Practice Questions

Q79.Let A = {1, 2, 3, 4} and R : A →A be the relation defined by R = {(1, 1), (2, 3), (3, 4), (4, 2)} . The correct statement is : (1) R does not have an inverse. (2) R is not a one to one function. (3) R is an onto function. (4) R is not a function. x2−x

Q82.The intercepts on the x-axis made by tangents to the curve, y = ∫ |t| dt, x ∈R, which are parallel to the line 0 y = 2x , are equal to (1) ±3 (2) ±4 (3) ±1 (4) ±2

Q88.If ^a,^b and ^c are unit vectors satisfying ^a −√3^b + ^c = 0, then the angle between the vectors ^a and ^c is : (1) π (2) π 4 3 (3) π (4) π 6 2

Q88.If →a and →b are non-collinear vectors, then the value of α for which the vectors →u = (α −2)→a + →b and →v = (2 + 3α)→a −3→b are collinear is : (1) 3 (2) 2 2 3 (3) −32 (4) −23

Q88.If the lines x−2 1 = y−31 = z−4−k and x−1k = y−42 = z−51 are coplanar, then k can have JEE Main 2013 (07 Apr) JEE Main Previous Year Paper (1) exactly two values. (2) exactly three values. (3) any value. (4) exactly one value.

Q89.If the projections of a line segment on the x, y and z-axes in 3-dimensional space are 2, 3 and 6 respectively, then the length of the line segment is : (1) 12 (2) 7 (3) 9 (4) 6

Q90.A multiple choice examination has 5 questions. Each question has three alternative answers out of which exactly one is correct. The probability that a student will get 4 or more correct answers just by guessing is : (1) 11 (2) 10 35 35 (3) 17 (4) 13 35 35 JEE Main 2013 (07 Apr) JEE Main Previous Year Paper

Q90.If the events A and B are mutually exclusive events such that P(A) = 3x+13 and P(B) = 1−x4 , then the set of possible values of x lies in the interval : (1) [0, 1] (2) [ 13 , 23 ] (3) [−13 , 59 ] (4) [−79 , 49 ] JEE Main 2013 (25 Apr Online) JEE Main Previous Year Paper

Q62.Let Z1 and Z2 be any two complex number. Statement 1: |Z1 −Z2| ≥|Z1| −|Z2| Statement 2: |Z1 + Z2| ≤|Z1| + |Z2| (1) Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation of Statement 1. (2) Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation of Statement 1. (3) Statement 1 is true, Statement 2 is false. (4) Statement 1 is false, Statement 2 is true.

Q63.If the number of 5-element subsets of the set A = {a1, a2, … , a20} of 20 distinct elements is k times the number of 5-element subsets containing a4 , then k is (1) 5 (2) 20 7 (3) 4 (4) 10 3

Q64.If the A.M. between pth and qth terms of an A.P. is equal to the A.M. between rth and sth terms of the same A.P., then p + q is equal to (1) r + s −1 (2) r + s −2 (3) r + s + 1 (4) r + s ,

Q66.If the point (1, a) lies between the straight lines x + y = 1 and 2(x + y) = 3 then a lies in interval (1) ( 23 , ∞) (2) (1, 23 ) (3) (−∞, 0) (4) (0, 12 )

Q68.If the line 2x + y = k passes through the point which divides the line segment joining the points (1, 1) and (2, 4) in the ratio 3 : 2, then k equals JEE Main 2012 (Offline) JEE Main Previous Year Paper (1) 29 (2) 5 5 (3) 6 (4) 115

Q69.Consider the straight lines L1 : x −y = 1 L2 : x + y = 1 L3 : 2x + 2y = 5 L4 : 2x −2y = 7 The correct statement is JEE Main 2012 (26 May Online) JEE Main Previous Year Paper (1) L1 ∥L4, L2∥L3, L1 intersect L4 . (2) L1 ⊥L2, L1∥L3, L1 intersect L2 . (3) L1 ⊥L2, L2∥L3, L1 intersect L4 . (4) L1 ⊥L2, L1 ⊥L3, L2 intersect L4 .

Q70.The logically equivalent preposition of p ⇔q is (1) (p ⇒q∧)q ⇒p ) (2) p ∧q (3) (p ∧q∨)q ≠p ) (4) (p ∧q ⇒q ∨(p )

Q70.The equation of the normal to the parabola, x2 = 8y at x = 4 is (1) x + 2y = 0 (2) x + y = 2 (3) x −2y = 0 (4) x + y = 6 y2

Q73.The Statement that is TRUE among the following is (1) The contrapositive of 3x + 2 = 8 ⇒x = 2 is (2) The converse of tan x = 0 ⇒x = 0 is x ≠0 ⇒ x ≠2 ⇒3x + 2 ≠8. tan x = 0. (3) p ⇒q is equivalent to p∨∼q . (4) p ∨q and p ∧q have the same truth table. JEE Main 2012 (07 May Online) JEE Main Previous Year Paper

Q73.The negation of the statement "If I become a teacher, then I will open a school" is (1) I will become a teacher and I will not open a (2) Either I will not become a teacher or I will not school open a school (3) Neither I will become a teacher nor I will open a (4) I will not become a teacher or I will open a school school

Q73.Let p and q be two Statements. Amongst the following, the Statement that is equivalent to p →q is (1) p∧∼q (2) ∼p ∨q (3) ∼p ∧q (4) p∨∼q

Q74.Let p and q denote the following statements p : The sun is shining q : I shall play tennis in the afternoon The negation of the statement "If the sun is shining then I shall play tennis in the afternoon", is (1) q ⇒∼p (2) q∧∼p (3) p∧∼q (4) ∼q ⇒∼p

Q76.Statement 1: If A and B be two sets having p and q elements respectively, where q > p. Then the total number of functions from set A to set B is qp Statement 2: The total number of selections of p different objects out of q objects is qCp . (1) Statement 1 is true, Statement 2 is false. (2) Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation of 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 of Statement 1.

Q78.Let A and B be non empty sets in R and f : A →B is a bijective function. Statement 1: f is an onto function. Statement 2: There exists a function g : B →A such that fog = IB . (1) Statement 1 is true, Statement 2 is false. (2) Statement 1 is true, Statement 2 is true; Statement 2 is 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 not the correct explanation for Statement 1.

Q78.A value of tan−1 (sin (cos−1 (√2 ))) (1) π (2) π 4 2 (3) π (4) π 3 6

Q80.Let f : (−∞, ∞) →(−∞, ∞) be defined by f(x) = x3 + 1 Statement 1: The function fhas a local extremum at x = 0 Statement 2: The function f is continuous and differentiable on (−∞, ∞) and f ′(0) = 0 (1) Statement 1 is true, Statement 2 is false. (2) Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 1. (3) Statement 1 is true, Statement 2 is true, (4) Statement 1 is false, Statement 2 is true. Statement 2 is not the correct explanation for Statement 1.

Q81.The weight W of a certain stock of fish is given by W = nw, where n is the size of stock and w is the average weight of a fish. If n and w change with time t as n = 2t2 + 3 and w = t2 −t + 2, then the rate of change of W with respect to t at t = 1 is (1) 1 (2) 8 (3) 13 (4) 5 JEE Main 2012 (19 May Online) JEE Main Previous Year Paper