Practice Questions

Q89.The values of a for which the two points (1, a, 1) and (−3, 0, a) lie on the opposite sides of the plane 3x + 4y −12z + 13 = 0, satisfy JEE Main 2012 (07 May Online) JEE Main Previous Year Paper (1) 0 < a < 31 (2) −1 < a < 0 (3) a < −1 or a < 13 (4) a = 0

Q89.The coordinates of the foot perpendicular from the point (1, 0, 0) to the line x −1 y + 1 z + 10 = = are 2 −3 8 (1) (2, −3, 8) (2) (1, −1, −10) (3) (5, −8, −4) (4) (3, −4, −2) ∑ni=1 i2

Q89.If →a = ^i −2^j + 3^k,→b = 2^i + 3^j −^k and →c = r^i + ^j + (2r −1^k are three vectors such that →c is parallel to the plane of →a and →b, then r is equal to (1) 1 (2) −1 (3) 0 (4) 2

Q89.The equation of a plane containing the line x+1 −3 = y−32 = z+21 and the point (0, 7, −7) is (1) x + y + z = 0 (2) x + 2y + z = 21 (3) 3x −2y + 5z + 35 = 0 (4) 3x + 2y + 5z + 21 = 0

Q89.If the lines x−1 2 = y+13 = z−14 and x−31 = y−k2 = 1z intersect, then k is equal to (1) −1 (2) 29 (3) 9 (4) 0 2

Q90.Three numbers are chosen at random without replacement from {1, 2, 3, … . .8} . The probability that their minimum is 3 , given that their maximum is 6 , is (1) 3 (2) 1 8 5 (3) 41 (4) 25 JEE Main 2012 (Offline) JEE Main Previous Year Paper

Q90.A line with positive direction cosines passes through the point P(2, −1, 2) and makes equal angles with the coordinate axes. If the line meets the plane 2x + y + z = 9 at point Q , then the length PQ equals (1) √2 (2) 2 (3) √3 (4) 1 JEE Main 2012 (07 May Online) JEE Main Previous Year Paper

Q90.If six students, including two particular students A and B, stand in a row, then the probability that A and B are separated with one student in between them is (1) 8 (2) 4 15 15 (3) 2 (4) 1 15 15 JEE Main 2012 (19 May Online) JEE Main Previous Year Paper

Q90.There are two balls in an urn. Each ball can be either white or black. If a white ball is put into the urn and there after a ball is drawn at random from the urn, then the probability that it is white is (1) 1 (2) 2 4 3 (3) 1 (4) 1 5 3 JEE Main 2012 (26 May Online) JEE Main Previous Year Paper

Q61.Let α, β be real and z be a complex number. If z2 + αz + β = 0 has two distinct roots on the line Re z = 1, then it is necessary that (1) β ∈(−1, 0) (2) |β| = 1 (3) β ∈(1, ∞) (4) β ∈(0, 1)

Q62.If ω(≠1) is a cube root of unity, and (1 + ω)7 = A + Bω. Then (A, B) equals (1) (1, 1) (2) (1, 0) (3) (−1, 1) (4) (0, 1)

Q64.A man saves Rs. 200 in each of the first three months of his service. In each of the subsequent months his saving increases by Rs. 40 more than the saving of immediately previous month. His total saving from the start of service will be Rs. 11040 after (1) 19 months (2) 20 months (3) 21 months (4) 18 months

Q65.The coefficient of x7 in the expansion of (1 −x −x2 + x3) 6 is (1) −132 (2) −144 (3) 132 (4) 144

Q66.If A = sin2 x + cos4 x, then for all real x (1) 13 16 ≤A ≤1 (2) 1 ≤A ≤2 (3) 3 4 ≤A ≤1316 (4) 43 ≤A ≤1 JEE Main 2011 JEE Main Previous Year Paper

Q68.The two circles x2 + y2 = ax and x2 + y2 = c2(c > 0) touch each other if (1) |a| = c (2) a = 2c (3) |a| = 2c (4) 2|a| = c

Q69.Equation of the ellipse whose axes are the axes of coordinates and which passes through the point (−3, 1) and has eccentricity is √25 (1) 5x2 + 3y2 −48 = 0 (2) 3x2 + 5y2 −15 = 0 (3) 5x2 + 3y2 −32 = 0 (4) 3x2 + 5y2 −32 = 0 Q70.$$ \lim _{x \rightarrow 2}\left(\frac{\sqrt{1-\cos \{2(x-2)\}}}{x-2}\right) (1) equals √2 (2) equals −√2 (3) equals 1 (4) does not exist √2

Q71.Consider the following statements P : Suman is brilliant Q : Suman is rich R : Suman is honest The negation of the statement "Suman is brilliant and dishonest if and only if Suman is rich" can be expressed as (1) ∼(Q ↔(P∧∼R)) (2) ∼Q ↔∼P ∧R (3) ∼(P∧∼R) ↔Q (4) ∼P ∧(Q ↔∼R)

Q72.If the mean deviation about the median of the numbers a, 2a, … , 50a is 50 , then |a| equals (1) 3 (2) 4 (3) 5 (4) 2

Q73.Let R be the set of real numbers This question has Statement −1 and Statement −2. Of the four choices given after the statements, choose the one that best describes the two statements. Statement-1 : A = {(x, y) ∈R × R : y −x is an integer } is an equivalence relation on R. Statement-2 : B = {(x, y) ∈R × R : x = αy for some rational number α} is an equivalence relation on R. (1) Statement −1 is true, Statement −2 is true; (2) Statement −1 is true, Statement- 2 is false. Statement −2 is not a correct explanation for Statement −1 (3) Statement −1 is false, Statement −2 is true. (4) Statement −1 is true, Statement −2 is true; Statement −2 is a correct explanation for Statement −1 JEE Main 2011 JEE Main Previous Year Paper

Q75.The number of values of k for which the linear equations 4x + ky + 2z = 0; kx + 4y + z = 0; 2x + 2y + z = 0 possess a non-zero solution is (1) 2 (2) 1 (3) zero (4) 3

Q76.The domain of the function f(x) = 1 is √|x|−x (1) (0, ∞) (2) (−∞, 0) (3) (−∞, ∞) −{0} (4) (−∞, ∞)

Q77. x x < 0 ⎧ sin(p+1)x+sinx The value of p and q for which the function f(x) = is continuous for all x in R, is ⎨ q , x = 0 √x+x2−√x , x > 0 ⎩ x3/2 (1) p = 52 , q = 12 (2) p = −32 , q = 12 (3) p = 21 , q = 32 (4) p = 12 , q = −32

Q78. d2x equals dy2 (1) d2y −1 dy −3 (2) d2y dy −2 −( dx2 ) ( dx ) ( dx2 )( dx ) (3) −( dx2d2y )( dxdy ) −3 (4) ( dx2d2y ) −1

Q79.The shortest distance between line y −x = 1 and curve x = y2 is (1) 3√2 (2) 8 8 3√2 (3) 4 (4) √3 √3 4 dx is

Q80.The value of ∫10 8 log(1+x)1+x2 (1) π 8 log 2 (2) π2 log 2 (3) log 2 (4) π log 2 tdt. Then f has