#1
18th December 2014, 01:15 PM
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Allahabad University MSc Entrance Exam Maths Question Paper
I want to get the MSc Entrance Exam Maths Question Paper of Allahabad university will you please provide me that ?
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#2
19th December 2014, 08:48 AM
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Re: Allahabad University MSc Entrance Exam Maths Question Paper
As you want to get MSc Entrance Exam Maths Question Paper of Allahabad university so here I am giving you some questions of that paper: 1. If a, B and,? are the roots of 13 + asz +bt * c: 0 then the value of. a2 + 02 + l2 is tAl a2 - 2b. tBl b2 - 2c. tcl c2 + 2a. tDl b2 + 2c. 2. Let / : IR -+ lR and f (r) : l, - 1l + lr * 21. Let,s1 : {r l / is continuous at r} and 52: {c | / is differentiable at r}. Then tA] Sr : lR, Sz : lR. [B] & : In, Sz : R' \ {1,2}. [C] Sr:lR\{1,2}, Sz:lR' [D] Sr:R,\{1,2}, Sz:lR\{1,2}' 3. Consider the following statements 51: If / is Riemann integrable in [0,1] then /2 is Riemann integrable in [0,1]. ^92: If /2 is Riemann integrable in [0,1] then / is Riemann integrable in [0,1]. Then tA] ,5r is true but ^92 is false. tB] 51 is false but ,92 is true. tC] both,Sr and ,Sz are false. tD], both & and ,52 are true. 4. The tunction /(t) : sin(r) * cos(r) is [A] increasing in l0,rl2l. [B] decreasing in l},nl2l. [C] increasing in l},nlal and decreasing in ltrla,nl2l' [D] decreasing in l},nl4 and increasing in lnla,rl2l. 5. Let Gr and Gzbetwo finite groups with lGrl : 100 and lG2l :25.If f : Gt - Gz is a surjective group homomorphism, then tAl lKer(f)l:2. [B] lKer(f)l: a. tcl lKer(/)l :5. tDl lKer(f)l :10' 6. Let {p"} be a strictly increasing sequence of prime numbers and let r,,-1)e"*'(t* 1)tn* ' tAl ;j8"" : -112. tBl j*", - -1. tcl j$r,,: 1. [D] ,,!gr" does not exist. 7. Let V be avector space of dimension n and {rr,ur,... ,?r,} be a basis of V. Let o € Sn and ? :V *--*+V be a linear transformation definedby T(u6): uoe).Then lA] 7 is nilpotent. tB] ? is one-one but not onto. lC] T is onto but not one-one. tD] ? is an isomorphism. 8. Let G be agroup and a € G be aunique element of order n where n) 7. Let Z(G) denote the center of the group G. Then lAl o(G) : n. tBl o(z(G)) > 1. tcl z(G) :6. tDl G : Sz. oo 9. If the series | (sinr)" converges to the value (4 + 2\/3) for some value of r in (0,r12),then"t:fe value of r is tAl rl3. tBl rl4. ICI rl5. tDl rl1. 10. If rn and M arcrespectively the greatest lower bound and the least upper bound of the ser s: { Tl:. " > o} tr,"n lr*2' ) lAl m€S, IvI#5. tBl rn#S,M#5. tcl rn4S,MeS. [D] m€S,MeS. 11. The value "f lTe (cosr;(1/'i"'") is [A] exp(-l). IBI exp(l). tCl exp(-1l2). [D] exp(1/2). 12. The graphs of the real valued functions f (r):2log(r) and 9(r) : log(2r) [A] do not intersect. tBl intersect at one point only. tC] intersect at two points. tD] intersect at more than two points. 13. The points of continuity of the function / : R. -+ IR defined by r/_-\ f lr' - tl, if r is irrational J(t/ : t o, if s is rational are tA] tr:-L,tr:A,r:1. iB] n:-I,r:1. lcl r: -7, r:0. tD] ,r:0, r: t. 14. The smallest positive integer n such that 5n - 1 is divisible by 36 is lAl 2. tBl 3. [c] 5. tDl 6. 15. Let f(r) : r5 + a1r4 * a2n7 * a3r2. Suppose /(-1) ) 0 and /(l) < 0 then lA] / has at least 3 real roots. tB] / has at most 3 real roots. lC] / has at most 1 real root. tDl all roots of / are real. 16. Let {u,u} be a linearly independent subset of a real vector space V. Then which of the following is not a linearly independent set? [A] {r, u * u}. [B] {u + t/1u,, - ,/zr}. tcl {a,2u - ul2}. iDl {2u + u, -4u - 2u}. L7. Let V be avector space of 2x2 realmatrices. Let A: I t ' I ,n.r, the dimension L 1 -1 I of the subspace spanned by {4, A', A',Aa} is lAl 2. [B] 3. [c] 4. [D] 5. 