Practice Questions

Q59.Which of the following statements about aspirin is not true? (1) It is effective in relieving pain. (2) It is a neurologically active drug. (3) It has antiblood clotting action. (4) It belongs to narcotic analgesics.

Q59.A compound with molecular mass 180 is acylated with CH3 COCl to get a compound with molecular mass 390 . The number of amino groups presents per molecule of the former compound is (1) 4 (2) 6 (3) 2 (4) 5

Q59.If a polythene sample contains two monodisperse fractions in the ratio 2 : 3 with degree of polymerization 100 and 200, respectively, then its weight average molecular weight will be : (1) 4900 (2) 4600 (3) 4300 (4) 5200

Q60.Natural glucose is termed D-glucose because : (1) −OH on the second carbon is on the right side in (2) −OH on the sixth carbon is on the right side in Fischer projection Fischer projection. (3) −OH on the fifth carbon is on the right side in (4) It is dextrorotatory. Fischer projection.

Q61.If α and β are roots of the equation x2 + px + 3p4 = 0 , such that |α −β| = √10 , then p belongs to the set : (1) {2, −5} (2) {−3, 2} (3) {−2, 5} (4) {3, −5}

Q61.The real number k for which the equation, 2x3 + 3x + k = 0 has two distinct real roots in [0, 1] belongs to (1) lies between −1 and 0. (2) does not exist. (3) lies between 1 and 2 . (4) lies between 2 and 3 .

Q61.If p and q are non-zero real numbers and α3 + β3 = −p, αβ = q , then a quadratic equation whose roots are α2 β2 β , α is : (1) px2 −qx + p2 = 0 (2) qx2 + px + q2 = 0 (3) px2 + qx + p2 = 0 (4) qx2 −px + q2 = 0

Q61.The least integral value α of x such that x−5 > 0, satisfies : x2+5x−14 (1) α2 + 3α −4 = 0 (2) α2 −5α + 4 = 0 (3) α2 −7α + 6 = 0 (4) α2 + 5α −6 = 0 , where z is any non-zero complex number. The set A = {a : |z| = 1 and z ≠±1} is equal

Q61.The values of ' a ' for which one root of the equation x2 −(a + 1)x + a2 + a −8 = 0 exceeds 2 and the other is lesser than 2 , are given by : (1) 3 < a < 10 (2) a ≥10 (3) −2 < a < 3 (4) a ≤−2 JEE Main 2013 (09 Apr Online) JEE Main Previous Year Paper

Q62.Let z satisfy |z| = 1 and z = 1 −¯z. Statement 1 : z is a real number. Statement 2 : Principal argument of z is π3 (1) Statement 1 is true Statement 2 is true; Statement (2) Statement 1 is false; Statement 2 is true 2 is a correct explanation for Statement 1 . (3) Statement 1 is true, Statement 2 is false. (4) Statement 1 is true; Statement 2 is true; Statement 2 is not a correct explanation for Statement 1 . JEE Main 2013 (25 Apr Online) JEE Main Previous Year Paper Q63.5 - digit numbers are to be formed using 2, 3, 5, 7 , 9 without repeating the digits. If p be the number of such numbers that exceed 20000 and q be the number of those that lie between 30000 and 90000 , then p : q is: (1) 6 : 5 (2) 3 : 2 (3) 4 : 3 (4) 5 : 3

Q62.If a complex number z statisfies the equation x + √2|z + 1| + i = 0 , then |z| is equal to : (1) 2 (2) √3 (3) √5 (4) 1

Q62.Let a = Im ( 1+z22iz ) to: (1) (−1, 1) (2) [−1, 1] (3) [0, 1) (4) (−1, 0]

Q62.If Z1 ≠0 and Z2 be two complex numbers such that Z2 is a purely imaginary number, then 2Z1+3Z2 is equal Z1 2Z1−3Z2 to: (1) 2 (2) 5 (3) 3 (4) 1

Q62.If the equations x2 + 2x + 3 = 0 and ax2 + bx + c = 0, a, b, c ∈R, have a common root, then a : b : c is: (1) 1 : 3 : 2 (2) 3 : 1 : 2 (3) 1 : 2 : 3 (4) 3 : 2 : 1 JEE Main 2013 (07 Apr) JEE Main Previous Year Paper (given z ≠−1)

Q63.A committee of 4 persons is to be formed from 2 ladies, 2 old men and 4 young men such that it includes at least 1 lady, at least 1 old man and at most 2 young men. Then the total number of ways in which this committee can be formed is : (1) 40 (2) 41 (3) 16 (4) 32 a1+a2+…+ap p3 a6 is equal to: = ; p ≠q . Then

Q63.The number of ways in which an examiner can assign 30 marks to 8 questions, giving not less than 2 marks to any question, is : (1) 30C7 (2) 21C8 (3) 21C7 (4) 30C8

Q63.If z is a complex number of unit modulus and argument θ, then arg ( 1+1+z−z ) can be equal to (1) θ (2) π −θ (3) −θ (4) π2 −θ

Q64.Given a sequence of 4 numbers, first three of which are in G.P. and the last three are in A.P. with common difference six. If first and last terms of this sequence are equal, then the last term is : (1) 16 (2) 8 (3) 4 (4) 2

Q64.Given sum of the first n terms of an A.P. is 2n+ 3n2 . Another A.P. is formed with the same first term and double of the common difference, the sum of n terms of the new A.P. is : JEE Main 2013 (22 Apr Online) JEE Main Previous Year Paper (1) n + 4n2 (2) 6n2 −n (3) n2 + 4n (4) 3n + 2n2

Q64.Let Tn be the number of all possible triangles formed by joining vertices of an n-sided regular polygon. If Tn+1 −Tn = 10 , then the value of n is : (1) 10 (2) 8 (3) 5 (4) 7

Q64.Let a1, a2, a3, … be an A.P, such that q3 a1+a2+a3+…+aq a21 (1) 41 (2) 31 11 121 (3) 11 (4) 121 41 1861

Q65. (1) 2925 (2) 1469 (3) 1728 (4) 1456

Q65.The sum 3 + 5 + 7 + … . upto 11-terms is: 12 12+22 12+22+32 (1) 7 (2) 11 2 4 (3) 11 (4) 60 2 11

Q65.If x, y, z are positive numbers in A. P. and tan−1 x, tan−1 y and tan−1 z are also in A. P., then which of the following is correct. (1) 6x = 3y = 2z (2) 6x = 4y = 3z (3) x = y = z (4) 2x = 3y = 6z

Q65.The sum of the series: 1 + 1+21 + 1+2+31 + … …. upto 10 terms, is: (1) 18 (2) 22 11 13 (3) 20 (4) 16 11 9 2 15