jee mains question paper - model test 1 maths, physics

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JEE MAINS QUESTION PAPER - MODEL TEST 1MATHS, PHYSICS, CHEMISTRY

1. Let A and B be nonempty sets in R and f : A B→ be a bijective functionStatement - 1 : f is an onto functionStatement - 2: There exists a function: g : B A→ such that fog = IB.1) Statement - 1 is true, Statement - 2 is true; Statement - 2 is a correct explanation for

Statement-12) Statement - 1 is true, Statement - 2 is true, Statement - 2 is not a correct explanation for

Statement -1.3) Statement -1 is true, Statement - 2 is false4) Statement - 1 is false, Statement - 2 is true.

2. 2 21 2 1 2Z Z Z Z+ + − is equal to :

1) ( )1 22 Z Z+ 2) 1 2Z Z 3) 2 21 2Z Z+ 4) ( )2 2

1 22 Z Z+

3. If a, b, c, d ∈R and 1 is a root of the equation ax2 + bx + c = 0, then the curve y = 4ax2 +3bx + 2c, a 0≠ intersects x axis on ---1) no point2) exactly one point3) exactly two distinct points4) two distinct points whose coordinates are always rational numbers.

4. Statement - 1 : If the system of equations x+ky+3z=0,3x+ky–2z=0, 2x+3y–4z=0 has a non-trivial

solution, then the value of k is 312

Statement - 2 : A system of three homogeneous equations in three variables has a non trivialsolution if the determinant of the coefficient matrix is zero.1) Statement is true, Statement -2 is true; statement - 2 is a correct explanation for statement-12) Statement is true, Statement -2 is true; statement - 2 is not a correct explanation for statement-13) Statement - 1 is true, statement -2 is false4) Statement - 1 is false, statement - 2 is true

5. If

1 0 0 1 0 0A 2 1 0 and B 2 1 0

3 2 1 7 2 1

⎡ ⎤ ⎡ ⎤⎢ ⎥ ⎢ ⎥= = −⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥− −⎣ ⎦ ⎣ ⎦

, then AB equals”

1) 0 2) I 3) A 4) B6. If seven women and seven men are to be seated around a circular table such that there is a man on

either side of every woman, then the number of seating arrangements is :1) (7!)2 2) (6!)2 3) 6! 7! 4) 7!

7. The middle term in the expansion of ( )n''11 1 x

x⎛ ⎞− −⎜ ⎟⎝ ⎠

in powers of x is

1) 2nnC 2) 2n

nC− 3) 2nn 1C −− 4) 2n

n 1C −


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8. If the A.M. between pth and qth terms of an AP is equal to the A.M. between rth and sth terms ofthe same A.P., then p + q is equal to :1) r + s 2) r + s –2 3) r + s –1 4) r + s + 1

9. If the sum of the series 2 2 2 2 2 21 2.2 3 2.4 5 2.6 .....+ + + + + + upto n terms, when n is even, is2n(n 1)

2+

, then the sum of the series, when n is odd, is :

1) n2 (n+1) 2)2n (n 1)

2−

3) n2 (n–1) 4)2n (n 1)

2+

10.( )2

2

sin cos xlimx 0 x

π

→ equals :

1) − π 2) π 3) –1 4) 1

11. If f(x) = |x| 3a sin x be c | x |+ + , where a, b, c ∈ R, is differentiable at x = 0, then:1) a = 0, b and c are any real numbers 2) a = 0, b = 0, c is any real number3) b = 0, c = 0, a is any real number 4) c = 0, a = 0, is any real number

12. Let ( ) ( )f : , ,−∞ ∞ → −∞ ∞ be defined by f(x) = x3 +1Statement -1 : The function f has a local extremum at x =0

Statement - 2: The function f is continuous and differentiable on ( ) ( )', and f 0 0−∞ ∞ =

1) Statement - 1 is true, Statement - 2 is true; Statement - 2 is a correct explanation forStatement-1

2) Statement - 1 is true, Statement - 2 is true, Statement - 2 is not a correct explanation forStatement -1.

