Practice Questions

Q5. 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? JEE Main 2017 (02 Apr) JEE Main Previous Year Paper 3 3 (1) (2) √2 √ 2 (3) √3 (4) 1 2

Q5. Moment of inertia of an equilateral triangular lamina ABC , about the axis passing through its centre O and perpendicular to its plane is I0 as shown in the figure. A cavity DEF is cut out from the lamina, where D, E, F are the mid points of the sides. Moment of inertia of the remaining part of lamina about the same axis JEE Main 2017 (08 Apr Online) JEE Main Previous Year Paper is: (1) 7 8 I0 (2) 1516 I0 (3) 4 3 I0 (4) 31I032

Q10.An engine operates by taking n moles of an ideal gas through the cycle ABCDA shown in figure. The thermal efficiency of the engine is: JEE Main 2017 (08 Apr Online) JEE Main Previous Year Paper (Take Cv = 1.5R, where R is gas constant) (1) 0. 24 (2) 0. 15 (3) 0. 32 (4) 0. 08

Q12.A block of mass 0. 1 kg is connected to an elastic spring of spring constant 640 N m−1 and oscillates in a damping medium of damping constant 10−2 kg s−1 . The system dissipates its energy gradually. The time taken for its mechanical energy of vibration to drop to half of its initial value, is closest to- (1) 2 s (2) 5 s (3) 3 s (4) 7 s

Q17. A 9 V battery with an internal resistance of 0.5 Ω is connected across an infinite network, as shown in the figure. All ammeters A1, A2, A3 and voltmeter V are ideal. Choose the correct statement. (1) Reading of A1 is 18 A . (2) Reading of V is 9 V . (3) Reading of V is 7 V . (4) Reading of A1 is 2 A .

Q19.A uniform wire of length l and radius r has a resistance of 100 Ω . It is recast into a wire of radius 2r . The resistance of new wire will be- (1) 1600 Ω (2) 100 Ω (3) 200 Ω (4) 400 Ω

Q24.In an experiment a convex lens of focal length 15 cm is placed coaxially on an optical bench in front of a convex mirror at a distance of 5 cm from it. It is found that an object and its image coincide, if the object is placed at a distance of 20 cm from the lens. The focal length of the convex mirror is- (1) 20. 0 cm (2) 30. 5 cm (3) 25. 0 cm (4) 27. 5 cm

Q26.According to Bohr's theory, the time averaged magnetic field at the centre (i.e., nucleus) of a hydrogen atom due to the motion of electrons in the nth orbit is proportional to: ( n = principal quantum number) (1) n−3 (2) n−2 (3) n−4 (4) n−5

Q44.The freezing point of benzene decreases by 0.45°C on adding 0 . 2 g of acetic acid to 20 g of benzene. If acetic acid associates to form a dimer in benzene, then what is the percentage association of acetic acid in benzene? Kf for benzene = 5 .12 K kg mol-1 (1) 80 . 4% (2) 74 . 6% (3) 94 . 6% (4) 64 . 6%

Q53.The major product obtained in the following reaction is, (1) C6H5CH = CHC6H5 (2) + C6H5CHOtBuCH2C6H5 (3) - C6H5CHOtBuCH2C6H5 (4) ± C6H5CHOtBuCH2C6H5

Q58.Among the following compounds, the increasing order of their basic strength is: (1) (II) < (I) < (III) < (IV) (2) (II) < (I) < (IV) < (III) (3) (I) < (II) < (IV) < (III) (4) (I) < (II) < (III) < (IV)

Q61.If, for a positive integer 𝑛, the quadratic equation, 𝑥𝑥+ 1 + 𝑥+ 1𝑥+ 2 + . .. + 𝑥+ 𝑛-¯ 1𝑥+ 𝑛= 10𝑛 has two consecutive integral solutions, then 𝑛 is equal to: (1) 12 (2) 9 (3) 10 (4) 11 JEE Main 2017 (02 Apr) JEE Main Previous Year Paper

Q64.For any three positive real numbers 𝑎, 𝑏 and 𝑐. If 925𝑎2 + 𝑏2 + 25𝑐2 - 3𝑎𝑐= 15𝑏3𝑎+ 𝑐. Then (1) 𝑏, 𝑐 and 𝑎 are in G.P. (2) 𝑏, 𝑐 and 𝑎 are in A.P. (3) 𝑎, 𝑏 and 𝑐 are in A.P. (4) 𝑎, 𝑏 and 𝑐 are in G.P.

