Practice Questions

Q52.Let α = −1+i√32 . If a = (1 + α) ∑100k=0 α2k and b = ∑100k=0 α3k , then a and b, are the roots of the quadratic equation. (1) x2 + 101x + 100 = 0 (2) x2 −102x + 101 = 0 (3) x2 −101x + 100 = 0 (4) x2 + 102x + 101 = 0

Q52.Let α and β be the roots of x2 −3x + p = 0 and γ and δ be the roots of x2 −6x + q = 0. If α, β, γ, δ from a geometric progression. Then ratio (2 q + p) : (2 q −p) is (1) 3 : 1 (2) 9 : 7 (3) 5 : 3 (4) 33 : 31

Q53.Let a1, a2, … , an be a given A.P. whose common difference is an integer and Sn = a1 + a2 + … + an . If a1 = 1, an = 300 and 15 ≤n ≤50, then the ordered pair (Sn−4, an−4) is equal to: (1) (2490, 249) (2) (2480, 249) (3) (2480, 248) (4) (2490, 248)

Q53.If the 10th , term of an A.P. is 201 , and its 20th , term is 101 , then the sum of its first 200 , terms is. (1) 50 (2) 50 14 (3) 100 (4) 100 12

Q53.Total number of 6− digit numbers in which only and all the five digits 1, 3, 5, 7 and 9 appears, is (1) 1 2 (6!) (2) 6! (3) 56 (4) 25 (6!)

Q53.There are 3 sections in a question paper and each section contains 5 questions. A candidate has to answer a total of 5 questions, choosing at least one question from each section. Then the number of ways, in which the candidate can choose the questions, is: (1) 3000 (2) 1500 (3) 2255 (4) 2250

Q53.If 210 + 29 ⋅31 + 28 ⋅32 + … … + 2 ⋅39 + 310 = S −211 , then S is equal to (1) 311 −212 (2) 311 (3) 3112 + 210 (4) 2. 311

Q53.The sum of the first three terms of G. P is S and their products is 27 . Then all such S lie in (1) (−∞, −9] ∪[3, ∞) (2) [−3, ∞) (3) (−∞, −3] ∪[9, ∞) (4) (−∞, 9]

Q53.Two families with three members each and one family with four members are to be seated in a row. In how many ways can they be seated so that the same family members are not separated ? (1) 2! 3! 4! (2) (3!)3 ⋅(4!) (3) (3!)2. (4!) (4) 3! (4!)3

Q53.If the number of five digit numbers with distinct digits and 2 at the 10th place is 336k , then k is equal to: (1) 4 (2) 6 (3) 7 (4) 8

Q53.If the sum of the series 20 + 19 35 + 19 51 + 18 54 +. . . . . . . . . . up to nth term is 488 and the nth term is negative, then : (1) nth term is −4 52 (2) n = 41 (3) nth term is −4 (4) n = 60 k, then 18k is equal to:

Q53.If the first term of an A. P. is 3 and the sum of its first 25 terms is equal to the sum of its next 15 terms, then the common difference of this A. P.is (1) 1 (2) 1 6 5 (3) 1 (4) 1 4 7

Q53.Let a1, a2, a3, … , be a G. P. such that a1 < 0, a1 + a2 = 4 and a3 + a4 = 16. If ∑9i=1 ai = 4λ, then λ, is equal to. (1) −513 (2) −171 (3) 171 (4) 5113

Q53.The common difference of the A. P. b1, b2, . . . . , bm is 2 more than common difference of A. P. a1, a2, . . . . . , an . If a40 = −159, a100 = −399 and b100 = a70 , then b1 is equal to : (1) 81 (2) −127 (3) −81 (4) 127 is 405 , then |k| equals :

Q53.If a, b and c are the greatest values of 19Cp, 20Cq and 21Cr respectively, then: (1) 11 a = 22b = 21c (2) 10a = 11b = 21c (3) 11 a = 22b = 42c (4) 10a = 11b = 42c

Q53.If z is a complex number satisfying |Re(z)| + |Im(z)| = 4, then |z| cannot be (1) √172 (2) √10 (3) √7 (4) √8

Q53.Let n > 2 be an integer. Suppose that there are n Metro stations in a city located around a circular path. Each pair of the nearest stations is connected by a straight track only. Further, each pair of the nearest station is connected by blue line, whereas all remaining pairs of stations are connected by red line. If number of red lines is 99 times the number of blue lines, then the value of n is (1) 201 (2) 200 (3) 101 (4) 199

Q54.If the sum of first 11 terms of an A.P. , a1, a2, a3 … … is 0(a1 ≠0) then the sum of the A.P a1, a3, a5, … . . a23 is ka1 where k is equal to (1) −12110 (2) 12110 (3) 725 (4) −725

Q54.If 1 + (1 −22 ⋅1) + (1 −42 ⋅3) + (1 −62 ⋅5) + … … + (1 −202 ⋅19) = α −220 β , then an ordered pair (α, β) is equal to: (1) (10, 97) (2) (11, 103) (3) (10, 103) (4) (11, 97)

Q54.Let two points be A(1, −1) and B(0, 2). If a point P(x', y') be such that the area of ΔPAB = 5 sq. units and it lies on the line 3x + y −4λ = 0, then a value of λ is (1) 4 (2) 3 (3) 1 (4) −3

Q54.The product 2 41 ∙4 161 ∙8 481 ∙16 1 128 ∙. . . . to ∞ is equal to: (1) 2 21 (2) 2 41 (3) 1 (4) 2

Q54.If the sum of the second, third and fourth terms of a positive term G.P. is 3 and the sum of its sixth, seventh and eighth terms is 243 , then the sum of the first 50 terms of this G.P. is : (1) 26 1 (349 −1) (2) 261 (350 −1) (3) 13 2 (350 −1) (4) 131 (350 −1)

Q54.If the term independent of x in the expansion of ( 23 x2 − 3x1 )9 is (1) 11 (2) 5 (3) 9 (4) 7

Q54.If the sum of the first 40 terms of the series, 3 + 4 + 8 + 9 + 13 + 14 + 18 + 19+. . . . is (102)m, then m is equal to (1) 20 (2) 25 (3) 5 (4) 10

Q54.Five numbers are in A. P. , whose sum is 25 and product is 2520. If one of these five numbers is −12 , then the greatest number amongst them is (1) 27 (2) 7 (3) 21 (4) 16 2