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1. The integrating factor of the DE 2 coshx cosy dx = sinhx siny dy is (a) sinhx (b) coshx (c) tanhx (d) cothx 2. Which of the following is false? (a) The topological space that are finite are always connected (b) The set of real numbers R with usual topology is not compact (c) The diameter of is always same as the diameter of A, where A R (d) There exist topological space with countably many points that have uncountably many open set 3. Let f(x) = |x|, for -1 ≤ x ≤ 2 and the partition of P = ( -1, -1/2, 0, 1/2, 1, 3/2, 2 ) then the value of L(f,p)= (a) 7/4 (b) 13/4 (c) 9/4 (d) 10/4 4. Find the functions that are not uniformly continuous on (0,1) (a) 1/ x^2 (b) x^2 (c) sinx (d) sinx/x 5. Let the bounded set S contains a sequence Sn of real numbers such that liminf Sn ≠ limsup Sn then which one of the following options is false? (a) The limit of the sequence Sn does not exist (b) The sequence Sn is not Cauchy (c) There exists an infinite number of domainant terms for Sn (d) There exists a convergent subsequence 6. Which of the following are Lebesgve integrable functions on [0,1]? (i) (x ln x)/(1+x^2) (ii) (sinΠx)/ln x (iii) ln (x) [ln (1-x)] (iv) lnx/√(1-x^2) (a) Both (i),(ii) (b) All (i),(ii) and (iv) (c) All (ii),(iii) and (iv) (d) All (i),(ii),(iii) and (iv)

1. The integrating factor of the DE 2 coshx cosy dx = sinhx siny dy is (a) sinhx (b) coshx (c) tanhx (d) cothx 2. Which of the following is false? (a) The topological space that are finite are always connected (b) The set of real numbers R with usual topology is not compact (c) The diameter of is always same as the diameter of A, where A R (d) There exist topological space with countably many points that have uncountably many open set
 
3. Let f(x) = |x|, for -1 ≤ x ≤ 2 and the partition of P = ( -1, -1/2, 0, 1/2, 1, 3/2, 2 ) then the value of L(f,p)= (a) 7/4 (b) 13/4 (c) 9/4 (d) 10/4 4. Find the functions that are not uniformly continuous on (0,1) (a) 1/ x^2 (b) x^2 (c) sinx (d) sinx/x 5. Let the bounded set S contains a sequence Sn of real numbers such that liminf Sn ≠ limsup Sn then which one of the following options is false? (a) The limit of the sequence Sn does not exist (b) The sequence Sn is not Cauchy (c) There exists an infinite number of domainant terms for Sn (d) There exists a convergent subsequence 6. Which of the following are Lebesgve integrable functions on [0,1]? (i) (x ln x)/(1+x^2) (ii) (sinΠx)/ln x (iii) ln (x) [ln (1-x)] (iv) lnx/√(1-x^2) (a) Both (i),(ii) (b) All (i),(ii) and (iv) (c) All (ii),(iii) and (iv) (d) All (i),(ii),(iii) and (iv)

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Grade:12th pass

1 Answers

Anish Singhal
askIITians Faculty 1192 Points
5 years ago
For 8thone answer will be option d as set A not is all real numbers and set A is null set.
and ask one question in one thread only.

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