Practice Questions

Q85.The solution of the differential equation ydx −(x + 2y2)dy = 0 is x = f(y). If f(−1) = 1, then f(1) is equal to (1) 2 (2) 3 (3) 4 (4) 1 −−−−−

Q86.Let y (x) be the solution of the differential equation (x log x) dxdy + y = 2x log x, (x ≥1). Then y (e) is equal to (1) 2e (2) e (3) 0 (4) 2 →

Q86.If y (x) is the solution of the differential equation (x + 2) dxdy = x2 + 4x −9, x ≠ −2 and y(0) = 0, then y(−4) is equal to (1) −1 (2) 1 (3) 0 (4) 2 × , then 2→c is equal to:

Q86.In a parallelogram ABCD, AB→ = a, AD→ = b & AC→ = c. DB→ ⋅AB→ has the value: (1) 1 2 (a2 + b2 + c2) (2) 14 (a2 + b2 −c2) (3) 3 1 (b2 + c2 −a2) (4) 12 (a2 −b2 + c2)

Q87.A plane containing the point (3, 2, 0) and the line x−11 = y−25 = z−34 also contains the point (1) (0, 7, −10) (2) (0, 7, 10) (3) (0, 3, 1) (4) (0, −3, 1)

Q87.Let →aand→b be two unit vectors such that →a+→b = √3. If →c=→a+ 2→b + (→a →b) (1) √51 (2) √37 (3) √43 (4) √55

Q87.Let →a, b and →c be three non - zero vectors such that no two of them are collinear and × →c→a. If θ is the angle between vectors b and →c, then a value of sin θ is = 13 b (→a → → → b) ×→c (1) −2√3 (2) 2√2 3 3 (3) −√2 (4) 2 3 3

Q88.If the points (1, 1, λ) & (−3, 0, 1), are equidistant from the plane, 3x + 4y −12z + 13 = 0, then λ satisfies the equation: (1) 3x2 + 10x + 7 = 0 (2) 3x2 + 10x −13 = 0 (3) 3x2 −10x + 7 = 0 (4) 3x2 −10x + 21 = 0 JEE Main 2015 (10 Apr Online) JEE Main Previous Year Paper

Q88.The distance of the point (1, 0, 2) from the point of intersection of the line x−23 = y+14 = z−212 and the plane x −y + z =16, is (1) 13 (2) 2√14 (3) 8 (4) 3√21

Q88.The shortest distance between the z - axis and the line x + y + 2z −3 = 0 = 2x + 3y + 4z −4, is (1) 1 (2) 2 (3) 3 (4) 4

Q89.The equation of the plane containing the line of intersection of 2x −5y + z = 3; x + y + 4z = 5, and parallel to the plane, x + 3y + 6z = 1, is (1) 2x + 6y + 12z = −13 (2) 2x + 6y + 12z = 13 (3) x + 3y + 6z = −7 (4) x + 3y + 6z = 7

Q89.If the shortest distance between the line x−1α = y+1−1 = 1z , (α ≠−1) , and x + y + z + 1 = 0 = 2x −y + z + 3 is 1 ,then value of α is : √3 (1) −1916 (2) 3219 (3) −1619 (4) 1932

Q89.If the mean and the variance of a binomial variate X are 2 & 1 respectively, then the probability that X takes a value greater than or equal to one is: (1) 1 (2) 9 16 16 (3) 3 (4) 15 4 16

Q90.If 12 identical balls are to be placed in 3 identical boxes, then the probability that one of the boxes contains exactly 3 balls is (1) 22( 13 )11 (2) 195 (3) 55( 32 )10 (4) 220( 31 )12 JEE Main 2015 (04 Apr) JEE Main Previous Year Paper

Q90.If the lengths of the sides of a triangle are decided by the three throws of a single fair die, then the probability that the triangle is of maximum area given that it is an isosceles triangle, is: (1) 1 (2) 1 69 26 (3) 1 (4) 1 21 15 JEE Main 2015 (11 Apr Online) JEE Main Previous Year Paper

Q90.Let X be a set containing 10 elements and P(X) be its power set. If A and B are picked up at random from P(X), with replacement, then the probability that A and B have equal number of elements is: (1) (210−1) (2) 20C10 220 220 (3) 20C10 (4) (210−1) 210 210 JEE Main 2015 (10 Apr Online) JEE Main Previous Year Paper

Q61.The sum of the roots of the equation, x2 + |2x −3| −4 = 0, is: (1) 2 (2) −2 (3) √2 (4) −√2

Q61.If 1 , 1 are the roots of the equation ax2 + bx + 1 = 0, (a ≠0, a, b ∈R), then the equation √α √β x(x + b3) + (a3 −3abx) = 0 has roots: 2 and β−32 (1) √αβ and αβ (2) α−3 (3) αβ 21 and α 21 β (4) α 23 and β 23

Q61.The equation √3x2 + x + 5 = x −3, where x is real, has (1) no solution (2) exactly four solutions (3) exactly one solution (4) exactly two solutions JEE Main 2014 (19 Apr Online) JEE Main Previous Year Paper

Q61.If a ∈ R and the equation −3(x − [x])2 + 2(x − [x]) + a2 = 0 (where [x] denotes the greatest integer ≤ x) has no integral solution, then all possible values of a lie in the interval (1) (−2, −1) (2) ( −∞, −2) ∪(2,∞) (3) (−1, 0) ∪(0, 1) (4) (1, 2)

Q61.If α and β are roots of the equation, x2 −4√2kx + 2e4 ln k −1 = 0 for some k, and α2 + β2 = 66, then α3 + β3 is equal to: (1) 248√2 (2) 280√2 (3) −32√2 (4) −280√2 + arg

Q62.If equations ax2 + bx + c = 0, (a, b, c ∈R, a ≠0) and 2x2 + 3x + 4 = 0 have a common root, then a : b : c equals : (1) 2 : 3 : 4 (2) 4 : 3 : 2 (3) 1 : 2 : 3 (4) 3 : 2 : 1

Q62.Let α and β be the roots of equation px2 + qx + r = 0, p ≠0. If p, q, r are in A.P. and α1 + β1 = 4, then the value of |α −β| is (1) √34 (2) 2√13 9 9 (3) √61 (4) 2√17 9 9

Q62.If z1, z2 and z3, z4 are 2 pairs of complex conjugate numbers, then arg ( z1z4 ) ( z2z3 ) equals: (1) 0 (2) π 2 (3) 3π (4) π 2 JEE Main 2014 (11 Apr Online) JEE Main Previous Year Paper

Q62.Let z ≠−i be any complex number such that z+iz−i is a purely imaginary number. Then z + 1z is: (1) 0 (2) any non-zero real number other than 1 . (3) any non-zero real number. (4) a purely imaginary number. Q63.8-digit numbers are formed using the digits 1, 1, 2, 2, 2, 3, 4, 4. The number of such numbers in which the odd digits do no occupy odd places, is: (1) 160 (2) 120 (3) 60 (4) 48