3) Statement -1 is true, Statement - 2 is false4) Statement - 1 is false, Statement - 2 is true.

13. If a metalic circular plate of radius 50 cm is heated so that its radius increases at the rate of 1 mmper hour, then the rate at which the area of the plate increases ( in cm2/hr) is1) 5π 2) 10 π 3) 50 π 4) 100 π

14. The integrating factor of the differential equation ( )2 dyx 1 2xy xdx

− + = is

1)2x 1x−

2) 2x

x 1− 3) x2 –1 4) 21

x 1−

15. 6dxf (x)

sin x− ∫ is a polynomial of degree

1) 3 in cot x 2) 5 in cot x 3) 3 in tan x 4) 5 in tan x

16. If [x] is the greatest integer ≤ x, then the value of the integral 0.9

2

0.9

2 xx log2 x−

⎛ − ⎞⎛ ⎞⎡ ⎤ + ⎜ ⎟⎜ ⎟⎣ ⎦ +⎝ ⎠⎝ ⎠∫ d x is

1) 0 2) 0.243 3) 0.486 4) 1.8


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natural numbers is ( )2n 4n 1

3+

1) Statement - 1 is true, Statement - 2 is true; Statement - 2 is a correct explanation forStatement-1

2) Statement - 1 is true, Statement - 2 is true, Statement - 2 is not a correct explanation forStatement -1.

3) Statement -1 is true, Statement - 2 is false4) Statement - 1 is false, Statement - 2 is true.

26. The chord PQ of the parabola y2 = x, where one end P of the chord is at point (4, –2), is perpendicular to the axis of the parabola. Then the slope of the normal at Q is :

1) 14− 2) 1

4 3) 4 4) – 4

27. The normal at 32 ,2

⎛ ⎞⎜ ⎟⎝ ⎠

to the ellipse, 2 2x y 1

16 3+ = touches a parabola, whose equation is :

1) y2 = 14 x 2) y2 =–104 x 3) y2 = –14 x 4) y2 = 26 x28. The number of common tangents of the circles given by 2 2x y 8x 2y 1 0+ − − + = and

2 2x y 6x 8y 0+ + + = is :1) one 2) two 3) three 4) four

29. Consider the straight lines

1L : x y 1− =

2L : x y 1+ =

3L : 2x 2y 5+ =

4L : 2x 2y 7− =The correct statement is :1) 1 2 1 3 1L L , L || L ,L⊥ intersects L2 2) 1 2 2 3 1L L , L || L ,L⊥ intersects L4

3) 1 4 2 3 2L || L , L || L ,L intersects L3 4) 1 2 1 3 2L L , L L ,L⊥ ⊥ intersects L4

30. The line parallel to x–axis and passing through the point of intersection of thelines ax 2by 3b 0+ + = and bx 2ay 3a 0− − = , where (a, b) (0,0)≠ is :1) above x–axis at a distance 3/2 from it2) above x–axis at a distance 2/3 from it3) below x–axis at a distance 3/2 from it4) below x–axis at a distance 2/3 from it

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frequency changes by 50 Hz. The dielectirc constant of the gas is :1) 3.01 2) 2.001 3) 1.001 4) 1.01

21. In Young’s double slit interfernce experiment, the slit widths are in the ratio 1 : 25. Then the ratio ofintensity at the maxima and minima in the interference pattern is :1) 1 : 5 2) 1 : 25 3) 9 : 4 4) 3 : 2

22. A telecope of aperture 23 10−× m diameter is focused on a window at. 80 m distance fitted with awire mesh of spacing 32 10 .m−×Given : 75.5 10λ −= × m, which of the following is true for observing the mesh through the telescope ?1) yes, it is possible with the same aperture size2) no, it is not possible3) possible also with an aperture half the present diameter4) given data is not sufficient

23. A beam of light consisting of red, green and blue colours is incident on a right-angled prism on faceAB. The refractive indices of the material for the above red, green and blue wavelengths are 1.39,1.44 and 1.47 respectively.

