Practice Questions

Q20.A conductor lies along the z-axis at −1.5 ≤z < 1.5 m and carries a fixed current of 10.0 A in −ˆaz direction → (see figure). For a field B = 3.0 × 10−4 e−0.2x ˆay T, find the power required to move the conductor at constant speed to x = 2.0 m, y = 0 m in 5 × 10−3 s. Assume parallel motion along the x-axis. (1) 1.57 W (2) 2.97 W (3) 14.85 W (4) 29.7 W

Q25.Interference pattern is observed at ' P ' due to superimposition of two rays coming out from a source ' S ' as shown in the figure. The value of ' l ' for which maxima is obtained at ' P ' is: ( R is perfect reflecting surface) (1) 1 = 2nλ (2) 1 = (2n−1)λ √3−1 2(√3−1 ) (2n−1)λ 1 = (3) 1 = (2n−1λ)√3 √3−1 4(2−√3 ) (4)

Q27.A beam of light has two wavelengths of 4972Å and 6216Å with a total intensity of 3.6 × 10−3 Wm−2 equally distributed among the two wavelengths. The beam falls normally on an area of 1 cm2 of a clean metallic surface of work function 2.3eV. Assume that there is no loss of light by reflection and that each capable photon ejects one electron. The number of photoelectrons liberated in 2 s is approximately: (1) 6 × 1011 (2) 9 × 1011 (3) 11 × 1011 (4) 15 × 1011

Q27.A photon of wavelength λ is scattered from an electron, which was at rest. The wavelength shift Δλ is three times of λ and the angle of scattering θ is 60∘ . The angle at which the electron recoiled is ϕ. The value of tan ϕ JEE Main 2014 (11 Apr Online) JEE Main Previous Year Paper is : (electron speed is much smaller than the speed of light) (1) 0.16 (2) 0.22 (3) 0.25 (4) 0.28

Q36.Which one of the following does not have a pyramidal shape? (1) (CH3)3 N (2) (SiH3)3 N (3) P(CH3)3 (4) P(SiH3)3

Q51.The equation which is balanced and represents the correct product(s) is (1) Li2O + 2KCl →2LiCl + K2O (2) [CoCl (NH3)5]+ + 5H+ →Co2+ + 5 NH+4 + Cl− (3)− [Mg (H2O)6]2+ + (EDTA)4−excess NaOH→ [Mg(EDTA)]2+(4) CuSO4+ +6H2O4KCN →K2[Cu (CN)4] + K2 SO4

Q63.Let w(Im w≠0) be a complex number. Then, the set of all complex numbers z satisfying the equation ¯w −wz = k(1 −z), for some real number k, is (1) {z : z ≠1} (2) {z : |z| = 1, z ≠1} ¯(3) {z : z = z} (4) {z : |z| = 1}

Q64.If (10)9 + 2(11)1(10)8 + 3(11)2(10)7 + ...... + 10(11)9 = k(10)9, then k is equal to : JEE Main 2014 (06 Apr) JEE Main Previous Year Paper (1) 100 (2) 110 (3) 121 (4) 441 10 100

Q64.Let f(n) = [ 13 + 1003n ]n, where [n] denotes the greatest integer less than or equal to n. Then ∑56n=1 f(n) is equal to (1) 56 (2) 1287 (3) 1399 (4) 689

Q66.If the sum 3 + 5 + 7 + .... .+ up to 20 terms is equal to 21k , then k is equal to 12 12+22 12+22+32 (1) 240 (2) 120 (3) 60 (4) 180

Q66.If 1 + x4 + x5 = ∑5i=0 ai (1 + xi), for all x in R, then a2 is: (1) −4 (2) 6 (3) −8 (4) 10 is expanded in the ascending powers of x and the coefficients of powers of x in two consecutive

Q66.If the coefficients of x3 and x4 in the expansion of (1 + ax + bx2)(1 −2x)18 in powers of x are both zero, then (a, b) is equal to (1) (14, 2723 ) (2) (16, 2723 ) (3) (16, 2513 ) (4) (14, 2513 )

Q71.The locus of the foot of perpendicular drawn from the centre of the ellipse x2 + 3y2 = 6 on any tangent to it is (1) (x2 + y2) 2 = 6x2 + 2y2 (2) (x2 + y2) 2 = 6x2 −2y2 (3) (x2 −y2) 2 = 6x2 + 2y2 (4) (x2 −y2) 2 = 6x2 −2y2

