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36. If f(t)=4 sin² 3t, then the Laplace Transform of f(t) is t (A) In +36 +36 (B) In (C) In (D) In +9 In (8²+9) d²x +4. dt² dt + 4x4 cosh2t is 37. The particular integral of the differential equation dx (A) e² +² e² 8 (B) -²²+ e-21 8 1 1 (C) fe²+ e-21 8 (D) e² + P² e21 38. A stationary value of a function f(x) is a value of x, where f(x) = 0. The number of distinct stationary val- ues of f(x) =8x-15x+10x², where f(x) has neither maximum nor minimum is. 39. The mean of a continuous random variable X with its probability density function f(x) given by f(x)= k(3+2x) ; 2≤x≤4 0 Is 83 (A) 27 91 (C) 27 ; otherwise 88 94 (D) 27 40. Which of the following statements is/are NOT TRUE? (I) The product of two symmetric matrices A and B is symmetric if and only ifAB-BA=0 (II) The product of two skew-symmetric matri- ces A and B is skew-symmetric if and only if AB+BA=0 (III) The eigenvectors corresponding to two distinct eigen values of a matrix are linearly independent

36. If f(t)=4 sin² 3t, then the Laplace Transform of f(t) is t (A) In +36 +36 (B) In (C) In (D) In +9 In (8²+9) d²x +4. dt² dt + 4x4 cosh2t is 37. The particular integral of the differential equation dx (A) e² +² e² 8 (B) -²²+ e-21 8 1 1 (C) fe²+ e-21 8 (D) e² + P² e21 38. A stationary value of a function f(x) is a value of x, where f(x) = 0. The number of distinct stationary val- ues of f(x) =8x-15x+10x², where f(x) has neither maximum nor minimum is. 39. The mean of a continuous random variable X with its probability density function f(x) given by f(x)= k(3+2x) ; 2≤x≤4 0 Is 83 (A) 27 91 (C) 27 ; otherwise 88 94 (D) 27 40. Which of the following statements is/are NOT TRUE? (I) The product of two symmetric matrices A and B is symmetric if and only ifAB-BA=0 (II) The product of two skew-symmetric matri- ces A and B is skew-symmetric if and only if AB+BA=0 (III) The eigenvectors corresponding to two distinct eigen values of a matrix are linearly independent

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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36. If f(t)=4 sin² 3t, then the Laplace Transform of f (t) t (A) In(136) 5² +36 S< (B) In (C) In In (1949) +9 37. The particular integral of the differential equation $² (D) In +9 S d²x dx +4. dt² dt + 4x4 cosh2t is (A) e² + f² e²² 8 (B) -²²+ e-21 8 1 (C) fe²+ e-21 8 (D) e² + f² e²² 38. A stationary value of a function f(x) is a value of x, where f(x)=0. The number of distinct stationary val- ues of f(x)=8x-15x+10x², where f(x) has neither maximum nor minimum is. 39. The mean of a continuous random variable X with its probability density function f(x) given by f(x)= k(3+2x) ; 2≤x≤4 0 Is 83 (A) 27 91 (C) 27° ; otherwise (B) (D) 8222 88 27 94 27 40. Which of the following statements is/are NOT TRUE? (I) The product of two symmetric matrices A and B is symmetric if and only ifAB-BA=0 (II) The product of two skew-symmetric matri- ces A and B is skew-symmetric if and only if AB+BA=0 (III) The eigenvectors corresponding to two distinct eigen values of a matrix are linearly independent
Transcribed Image Text:36. If f(t)=4 sin² 3t, then the Laplace Transform of f (t) t (A) In(136) 5² +36 S< (B) In (C) In In (1949) +9 37. The particular integral of the differential equation $² (D) In +9 S d²x dx +4. dt² dt + 4x4 cosh2t is (A) e² + f² e²² 8 (B) -²²+ e-21 8 1 (C) fe²+ e-21 8 (D) e² + f² e²² 38. A stationary value of a function f(x) is a value of x, where f(x)=0. The number of distinct stationary val- ues of f(x)=8x-15x+10x², where f(x) has neither maximum nor minimum is. 39. The mean of a continuous random variable X with its probability density function f(x) given by f(x)= k(3+2x) ; 2≤x≤4 0 Is 83 (A) 27 91 (C) 27° ; otherwise (B) (D) 8222 88 27 94 27 40. Which of the following statements is/are NOT TRUE? (I) The product of two symmetric matrices A and B is symmetric if and only ifAB-BA=0 (II) The product of two skew-symmetric matri- ces A and B is skew-symmetric if and only if AB+BA=0 (III) The eigenvectors corresponding to two distinct eigen values of a matrix are linearly independent
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