18. Let A € MB(Q). Consider the statements P: Matrix A is nilpotent. Q: A3 :0. Pick up true statements from the following. iAl P+Q. tBl Q+PandP+A. [C] P # Q andQ + P. tDl None of [A], [B], [C] is true. 19. Consider the statements & : 1- 1+ 1 - 1+ 1* 1+...: *1. Sz, #- 1 - 2 +22 - 23 +.... Then tA] ,S1 is true but ,Sz is false. iB] s1 is false but ^g2 is true. lC] both ^9r and ,s2 are true. IDI both s1 and ^gz are false. 20. Let ts I n1 tA] there exists a unique continuous function / such that F'(r : y5 for alI i. tB] there exists a unique differentiabie function / such that F(r : gi for all e. IC] there exists a unique n times differentiable function / such tltat F(r6) : y6 for all i. lD] there exists a unique polynomial function / of degree n such that F(r1) : yi for all i. 21. Solution of the differential equation g" - n (y,)' :0, subject to the boundary condi_ tions g(0) :0, g'(0): -1 is r:, ./ r \ tA] a : | --7 6n-t 16,)* b, where a and b are arbitrary constants. tBl y: -t/it*,-' (fr) lt ,/ r \ tc] y : \f l tan-' \d * b, where a and b are arbitrary constants. tDl a: -iran-l (Jr") 22. Let V be the vector space of all continuous functions on lR. over the field IR. Let S : {lsl, l" - 11, lx - Zli. tA] ,9 is linearly independent and does not span V. lB] ,9 is linearly independent and spans V. tC] ,S is linearly dependent and does not span V. tD] ,S is linearly dependent and spans I,/. 23. 10 red balls (all alike) and 10 blue balls (all alike) are to be arranged in a row. If every arrangement is equally likely, then the probability that the balls at two ends of the arrangement are of the same colour is tAl eaual to ]. iBl eoual to |. tcl less than ] IDI greater than ;. 24. 3 studeuts are to be selected to forrn a cornmittee from a class of 100 students. The chances that the tallest student is one among them is lAj less than 5%. tBl 6 to 10%. tcl r5Yo. tDl 50%. 25. Let f-be a smooth vector valued function of a real variable. Consider the two statements 51 : div curl/: g. ,91 : grad div /:0. Then lA] both Sr and ,92 are true. tC] ,91 is true but 52 is false, |
#3
8th January 2016, 08:58 AM
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Re: Allahabad University MSc Entrance Exam Maths Question Paper
Hello sir I want to know about Allahabad University MSc Entrance Exam Maths Question Paper so here can you please give me details ?
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#4
8th January 2016, 09:03 AM
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Re: Allahabad University MSc Entrance Exam Maths Question Paper
Hey as The University of Allahabad, informally known as Allahabad University, is a public central university located in Allahabad, Uttar Pradesh, India. Established on September 23, 1887, Paper Pattern: There are a maximum of two parts of the M.Sc (Math/Applied Math) Exam Papers A and B respectively. The first part consists of 25 questions and all the questions are compulsory for every student. Each question is of 1 mark and each wrong answer gets -1/4 marks deducted. The 2nd part consists of 15 questions and candidates are asked to attempt as much question as they can answer the maximum marks one can score is 75 from this section. Each question is of 5 marks Here I am attaching PDF for Allahabad University MSc Entrance Exam Maths Question Paper Allahabad University MSc Entrance Exam Maths Question Paper Address: University Of Allahabad Senate House Campus, University Road, Old Katra, Allahabad, Uttar Pradesh 211002 Phone: 0532 246 1083 Last edited by sumit; 25th December 2019 at 03:48 PM. |
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