a) -i/2, 2i b) 2i, -i/2 c) 2i, i/2 d) -2i, i/2
2) Fifth term of a GP is 2; then the product of its first 9 terms is
a) 256 b) 1024 c) 512 d) none
3) The number of numbers that can be formed using the digits 1,2,3,4,5(repetition of digits is not permissible) such that the ten's digit is greater than thousand's digits, is
a) 60 b) 45 c) 30 d) none
4) Total number of 4 digit odd numbers that can be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7 are
a) 216 b) 375 c) 720 d) 400
5) The number of diagonals of a polygon of 20 sides is
a) 150 b) 170 c) 125 d) 210
6) 10ⁿ + 3. 4ⁿ⁺² +5 is always divisible by (for all n ∈ N)
a) 7 b) 5 c) 17 d) 9
7) Six line segments of lengths 2, 3, 4, 5, 6, 7 units are given. The number of triangles that can be formed by these lines is
a) ⁶C₃ - 7 b) ⁶C₃ - 6 c) ⁶C₃ - 5 d) ⁶C₃ - 8
8) For all positive values of x and y the value of {(1+ x+ x²)(1+ y+ y²)/xy} is
a) > 9 b) < 9 c) ≤ 9 d) ≥ 9
9) The point of represented by the complex number (2- i) is rotated about origin through an angle of π/2 in clockwise direction. The new position of the point will be..
a) 1+ 2i b) - 1- 2i c) 2+ i d) - 1+ 2i
10) The value of 1³- 2³+3³-4³+.......+9³ is
a) - 425 b) 475 c) 425 d) -475
11) A point z moves in the argand plane such that |z - 3i| =2, then its locus is
a) y-axis b) straight line c) a circle d) none of these
12) The number of terms of the AP 3,7,11, 15,..... to be taken so that the sum is 406, is
a) 14 b) 16 c) 20 d) 24
13) a,b,c,d are all real numbers and (a²+ b²)d² - 2(a+ c)bd + (b²+ c²)= 0, then a, b, c are in
a) GP b) AP c) HP d) none
14) The coefficient of x⁶ in the expansion of (x²+ x - 1)⁴ is
a) -2 b) -4 c) 2 d) 4
15) How many 9 digit numbers can be formed using the digits 2,2,3,3,5,5,8,8,8 so that odd digits occupy even positions?
a) 240 b) 180 c) 120 d) 60
16) if a,b,c,d,e are in AP then the value of (a + b + 5c - 5d+e) in terms of a is
a) 5a b) 4a c) 3a d) 2a
17) If x+ 1/x =√3, then one value of x is
a) cos(π/3)+ i sin(π/3) b) cos(π/6)+ i sin(π/6) c) sin(π/6)+ i cos(π/6) d) cos(π/2)+ i sin(π/2)
18) Two variable x and y are related by y= 8+ 2x; if the S. D of x is 3, then the SD of y will be
a) 10 b) 14 c) 11 c) 6
19) If in the binomial expansion of (1+ x)ⁿ where n is a natural number, the coefficients of 5th, 6th and 7th terms are in AP , then n is equals to
a) 7 or 13 b) 7 or 15 c) 7 or 14 d) 18 or 14
20) if z and w are two non-zero 290 complex numbers such that |zw| =1 and arg z- arg w =π/2, then (conjugate of z)w is equals to
a) - i b) 1 c) - 1 d) i
21) Solution set of the inequation is |2/(x -4)| > 1 (x≠ 4) is
a) x∈ (2,6) b) x∈( 2,4)U (4,6) c) x ∈(4,6) d) x ∈( 2,4]
22) If the fifth term of a GP is x, then the product of its first nine terms is
a) x⁵ b) x⁷ c) x⁹ d) x¹⁰
23) Number of 6-digit numbers that can be formed with the digits of the number 112233 is
a) 30 b) 60 c) 90 d) 120
24) The first term and the common difference of an AP are a and d respectively. If m-th and n-th terms of this AP are 1/n and 1/m respectively, then the value of (a -b) is
a) 1/mn b) 0 c) 1 d) (m + n)/mn
25) 3rd term from the end in the expansion of (4x/5 - 5/2x)⁸ is
a) 4375/x⁴ b) - 4375/x⁴ c) 4325/x² d) - 4325/x²
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