Q66.The coefficient of x−5 in the binomial expansion of ( x 32 −x 31 +1 − x−x 21 ) where x ≠0,1 is (1) −1 (2) 4 (3) 1 (4) −4

Q66.If 5tan2⁡𝑥- cos2⁡𝑥= 2cos⁡ 2𝑥+ 9, then the value of cos⁡4𝑥 is 3 1 (1) - (2) 5 3 2 7 (3) (4) - 9 9

Q67.Let 𝑘 be an integer such that the triangle with vertices 𝑘, - 3𝑘, 5, 𝑘 and -𝑘, 2 has area 28 sq. units. Then the orthocenter of this triangle is at the point: (1) 2, - 1 (2) 1, 3 2 4 3 1 (3) 1, - (4) 2, 4 2

Q68.The radius of a circle, having minimum area, which touches the curve 𝑦= 4 - 𝑥2 and the lines, 𝑦= 𝑥 is: (1) 2√2 + 1 (2) 2√2 - 1 (3) 4√2 - 1 (4) 4√2 + 1 1

Q78.Let 𝑎, 𝑏, 𝑐∈𝑅 . If 𝑓𝑥= 𝑎𝑥2 + 𝑏𝑥+ 𝑐 is such that 𝑎+ 𝑏+ 𝑐= 3 and 𝑓𝑥+ 𝑦= 𝑓𝑥+ 𝑓𝑦+ 𝑥𝑦, ∀ 𝑥, 𝑦∈𝑅 , 10 then ∑ 𝑓(𝑛) is equal to: 𝑛= 1 (1) 330 (2) 165 (3) 190 (4) 255 1 6𝑥√𝑥

Q79.Let f(x) = 210x + 1 and g(x) = 310x −1. If (fog)(x) = x, then x is equal to: JEE Main 2017 (08 Apr Online) JEE Main Previous Year Paper (1) 210−1 (2) 1−2−10 210−3−10 310−2−10 (3) 310−1 (4) 1−3−10 310−2−10 210−3−10 15 15 dy is equal to + + x dx , then (x2 −1) dx2d2y

Q83.If n→∞( (1) 17 (2) 15 2 2 (3) 7 (4) 8

Q84.The area (in sq. units) of the region 𝑥, 𝑦: 𝑥≥0, 𝑥+ 𝑦≤3, 𝑥2 ≤4𝑦 and 𝑦≤1 + √𝑥 is 59 3 (1) sq . units (2) sq . units 12 2 (3) 7 sq . units (4) 5 sq . units 3 2

Q84.The area (in sq. units) of the smaller portion enclosed between the curves, x2 + y2 = 4 and y2 = 3x, is: (1) √3 1 + 4π3 (2) √31 + 2π3 (3) 2√3 1 + π3 (4) 2√31 + 2π3

Q86.Given, →𝑎= 2 ^𝑖+ ^𝑗- 2 ^𝑘 and 𝑏= ^𝑖+ ^𝑗. Let →𝑐 be a vector such that →𝑐- →𝑎= 3, →𝑎× 𝑏× →𝑐= 3 and the angle between →𝑐 and →𝑎× →𝑏 be 30° . Then →𝑎⋅ →𝑐 is equal to: 25 (1) (2) 2 8 (3) 5 (4) 1 8

Q87.If the image of the point 𝑃1, - 2, 3 in the plane, 2𝑥+ 3𝑦- 4𝑧+ 22 = 0 measured parallel to the line, 𝑥 𝑦 𝑧 = = is 𝑄, then 𝑃𝑄 is equal to: 1 4 5 (1) 3√5 (2) 2√42 (3) √42 (4) 6√5

Q87.The coordinates of the foot of the perpendicular from the point (1, −2, 1) on the plane containing the lines x+1 6 = y−17 = z−38 and x−13 = y−25 = z−37 , is: (1) (2, −4, 2) (2) (1, 1, 1) (3) (0, 0, 0) (4) (−1, 2, −1) = 2, is,