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$\int_c \frac{sin^6z}{(z-\frac{\pi}{6})^3}$ dz where c is the circle |z|=1
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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Expand f(z) = $\frac{1}{z^2(z-1)(z+2)}$ about z=0 for i)|z|<1 ii)1<|z|<2 iii)|z|>2
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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Show that $\int_c log z dz= 2 \pi i $ where c is the unit circle in z-plane.
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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Using cauchy residue theorem evaluate the following integral 1) $\int_0^{2\pi} \frac{d\theta}{5+3sin\theta}$ 2) $\int_{-\infty} ^\infty \frac {x^2}{(x^2+a^2)(x^2+b^2)}dx$ a>0,b>0
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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Obtain Taylor series and two distinct laurent series expansion of f(z)=$\frac{z-1}{z^2-2z-3}$ indicating the region of convergence.
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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Evaluate $\oint_c \frac{e^{2z}}{ (z+1)^4} dz$ where C is the circle |z-1|=3
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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Evaluate $\int_0^{1+i} z^2 dz$ along 1)the line y=x 2) the parabola x = $y^2$ is the line integral independant of the path p.
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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Calculate Rank correlation co-efficient for the following data \begin{array}{|c|c|c|c|} \hline X& 10 & 12 & 18&18&15&40 \\ \hline y& 12& 18&25&25&50&25 \\ \hline \end{array}
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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Calculate R(pearman's rank correlation) and r(karl-pearson's) from the following data. interpret our result.
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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In an examination marks obtained by students in maths ,physics and chemistry are normally distributed with mean 51,53,46 and with standard deviation 15,12,16 respctively find the probability of
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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Find the m.g.f.of a Random variable ,whose probability density function is , $p(X=x) = \begin{cases} (\frac{1}{2})^x, & \ x \ = 1,\ 2, \ 3... \\ 0, & elsewhere \end{cases}$ Hence find mean & variance.
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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The Number of accidents in a year attributed to taxi driver in a city follows poison distribution with mean 3.out of 1000 taxi drivers ,find approximately the number of drivers with
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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Let x be continous Random variable with probability distribution $p(X=x) = \begin{cases} \frac{x}{6}+k, \ if \ & 0 \leq x\leq3 \\ 0, & elsewhere \end{cases}$. evaluate K and find P(1$\le x\le 2)$
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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The marks obtained by 1000 students in an examination are found to be normally distributed with mean 70 and standard deviation 5.estimate the number of students whose marks will be between 60to70,>75
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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A transmission channel has a per digit error probability p=0.01.Calculate the probability of more than 1 error in 10 received digit using 1) Binomial 2) Poison Distribution
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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A random variable X has the following density function,, $f(x)=\{_{0,x<0}^ {2e^{-2x}, x>0}$ find the M.g.f.& hence its mean and variance..
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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A random variable X has the following probability mass distribution
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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$A=\begin{bmatrix} 1 & 0 & 0 \\ 1 & 0 & 1 \\ 0& 1 & 0 \end{bmatrix} find A^{50}$
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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Verify cayley-Verify cayley-hamilton Theorem and Find $A^{-1}$ for $A=\begin{bmatrix} 1 & 4 \\ 2 & 3 \\ \end{bmatrix}$ Hence Find $A^5-4A^4-7A^3+11A^2-A-10I$ in terms of A.
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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If $A=\begin{bmatrix} 2 & 4 \\ 0 & 3 \end{bmatrix}$ then find the eigen values of $6A^{-1}+A^3+2I$
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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S.T.$A=\begin{bmatrix} 4 & -2 & 2 \\ 6 & -3 & 4 \\ 3 & -2 & 3 \end{bmatrix}$ is derogatory find its Minimal polynomial.
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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Verify caylay hamilton theorem for matrix A and hence find $A^{-1}$ if it exists where $A=\begin{bmatrix} 0 &c & -b \\ -c & 0& a \\ b & -a & 0 \end{bmatrix}$
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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Show that the matrix A is diagonalizable. Also find the transforming matrix and the diagonal matrix where $A=\begin{bmatrix} 4 & 1 & -1 \\ 2 & 5 & -2 \\ 1 & 1 & 2 \end{bmatrix}$
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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891
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If $\lambda_1,\lambda_2...\lambda_n$ are eigen values of A then show that $\frac{1}{\Lambda_1} ,\frac{1}{\lambda_2}...$Are eigen values of $A^{-1}$
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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Show that the matrix $A = \begin{bmatrix} 7 & 4 & -1 \\ 4 & 7 & -1 \\ -4 & -4 & -4 \end{bmatrix}$ is derogatory
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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