LBS Centre for Science & Technology State Eligibility Test Mathematics Question Paper : lbscentre.info

Name of the Organisation : LBS Centre for Science & Technology
Exam : State Eligibility Test
Subject : Mathematics
Year : 2017 Feb
Document Type : Model & Past Question Papers

Website : https://lbscentre.in/
Mathematics 2010 : https://www.pdfquestion.in/uploads/13420-Maths2010..pdf
Mathematics 2011 : https://www.pdfquestion.in/uploads/13420-Maths2011.pdf
Mathematics 2013 : https://www.pdfquestion.in/uploads/13420-Maths2013.pdf
Mathematics 2013-Jun :  https://www.pdfquestion.in/uploads/13420-Maths2015.pdf
Mathematics 2015-Jun : https://www.pdfquestion.in/uploads/13420-Maths2015.pdf

State Eligibility Test Mathematics Question Paper :

Time : 120 Minutes

Related : LBS Centre for Science & Technology State Eligibility Test Islamic History Question Paper : www.pdfquestion.in/13417.html

1. The maximum value of jzj when z satises the condition jz+ 1zj = 4 is
A) 2 – 5
B) 2 + 5
C) 4 – 5
D) 4 + 5

2. If 1; !1; !2; : : : !9 are the 10th roots of unity, then (1 + !1)(1 + !2) (1 + !9) is
A) 0
B) 1
C) -1
D) 9

3. If x is a real number, then (x-1)2 +(x-2)2 + +(x?-00)2 is least when x is
A) 50
B) 100
C) 101
D) 101

4. The sum 100C0 + 101C1 + 102C2 + + 150C50 is
A) 200C100
B) 201C50
C) 201C100
D) 151C50

5. For what value of Y will the equation yx2-10xy+12y2+5x-16y+3 = 0 represent a pair of straight lines
A) 4
B) 2
C) -2
D) 3

6. The spheres x2+y2+z2 = 25 and x2+y2+z2+24x-40y+225=0
A) touch internally
B) touch externally
C) do not touch each other
D) intersect each other

7. cos 2x + a sin x = 2a ?? 7 possesses a solution for
A) all a
B) a > 6
C) a < 2
D) a 2 [2; 6]

8. The lowest degree of the polynomial with real coecients having roots 2;-3; 2 + i; 1 + i is
A) 2
B) 4
C) 6
D) 8

9. If f(x) = 2x + 2x+1 + + 2x+9 then f0(2) is
A) 1023 loge 16
B) 1023 loge 8
C) 1023 loge 4
D) 1023 loge 2

10. Which of the following groups is cyclic
A) Z6 + Z8
B) Z3 + Z16
C) Z4 + Z12
D) Z2 + Z24

11. The curve represented by the equation Re ( z 2) = C, where C >0 is a
A) Circle
B) Ellipse
C) Parabola
D) Hyperbola

12. Which one of the following is true for the system 2x + 3y = 1?
A) The system is non-consistent
B) The system is consistent and has a unique solution
C) The system is consistent and has two solutions
D) The system is consistent and has infinite number of solutions

13. If the circle x2 + y2 + 2gy + c = 0 contains the point (g, o), then
A) c = 0
B) c < 0
C) c > 0
D) c = g/2

14. If the two circles x2 + y2 + 8x – 6y + 4 = 0 and x2 + y2 + 10x + c (y + 1) = 0 cut orthogonally, then the value of c is
A) 9
B) 8
C) 10
D) 5

15. If e is the eccentricity of the hyperbola conjugate to the hyperbola 9×2 – 16y2 + 72x – 32y – 16 = 0, then e is
A) 3/5
B) 4/5
C) 5/3
D) 5/4

16. The number of mappings which are not onto on a set A = {1, 2, 3, 4} is
A) 256
B) 232
C) 16
D) 24

17. Let E be a subset of R and let m* denote the Lebesque outer measure. Then which of the following statements is not true?
A) m*(E) = 0, if E is countable
B) If m*(E) = 0, then E is countable
C) m*(E) = 1, if E = [0, 1]
D) If m*(E) = 0, then E is measurable

18. The number of fixed points of the Mobius-transformation S(z) = az + b, a ? 0 is
A) 2
B) 1
C) 0
D) 3

19. The value of the cross ratio (0, 1, i, -1) is
A) 1
B) i
C) 1 – i
D) 1 + i

20. Consider the harmonic function U (x, y) = (x cos y – y sin y) ex, where x + iy+C. Its harmonic conjugate V(x, y) is given by
A) ( – y cos y + x sin y ) ex
B) ( y cos y – x sin y ) ex
C) ( -y cos y – x sin y ) ex
D) ( y cos y + x sin y ) ex

21. Let f be a function analytic on a region G. Suppose there exists a point z0 in G such that f(n)(z0) = 0 for n = 1, 2, 3, — . Then which of the following statements is not necessarily true?
A) f = 0 in G
B) f ‘ = 0 in G
C) f attains its maximum on G
D) f is a constant on G

22. Which of the following is a zero divisor in the ring Z15?
A) 2
B) 4
C) 6
D) 8

23. Which of the following is an irreducible polynomial in Z3[x]?
A) x3 + 2
B) x3 + 2x + 1
C) x3 + 2×2 + 2
D) 2×3 + 2x + 1

24. Let F be the splitting field of (x – 1) (x2 – 2) over Q. Then [ F : Q ] is
A) 1
B) 2
C) 3
D) 6

25. Which of the following is not the order of a finite field?
A) 3
B) 5
C) 15
D) 25