Practice Questions

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

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)

Q63.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 : The number of ways of distributing 10 identical balls in 4 distinct boxes such that no box is empty is 9C3 Statement-2: The number of ways of choosing any 3 places from 9 different places is 9C3 . (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

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

Q67.The lines L1 : y −x = 0 and L2 : 2x + y = 0 intersect the line L3 : y + 2 = 0 at P and Q respectively. The bisector of the acute angle between L1 and L2 intersect L3 at R. 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 : The ratio PR : RQ equals 2√2 : √5 . Statement-2 : In any triangle, bisector of an angle divides the triangle into two similar triangles. (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

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

Q74.Let A and B be two symmetric matrices of order 3 . 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(BA) and (AB)A are symmetric matrices. Statement - 2 : AB is symmetric matrix if matrix multiplication of A and B is commutative. (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

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

Q81.For x ∈(0, 5π2 ), define f(x) = ∫x0 √t sin (1) local minimum at π and 2π (2) local minimum at π and local maximum at 2π (3) local maximum at π and local minimum at 2π (4) local maximum at π and 2π

Q82.The area of the region enclosed by the curves y = x, x = e, y = x1 and the positive x-axis is JEE Main 2011 JEE Main Previous Year Paper (1) 1 square units (2) 3 square units 2 (3) 5 square units (4) 1 square units 2 2

Q83.If dy = y + 3 > 0 and y(0) = 2, then y(ln 2) is equal to dx (1) 5 (2) 13 (3) -2 (4) 7

Q84.Let I be the purchase value of an equipment and V(t) be the value after it has been used for t years. The value V(t) depreciates at a rate given by differential equation dV(t)dt = −k(T −t), where k > 0 is a constant and T is the total life in years of the equipment. Then the scrap value V(T) of the equipment is (1) I −kT2 (2) 1 −k(T−t)22 (3) e−kT (4) T2 −1k → → → → 1 1 is

Q85.If →a = (3^i + ^k) and b = 7 (2^i + 3^j −6^k), then the value of (2→a− b) ⋅[(→a× b) × (→a+ 2 b)] √10 (1) −3 (2) 5 (3) 3 (4) −5