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Engineering Mathematics

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Evaluate $\int\int\int x^2 \ y \ z \ dx \ dy \ dz$ over the volume bounded by the planes x = 0, y = 0, z = 0 and $\frac{x}{a} + \frac{y}{b} + \frac{z}{c} = 1$
engineering mathematics updated 4.9 years ago by teamques10 ★ 69k
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Using Gauss divergence theorem evaluate $\int\limits_{C}\bar{F} \cdot \overline{ds}$ where $F = 2x^2yi - y^2j + 4xz^2k$ and S is the region bounded by $y^2 + z^2 = 9$ and x = 2 in the first octant.
engineering mathematics updated 4.9 years ago by teamques10 ★ 69k
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Jacobians : If $ u = \frac{x+y}{1-xy} , \; v \; = \; tan^{-1}x \; + \; tan^{-1}y , \; Find \frac{\partial (u,v)}{\partial (x,y)} $
engineering mathematics updated 4.9 years ago by teamques10 ★ 69k
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Change to polar co-ordinates and evaluate $\int_{0}^{2}\int_{0}^{\sqrt{2x-x^2}}\frac{x\,dy\,dx}{\sqrt{x^2+y^2}}$ .
engineering mathematics updated 4.9 years ago by teamques10 ★ 69k
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Define Solenoidal vector. Hence prove that $\bar{F} = \frac{\bar{a} \times \bar{r}}{r^n}$ is a solenoidal vector.
engineering mathematics updated 4.9 years ago by teamques10 ★ 69k
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Using Taylor's series method, obtain the solution of the differential equation $\frac{dy}{dx}=3x+y^2$ with $x_0=0,\,y_0=0$ at $x=0.1$ correct to four decimal places.
engineering mathematics updated 4.9 years ago by teamques10 ★ 69k
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Find the constants a,b,c so that $\bar{F} = (x + 2y + az)\hat{i} + (bx - 3y - z)\hat{j} + (4x + cy + 2z)\hat{k}$ is irrotational
engineering mathematics updated 4.9 years ago by teamques10 ★ 69k
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Find the Fourier series expansion for $f(x) = \sqrt{1 - cosx}$ in $(0, 2\pi)$, Hence deduce that $\frac{1}{2} = \sum\frac{1}{4n^2 - 1}$
engineering mathematics updated 5.5 years ago by teamques10 ★ 69k
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Find half range sine series for $f(x) = \pi x - x^2$ is $(0, \pi)$ Hence deduce that $\frac{\pi^3}{32} = 1 - \frac{1}{3^3} + \frac{1}{5^3} - \frac{1}{7^3}$
engineering mathematics updated 5.5 years ago by teamques10 ★ 69k
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Find half range cosine series of $f(x) = sinx$ in $(0, \pi)$ Hence deduce that $\frac{1}{1.3} + \frac{1}{3.5} + \frac{1}{5.7} +..... = \frac{1}{2}$
engineering mathematics updated 5.5 years ago by teamques10 ★ 69k
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Find smallest positive integer moduls 5 to which
engineering mathematics updated 5.0 years ago by prashantsaini • 0
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$\oint \frac{e^{2z}}{(Z+1)^4}dz$ where c is the circle |z-1|=3.
engineering mathematics updated 3.3 years ago by teamques10 ★ 69k
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Solve the system of linear equation by Crout's method x - y + 2z = 2; 3x + 2y - 3z = 2; 4x - 4y + 2z = 2
engineering mathematics updated 3.8 years ago by teamques10 ★ 69k
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Solve by Crout's Method the system of equaition 2x+3y+z=-1, 5x+y+z=9, 3x+2y+4z=11
engineering mathematics updated 3.8 years ago by teamques10 ★ 69k
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Solve by crouts methods the system of equations 3x+2y+7z=4 2x+3y+z=5 3x+4y+z=7.
engineering mathematics updated 3.8 years ago by teamques10 ★ 69k
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Apply Crout's method to solve \[ \left\{\begin{matrix} x-y + 2z=2 \ \ \\ 3x+2y-3z=2 \\ 4x -4y+2z=2 \end{matrix}\right. \]
engineering mathematics updated 3.8 years ago by teamques10 ★ 69k
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i. Draw a complete graph of 5 vertices.
engineering mathematics updated 5.0 years ago by prashantsaini • 0
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Given L= {1,2,4,5,10,20} with divisibility relation.
engineering mathematics updated 5.0 years ago by prashantsaini • 0
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Solvle x = 1(mod3), x=2(mod 5) and x = 3(mod7)
engineering mathematics updated 4.9 years ago by sanketshingote • 100
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Find the Jacob's symbol of
engineering mathematics updated 4.9 years ago by sanketshingote • 100
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i. Find inverse of
engineering mathematics updated 5.0 years ago by prashantsaini • 0
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It was found that the burning life of electric bulbs of a particular brand was normally distributed
engineering mathematics updated 5.0 years ago by prashantsaini • 0
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Derive the MGF of binomial distribution and hence finds it's mean and variance.
engineering mathematics updated 5.0 years ago by prashantsaini • 0
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i) The average marks scored by 32 boys is 72 with standard deviation of 8 while that for 36 girls is 70 with standard deviation of 6. Test at 5% los whether the boys perform better than the girls.
engineering mathematics updated 5.0 years ago by prashantsaini • 0
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Find the characteristic equation of the matrix A given below and hence ,find the matrix represented by $A^8-5A^7+7A^6-3A^5+A^4-5A^3+8A^2-2A+I$
engineering mathematics updated 6.9 years ago by teamques10 ★ 69k
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