Practice Questions

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

Q63.Let w(Im w≠0) be a complex number. Then, the set of all complex numbers z satisfying the equation ¯w −wz = k(1 −z), for some real number k, is (1) {z : z ≠1} (2) {z : |z| = 1, z ≠1} ¯(3) {z : z = z} (4) {z : |z| = 1}

Q63.If z is a complex number such that |z| ≥2, then the minimum value of z + 12 : (1) Is strictly greater than 5 (2) Is strictly greater than 3 but less than 5 2 2 2 (3) Is equal to 5 (4) Lies in the interval (1, 2) 2

Q63.Two women and some men participated in a chess tournament in which every participant played two games with each of the other participants. If the number of games that the men played between them-selves exceeds the number of games that the men played with the women by 66 , then the number of men who participated in the tournament lies in the interval (1) (11, 13] (2) (14, 17) (3) [10, 12) (4) [8, 9]

Q63.An eight digit number divisible by 9 is to be formed using digits from 0 to 9 without repeating the digits. The number of ways in which this can be done is: (1) 72(7!) (2) 18(7!) (3) 40(7!) (4) 36(7!)

Q64.Let G be the geometric mean of two positive numbers a and b, and M be the arithmetic mean of 1a and 1b . If 1 : G is 4 : 5, then a : b can be: M JEE Main 2014 (12 Apr Online) JEE Main Previous Year Paper (1) 1 : 4 (2) 1 : 2 (3) 2 : 3 (4) 3 : 4

Q64.In a geometric progression, if the ratio of the sum of first 5 terms to the sum of their reciprocals is 49 , and the sum of the first and the third term is 35. Then the first term of this geometric progression is: (1) 7 (2) 21 (3) 28 (4) 42

Q64.Let f(n) = [ 13 + 1003n ]n, where [n] denotes the greatest integer less than or equal to n. Then ∑56n=1 f(n) is equal to (1) 56 (2) 1287 (3) 1399 (4) 689

Q64.The sum of the digits in the unit's place of all the 4 - digit numbers formed by using the numbers 3, 4, 5 and 6 , without repetition is : (1) 18 (2) 36 (3) 108 (4) 432

Q64.If (10)9 + 2(11)1(10)8 + 3(11)2(10)7 + ...... + 10(11)9 = k(10)9, then k is equal to : JEE Main 2014 (06 Apr) JEE Main Previous Year Paper (1) 100 (2) 110 (3) 121 (4) 441 10 100

Q65.Three positive numbers form an increasing G. P. If the middle term in this G. P. is doubled, the new numbers are in A. P. Then the common ratio of the G. P. is : (1) 2 −√3 (2) 2 + √3 (3) √2 + √3 (4) 3 + √2

Q65.The number of terms in an A. P. is even, the sum of the odd terms in it is 24 and that the even terms is 30. If the last term exceeds the first term by 10 12 , then the number of terms in the A. P. is (1) 4 (2) 8 (3) 16 (4) 12

Q65.Given an A.P. whose terms are all positive integers. The sum of its first nine terms is greater than 200 and less than 220. If the second term in it is 12 , then its 4th term is : (1) 8 (2) 24 (3) 20 (4) 16

Q65.The sum of the first 20 terms common between the series 3 + 7 + 11 + 15+ and 1 + 6 + 11+ 16 + … .. is (1) 4000 (2) 4020 (3) 4200 (4) 4220

Q65.The least positive integer n such that 1 −23 − 322 −… . − 3n−12 < 1001 , is: (1) 4 (2) 5 (3) 6 (4) 7

Q66.If 1 + x4 + x5 = ∑5i=0 ai (1 + xi), for all x in R, then a2 is: (1) −4 (2) 6 (3) −8 (4) 10 is expanded in the ascending powers of x and the coefficients of powers of x in two consecutive

Q66.The coefficient of x1012 in the expansion of (1 + xn + x253) 10, (where n≤22 is any positive integer), is (1) 253C4 (2) 10C4 (3) 4n (4) 1

Q66.If the coefficients of x3 and x4 in the expansion of (1 + ax + bx2)(1 −2x)18 in powers of x are both zero, then (a, b) is equal to (1) (14, 2723 ) (2) (16, 2723 ) (3) (16, 2513 ) (4) (14, 2513 )

Q66.If the sum 3 + 5 + 7 + .... .+ up to 20 terms is equal to 21k , then k is equal to 12 12+22 12+22+32 (1) 240 (2) 120 (3) 60 (4) 180

Q66.The coefficient of x50 in the binomial expansion of (1 + x)1000 + x(1 + x)999 + x2(1 + x)998 + … +x1000 is: (1) (1000)! (2) (1000)! (50)(!95φ! (49)(!95)! (3) (1001)! (4) (1001)! (51)(!95ϕ! (50)(!95)!

Q67.If (2 + x3 ) 55 terms of the expansion are equal, then these terms are: (1) 7th and 8th (2) 8th and 9th (3) 28th and 29th (4) 27th and 28th

Q67.If 2 cos θ + sin θ = 1 (θ ≠π2 ), then 7 cos θ + 6 sin θ is equal to: (1) 1 (2) 2 2 (3) 11 (4) 46 2 5

Q67.Let fk(x) = k1 (sink x + cosk x) where x ∈R and k≥1. Then f4(x) −f6(x) equals (1) 1 (2) 1 4 12 (3) 1 (4) 1 6 3

Q67.The number of terms in the expansion of (1 + x)101(1 −x + x2) 100 in powers of x is (1) 301 (2) 302 (3) 101 (4) 202

Q67.If a line L is perpendicular to the line 5x −y = 1, and the area of the triangle formed by the line L and the coordinate axes is 5 sq units, then the distance of the line L from the line x + 5y = 0 is (1) 7 units (2) 7 units √13 √5 (3) 5 units (4) 5 units √13 √7