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Sample Question Paper Quantitative 03

01. Let X be the set of integers {9, 15, 21, 27, ……375}. Y denotes a subset of X, such that the sum of no two elements of Y is 384. Find the maximum number of elements in Y
(a) 29 (b) 30 (c) 31 (d) 32
02. The digits of a three-digit number A are written in the reverse order to form another three digit number B. If B > A and B – A is perfectly divisible by 7, then which of the following is necessarily true ?
(a) 100 < A < 299 (b) 106 < A < 305 (c) 112 < A < 311 (d) 118 < A < 317
03. If a= 1 and an+1 – 3a+ 2 = 4n for every positive integer n, then a100 equals ?
(a) 399 – 200 (b) 399 + 200 (c) 3100 – 200 (d) 3100 + 200
04. The total number of integer pairs (x, y) satisfying the equation x + y = xy is/are
(a) 0 (b) 1 (c) 2 (d) None of these
05. What is the number of distinct triangles with integral values sides and perimeter as 14 ?
(a) 6 (b) 5 (c) 4 (d) 3
06. Sample_Question_paper_Solution_03Q_06
(a) 27/14 (b) 21/13 (c) 49/27 (d) 256/147
07. The number of common roots between the two equations x3 + 3x2 + 4x + 5 = 0,             x3 + 2x2 + 7x + 3 = 0
(a) 0 (b) 1 (c) 2 (d) 3
08. If both a and b belong to the set {1, 2, 3, 4} then the number of equations of the form  ax2 + bx + 1 = 0 having real roots is
(a) 10 (b) 7 (c) 6 (d) 12
09. In a Public Sector Unit (PSU), there are 45600 employees. When the PSU offered a Voluntary Retirement Scheme(VRS), 40% of the employees applied for the VRS. After scrutinizing, PSU has rejected 15% of the applications. But only 9120 employees took the retirement through the scheme. What percentage of the total number of employees did not take retirement even though their applications are not rejected ?
(a) 25% (b) 14% (c) 24% (d) 12.75%
10. If three-digit number is eleven times the two-digit number formed by using the hundred’s and the unit’s digit of the three-digit number respectively, in the ten’s and unit’s place of the two-digit number. If the difference between the digit in ten’s place and the digit in hundred’s place is 1, then what is the digit in the unit’s place ?
(a) 2 (b) 3 (c) 4 (d) 1

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