A person looking on surface AC of the prism will see :1) No light 2) red colour only 3) red and green colours 4) green and blue colours

24. The counting rate observed from a radioactive source at t = 0 was 1600 counts s-1 , and at t = 8 s, itwas 100 counts s-1. The counting rate observed as counts s-1 at t = 6 s will be :1) 400 2) 300 3) 250 4) 200

25. Photo electrons are ejected from a metal when light of frequency v falls on it. Pick out the wrongstatement from the following :1) The maximum energy of the photo electrons is hv2) The ejection of the photo electrons is instantaneous3) The maximum energy of the photo electrons is independent of the intensity of the light4) No electrons are emitted if v is less W/h , where W is the work funciton of the metal

26. The figure shows a combination of two NOT gates and a NOR gate.

The combination is equivalent to a :1) NOR gate 2) NAND gate 3) OR gate 4) AND gate

27. A radio transmitter transmits at 830 kHz. At a certain distance from the transmitter magnetic field hasamplitude 4.82 x 10-11 T. The electric field and the wavelength are respectively :


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1) 0.014 N/C, 36 m 2) 0.014 N/C 360 m 3) 0.14 N/C, 36 m 4) 0.14 N/C, 360 m28. In an experiment of potentiometer for measuring the internal resistance of a primary cell a balancing

length l is obtained on the potentiometer wire when the cell is in open circuit. Now the cell is shortcircuited by a resistance R. If R is to be equal to the internal resistance of the cell the balancinglength on the potentiometer wire will be :1) l / 2 2) l / 4 3) 2l 4) l

29. The requency or X-rays ; raysγ − and ultraviolet rays are respectively a, b and c then :

1) ;A b b c< > 2) ;A b b c> > 3) a b c= = 4) a b C< <30. Which of the plots shown in the figure represents speed (v) of the electron in a hydrogen atom as a

function of the principal quantum number (n) ?

1) A 2) B 3) C 4) D

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1. A transition metal M forms a volatile chloride which hyas a vapour density of 94.8. If it contains74.75% of chlorine the formula of the metal chloride will be1) 4MCl 2) 2MCl 3) 3MCl 4) 5MCl

2. The relationship among most probable velocity, average velocity and root mean square velocity isrespectively:1) 2 : 8 / : 3π 2) 8 / : 3 : 2π 3) 3 : 8 / : 2π 4) 2 : 3 : 8 / π

3. Among the following the incorrect statement is :1) Electrical conductivity of semiconductors and metals increases with increase in temperature2) In BCC unit cell the void space is 32%3) Density of crystals decreases due to Schottky defect4) Density of crystals remains unaffected due to Frenkel defect

4. The following sets of quantum numbers represent four electrons in an atom:i) n = 4, I = 1 ii) n = 4, I = 0, iii) n = 3, I = 2 iv) n = 3, I = 1The sequence representing increasing order of energy, is1) iv < ii < iii < i 2) ii < iv < i < iii 3) i < iii < ii < iv 4) iii < i < iv < ii

5. Which one of the following depletes ozone layer?1) SO2 2) CO2 3) CO 4) NO and freons

6. One mole of an ideal gas is expanded isothermally and reversibly to half its initial pressure. SΔ forthe process in J K –1 mol–1 is [In 2 = 0.693 and R = 8.314, J/(mol K)].1) 6.76 2) 8.03 3) 5.76 4) 10.76

7. The freezing point of a 1.00 m aqueous solution of HF is found to be –1.910C. The freezing pointconstant of water Kf , is 1.86 K kg mol–1. The percentage dissociation of HF at this concentration is1) 2.7% 2) 5.2 % 3) 10% 4) 30%

8. One mole of O2(g) and two moles of SO2 (g) were heated in a closed vessel of one–litre capacity at1098 K. At equilibrium 1.6 moles of SO3 (g) were found. The equilibrium constant KC of thereaction would be:1) 30 2) 40 3) 60 4) 80

9. The solubility of PbI2 at 250C is 0.7 g L–1. The solubility product of PbI2 at this temperature is(molar mass of PbI2 = 461.2 g mol–1)1) 1.40 x 10–9 2) 14.0 x 10–9 3) 0.14 x 10–9 4) 140 x 10–9