Q71.Let a and b be any two numbers satisfying 1 + 1 = 14 . Then, the foot of perpendicular from the origin on a2 b2 the variable line x a + yb = 1 lies on : (1) A circle of radius = 2 (2) A hyperbola with each semi-axis = √2 . (3) A hyperbola with each semi-axis = 2 (4) A circle of radius = √2

Q72.Let P(3 sec θ, 2 tan θ) and Q(3 sec ϕ, 2 tan ϕ) where θ + ϕ = π2 , be two distinct points on the hyperbola x2 . Then the ordinate of the point of intersection of the normals at P and Q is: 9 −y24 = 1 (1) 11 3 (2) −113 (3) 13 2 (4) −132 = 5, then k is equal to:

Q73.Let p, q, r denote arbitrary statements. Then the logically equivalent of the statement p ⇒(q ∨r) is: (1) (p ∨q) ⇒r (2) (p ⇒q) ∨(p ⇒r) (3) (p ⇒∼q) ∧(p ⇒r) (4) (p ⇒q) ∧(p ⇒∼r)

Q75.Two ships A and B are sailing straight away from a fixed point O along routes such that ∠AOB is always 120∘ . At a certain instance, OA = 8 km, OB = 6 km and the ship A is sailing at the rate of 20 km/hr while the ship B sailing at the rate of 30 km/hr. Then the distance between A and B is changing at the rate (in km/hr ): (1) 260 (2) 260 √37 37 (3) 80 (4) 80 √37 37

Q79.If a, b, c are non - zero real numbers and if the system of equations (a −1)x = y + z JEE Main 2014 (09 Apr Online) JEE Main Previous Year Paper (b −1)y = x + z (c −1)z = x + y has a non - trivial solution, then ab + bc + ca equals : (1) −1 (2) a + b + c (3) abc (4) 1 is equal to :

Q79.Let for i = 1, 2, 3, pi(x) be a polynomial of degree 2 in x, p′i(x) and p′′i(x) be the first and second order derivatives of pi(x) respectively. Let, p1(x) p′1(x) p′′1x( A(x) = ⎡ p2(x) p′2(x) p′′2( ⎤ ⎞ p3(x) p′3(x) p′′3(x ⎣ ⎦ ⎠ and B(x) = [A(x)]TA(x). Then determinant of B(x) : (1) is a polynomial of degree 6 in x. (2) is a polynomial of degree 3 in x. (3) is a polynomial of degree 2 in x. (4) does not depend on x.

Q81.Let f(x) = x|x|, g(x) = sin x and h(x) = (g ∘f)(x). Then (1) h(x) is not differentiable at x = 0. (2) h(x) is differentiable at x = 0, but h′(x) is not continuous at x = 0 (3) h′(x) is continuous at x = 0 but it is not (4) h′(x) is differentiable at x = 0 differentiable at x = 0

Q83.If m is a non-zero number and ∫x5m−1+2x4m−1 dx = f(x) + c, then f(x) is equal to (x2m+xm+1)3 (1) (x5m−x4m) (2) 1 x4m 2m(x2m+xm+1)2 2m (x2m+xm+1)2 (3) x5m (4) 2m(x5m+x4m) 2m(x2m+xm+1)2 (x2m+xm+1)2

Q85.The area (in sq. unit) of the region described by A = {(x, y) : x2 + y2 ≤1 and y2 ≤1 −x} is (1) π 2 −23 (2) π2 + 32 (3) π 2 + 34 (4) π2 −43

Q87.If ^x, ^y and ^z are three unit vectors in threedimensional space, then the minimum value of |^x + ^y|2 + |^y + ^z|2 + |^z + ^x|2 (1) 3 (2) 3 2 (3) 3√3 (4) 6

Q88.The image of the line x−1 3 = 1 = z−4−5 in the plane 2x −y + z +3=0 is the line (1) x−3 3 = y+51 = z−2−5 (2) x−3−3 = y+5−1 = z−25 (3) x+3 3 = y−51 = z−2−5 (4) x+3−3 = y−5−1 = z+25

Q89.Equation of the line of the shortest distance between the lines x 1 = −1 = 1z and x−10 = y+1−2 = 1z is JEE Main 2014 (19 Apr Online) JEE Main Previous Year Paper (1) −2 x = 1y = 2z (2) x1 = −1y = −2z y+1 (3) x−1 1 = −1 = −2z (4) x−11 = y+1−1 = 1z