl.H O. pk a of a weak acid (HA) and Ans. pk b of a weak base (BOH) are. and., respectively. The ph of their salt (AB) solution is : 6.9 () The increasing order of the reactivity of the following halides for the S N reaction is : Ans. CHMgBr, H /CHOH, [Ag(NH ) ] OH () CH MgBr, [Ag(NH ) ] OH, H /CHOH [Ag(NH ) ] OH, CH MgBr, H /CHOH [Ag(NH ) ] OH, H /CHOH, CHMgBr 8. The products obtained when chlorine gas reacts with cold and dilute aqueous NaOH are : ClO and ClO () Cl and ClO (II) < (I) < (III) () (I) < (III) < (II) (II) < (III) < (I) (III) < (II) < (I) Ans. 6. Both lithium and magnesium display several similar properties due to the diagonal relationship; however, the one which is incorrect is : both form soluble bicarbonates Cl and ClO ClO and ClO 9. Which of the following compounds will form significant amount of meta product during mono-nitration reaction? () () both form nitrides nitrates of both Li and Mg yield NO and O on heating both form basic carbonates Ans. Campus Patiala : SCF 99-0, Chotti Barandari. Tel , 000, Campus Chandigarh : SCO No.-0--, Sector A, Tel , Campus Panchkula : SCO-6, nd Floor, Sector-, Tel , 0008

12 ( C M P ) 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 Six Ans. 8. Two reactions R and R have identical preexponential factors, Activation energy of R exceeds that of R by 0 k] 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. The radius of the second Bohr orbit for hydrogen atom is : (Planck s Const. h = Js; Mass of electron = kg; Charge of electron e = C; Permittivity of vacuum kg m A ).6 Å () 0.9 Å. Å.6 Å Ans. 8. The major product obtained in the following reaction is : () 6 8 Ans. 8. Which of the following molecules is least resonance stabilized? () () Ans. 8. The group having isoelectronic species is : O,F,Na,Mg () O,F,Na,Mg O,F,Na,Mg Ans. O,F,Na,Mg Ans. Campus Patiala : SCF 99-0, Chotti Barandari. Tel , 000, Campus Chandigarh : SCO No.-0--, Sector A, Tel , Campus Panchkula : SCO-6, nd Floor, Sector-, Tel , 0008

13 ( C M P ) 86. Which of the following reactions is an Ans. example of a redox reaction? XeF PF [XeF] PF6 () XeF6 HO XeOF HF XeF6 HO XeOF HF XeF OF XeF6 O 8. 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 Ans. a () a 88. Sodium salt of an organic acid X produces a effervescence with conc. H SO. X reacts 89. A water sample has ppm level concentration of following anions F 0; SO 00; NO 0 The anion/anions that make/makes the water sample unsuitable for drinking is/are : both SO () only F only SO only NO and NO 90. Which of the following, upon treatment with tert-buona followed by addition of bromine water, fails to decolourize the colour of bromine? with the acidified aqueous CaCl solution to give a white precipitate which decolourises acidic solution of KMnO. X is : () HCOONa () CH COONa Ans. Na C O C6HCOONa Ans. Dream on!! Campus Patiala : SCF 99-0, Chotti Barandari. Tel , 000, Campus Chandigarh : SCO No.-0--, Sector A, Tel , Campus Panchkula : SCO-6, nd Floor, Sector-, Tel , 0008

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