10. Given 2oCu /Cu

E 0.34V+ =

2oCu /Cu

E 0.15V+ + =

Standard electrode potential for the half cell Cu+/Cu is1) 0.53 V 2) 0.49 V 3) 0.19 V 4) 0.38 V

11. The activation energy for a reaction which doubles the rate when the temperature is raised from298 K to 308 K is1) 52.9 kJ mol–1 2) 59.2 kJ mol–1 3) 29.5 kJ mol–1 4) 39.2 kJ mol–1

12. Colloidal solutions can be purified by1) peptization 2) emulsification 3) using Tyndall effect 4) electrodialysis

13. Which of the following presents the correct order of second ionization enthalpies of C, N, O and F?1) C > N > O > F 2) O > F > N > C 3) O > N > F > C 4) F > O > N > C


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14. The substance used as froth stabilisers in froth-floatation process is1) Potassium ethyl xanthate 2) Copper sulphate3) Sodium cyanide 4) Aniline

15. Which of the following forms stable + 4 oxidation state?1) La)Z=57) 2) Ce ( Z = 58) 3) Eu ( Z = 63) 4) Gd ( Z = 64)

16. Fire extinguishers contain H2SO4 and which one of the following?1) NaHCO3 2) Na2CO3 3) NaHCO3 & Na2CO3 4) CaCO3

17. The number of S–S bonds in SO3, 2 2

2 3 2 6S O ,S O− − and 22 8S O − respectively are

1) 1, 0, 1, 0 2) 0, 1, 1, 0 3) 0, 1, 0, 1 4) 1, 0, 0, 118. The number of unpaired electrons in Gadolinium [Z = 64] is

1) 2 2) 3 3) 6 4) 819. The complex ion [Pt (NO2) (Py) (NH3) (NH2OH)]+ will give:

1) 3 isomers (Geometrical) 2) 4 isomers (Geometrical)3) 2 isomers (Geometrical) 4) 6 isomers (Geometrical)

20. Which one of the following depletes ozone layer?1) SO2 2) CO2 3) CO 4) NO and freons

21. Dipole moment is shown by :1) 1, 4 – dichlorobenzene 2) 1, 2 –dichlorobenzene3) trans –1, 2 –dinitroethene 4) trans 2, 3 –dichloro –2– butene

22. Maleic acid and fumaric acids are1) Chain isomers 2) Functional isomers 3) Geometrical isomers 4) Tautomers

23. Which of the following compounds are antiaromatic:

1) III & VI 2) I & IV 3) II & V 4) I & V24. Consider the following sequence of reactions:

2 32 CO3 2 420 K,12 atm

NaC (i)HOCI700 K (ii) NaOHCH CH CH A B C= ⎯⎯⎯→ ⎯⎯⎯⎯⎯→ ⎯⎯⎯⎯⎯→l compound ‘C’ is

1) 2) 3) 4) 2 2HO CH CH CH− =

25. The hydration of propyne results in formation of1) Propanal 2) Acetone 3) Propanol –1 4) Propene

26. In the following compounds:


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The order of basicity is as follows:1) III > I > II > IV 2) I > III > II > IV 3) II > III > I > IV 4) IV > III > II > I

27. Bakelite is obtained from phenol by reacting it with:1) Acetaldehyde 2) Acetamide 3) Formaldehyde 4) Chlorobenzene

28. Which of the following statements is correct?1) DNA mainly occurs in the cytoplasm of the cell2) RNA has double stranded α–helix structure3) The sugar present in DNA is D – (–) – ribose4) RNA controls the synthesis of proteins.

29. Sulphonamides act as :1) Antimicrobials 2) Antiseptic 3) Antipyretic 4) Analgesic

30. Tollen’s reagent and Fehling solutions are used to distinguish between:1) acids and alcohols 2) n–alkanes and branched alkanes3) ketones and aldehydes 4) alkanes and alcohols

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jee mains question paper - model test 1 maths, physics

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