VISION40 IIT-JEE Main Exam Model Question Paper 2017

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Exam : VISION40 IIT-JEE Main Exam
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VISION40 IIT-JEE Main Exam Model Question Paper

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Part A – Physics

1. 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 (2)

2. The temperature of an open room of volume 30 m3 increases from 17°C to 27°C due to sunshine. The atmospheric pressure in the room remains 1 × 105 Pa. If ni and nf are the number of molecules in the room before and after heating, then nf – ni will be
(1) 2.5 × 1025
(2) –2.5 × 1025
(3) –1.61 × 1023
(4) 1.38 × 1023
Ans (2)

3. Which of the following statements is false ?
(1) A rheostat can be used as a potential divider
(2) Kirchhoff’s second law represents energy conservation
(3) Wheatstone bridge is the most sensitive when all the four resistances are of the same order of magnitude.
(4) In a balanced wheatstone bridge if the cell and the galvanometer are exchanged, the null point is disturbed.
Ans. (4)

4. The following observations were taken for determining surface tensiton T of water by capillary method :
Diameter of capilary, D = 1.25 × 10–2 m rise of water, h = 1.45 × 10–2 m Using g = 9.80 m/s2 and the simplified relation T = rhg 2 × 103 N/m, the possible error in surface tension is closest to :
(1) 2.4%
(2) 10%
(3) 0.15%
(4) 1.5%
Ans. (4)

5. 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 ?
(1) wm + wc
(2) wc – wm
(3) wm
(4) wc
Ans. (3)

6. A diverging lens with magnitude of focal length 25 cm is placed at a distance of 15 cm from a converging lens of magnitude of focal length 20 cm. A beam of parallel light falls on the diverging lens. The final image formed is :
(1) real and at a distance of 40 cm from the divergent lens
(2) real and at a distance of 6 cm from the convergent lens
(3) real and at a distance of 40 cm from convergent lens
(4) virtual and at a distance of 40 cm from convergent lens.
Ans. (3)

7. The moment of inertia of a uniform cylinder of length ? and radius R about its perpendicular bisector is I. What is the ratio ?/R such that the moment of inertia is minimum ?
(1) 1
(2) 3/2
(3) 32
(4) 3/2
Ans. (3)

Part B – Mathematics

31. Let k be an integer such that triangle with vertices (k, –3k), (5, k) and (–k, 2) has area 28 sq. units. Then the orthocentre of this triangle is at the point :
(1) 1 2, 2
(2) 1 2, 2
(3) 3 1, 4
(4) 3 1, 4
Ans. (1)

32. If, for a positive integer n, the quadratic equation,
x(x + 1) + (x + 1) (x + 2) + ….. + (x + n ?1 ) (x + n) = 10n has two consecutive integral solutions, then n is equal to :
(1) 11
(2) 12
(3) 9
(4) 10
Ans. (1)

33. The function f : R 1 1 2 2 defined as f(x) = 2 x 1? x , is :
(1) neither injective nor surjective.
(2) invertible.
(3) injective but not surjective.
(4) surjective but not injective
Ans. (4)

34. The following statement
(p -> q ) -> [(~p -> q) -> q] is :
(1) a fallacy
(2) a tautology
(3) equivalent to ~ p -> q
(4) equivalent to p -> ~q
Ans. (2)

35. If S is the set of distinct values of ‘b’ for which the following system of linear equations
x + y + z = 1
x + ay + z = 1
ax + by + z = 0
has no solution, then S is :
(1) a singleton
(2) an empty set
(3) an infinite set
(4) a finite set containing two or more elements
Ans. (1)

37. For any three positive real numbers a, b and c, 9(25a2 + b2) + 25(c2 – 3ac) = 15b(3a + c). Then
(1) a, b and c are in G.P.
(2) b, c and a are in G.P.
(3) b, c and a are in A.P.
(4) a, b and c are in A.P.
Ans. (3)

38. A man X has 7 friends, 4 of them are ladies and 3 are men. His wife Y also has 7 friends, 3 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 3 ladies and 3 men, so that 3 friends of each of X and Y are in this party, is :
(1) 484
(2) 485
(3) 468
(4) 469
Ans. (2)

44. 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 :-
(1) 30
(2) 12.5
(3) 10
(4) 25
Ans. (4)

45. A box contains 15 green and 10 yellow balls. If 10 balls are randomly drawn, one–by–one, with replacement, then the variance of the number of green balls drawn is :-
(1) 6/25
(2) 12/5
(3) 6
(4) 4

46. If two different numbers are taken from the set {0, 1, 2, 3, ……., 10), then the probability that their sum as well as absolute difference are both multiple of 4, is :-
(1) 7/55
(2) 6/55
(3) 12/55
(4) 14/45

Part C – Chemistry

62. U is equal to
(1) Isochoric work
(2) Isobaric work
(3) Adiabatic work
(4) Isothermal work
Ans. (3)

63. The increasing order of the reactivity of the following halides for the SN1 reaction is CH3CHCH2CH3 CH3CH2CH2Cl
(1) (III) < (II) < (I)
(2) (II) < (I) < (III)
(3) (I) < (III) < (II)
(4) (II) < (III) < (I)
Ans. (2)

64. The radius of the second Bohr orbit for hydrogen atom is :
(Plank’s const. h = 6.6262 × 10–34 Js ; mass of electron = 9.1091 × 10–31 kg ; charge of electron e = 1.60210 × 10–19 C ; permittivity of vaccum = 8.854185 × 10–12 kg–1 m–3 A2)
(1) 1.65Å
(2) 4.76Å
(3) 0.529Å
(4) 212Å

65. pKa of a weak acid (HA) and pKb of a weak base (BOH) are 3.2 and 3.4, respectively. The pH of their salt (AB) solution is
(1) 7.2
(2) 6.9
(3) 7.0
(4) 1.0
Ans. (2)

66. The formation of which of the following polymers involves hydrolysis reaction ?
(1) Nylon 6
(2) Bakelite
(3) Nylon 6,
6 (4) Terylene
Ans. (1)

67. The most abundant elements by mass in the body of a healthy human adult are : Oxygen (61.4%) ; Carbon (22.9%), Hydrogen (10.0%) ; and Nitrogen (2.6%). The weight which a 75 kg person would gain if all 1H atoms are replaced by 2H atoms is
(1) 15 kg
(2) 37.5 kg
(3) 7.5 kg
(4) 10 kg
Ans. (3)

68. Which of the following , upon treatment with tert-BuONa followed by addition of bromine water, fails to decolourize the colour of bromine ?
Ans. (1)

69. In the following reactions, ZnO is respectively acting as a/an :
(a) ZnO + Na2O = Na2ZnO2
(b) ZnO + CO2 = ZnCO3
(1) base and acid
(2) base and base
(3) acid and acid
(4) acid and base
Ans. (4)

70. Both lithium and magnesium display several similar properties due to the diagonal relationship ; however, the one which is incorrect is :
(1) Both form basic carbonates
(2) Both form soluble bicarbonates
(3) Both form nitrides
(4) Nitrates of both Li and Mg yield NO2 and
O2 on heating
Ans. (1)