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10
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Verify Green's theorem for $\oint(3x^2 - 8y^2)dx + (4y - 6xy)dy$ where c is boundary of the region defined by x = 0, y = 0 & x+ y = 1
engineering mathematics updated 3 months ago by vikaskandunoori173 • 30
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If \[ \ \tanh x=\dfrac {2}{3} \]. Find the value of x and then cosh 2x.
engineering mathematics updated 5 months ago by sagarkolekar ★ 10k
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Obtain the equation of the line of regression of cost on age from the following table giving the age of a car of certain make and the annual maintenance cost.
engineering mathematics updated 6 months ago by sagarkolekar ★ 10k
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In a distribution exactly normal 7% of items are under 35 and 89% of the items are under 63. Find the probability that an item selected at random lies between 45 & 56.
engineering mathematics updated 6 months ago by sagarkolekar ★ 10k
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A continuous random variable has probability density function $f(x) = 6(x - x)^2, 0\leq x\leq i,$ Find (i) mean (ii) variance.
engineering mathematics updated 6 months ago by sagarkolekar ★ 10k
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For special security in a certain protected area, it was decided to put three lighting bulbs on each pole. If each bulb has a probability p of burning out in the first 100 hours of service,
engineering mathematics updated 6 months ago by sagarkolekar ★ 10k
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It is given that the means of x and y are 5 and 10. If the line of regression of y on x is parallel to the line $20y = 9x + 40,$ estimate the value of y for $x = 30. $
engineering mathematics updated 6 months ago by sagarkolekar ★ 10k
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Average mark 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 1% LoS whether the boys perform better than the girls.
engineering mathematics updated 6 months ago by sagarkolekar ★ 10k
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The means of two random samples of size 9 and 7 are 196.42 and 198.82 respectively. The sums of the squares of the deviation from the means are $26.94$ and $18.73$ respectively.
engineering mathematics updated 6 months ago by sagarkolekar ★ 10k
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State true or false with justification : If the two line of regression are $x + 3y - 5 = 0$ and $4x + 3y - 8 = 0$ then the correlation coefficient is $+0.5.$
engineering mathematics updated 6 months ago by sagarkolekar ★ 10k
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Using Cauchy's integral formula, evaluate $\int\dfrac {(12z-7)}{(z-1)^2(2z+3)}$ where $C:|z+1|=\sqrt3$
engineering mathematics updated 6 months ago by sagarkolekar ★ 10k
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Evaluate $\int(\overline z + 2z)dz$ along the circle $x^2+y^2 = 1.$
engineering mathematics updated 6 months ago by sagarkolekar ★ 10k
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Explain in detail a. The Multistage Algorithm b. The multihash Algorithm
engineering mathematics updated 6 months ago by sagarkolekar ★ 10k
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A box contains 6 white balls and 5 red balls. in how many ways 4 balls can be drawn from the box if 1. They are to be any color 2. All the balls to be of same color.
engineering mathematics updated 6 months ago by yashbeer ★ 11k
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If $A = \begin{bmatrix} \ 2 & 2 & 1 \\ \ 1 & 3 & 1 \\ \ 1& 2 & 2 \\ \end{bmatrix}$ , find the eigen values & eigen vectors of $A^3 +I$ .
engineering mathematics updated 6 months ago by sagarkolekar ★ 10k
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A continuous random variable X has the p.d.f f(x) = kx$^2$e$^{-x}$ ; x $\geq$ 0 . Find k , mean & variance .
engineering mathematics updated 7 months ago by sagarkolekar ★ 10k
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If the vector field $\overline{F}$ is irrotational, find the constant a,b,c where $\overline{F} = (x + 2y + az)i + (bx - 3y -z)j + (4x + cy + 2z)k$. Also show the following.
engineering mathematics updated 7 months ago by sagarkolekar ★ 10k
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The means of two samples of sizes 1000 and 2000 respectively are 67.50 and 68.0 inches. Can the samples b regarded as drawn from the same population of S. D. 2.5 inches?
engineering mathematics updated 7 months ago by sagarkolekar ★ 10k
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A certain injection administered to 12 patients resulted in the following changes of blood pressure: 5, 2, 8, -1, 3, 0, 6, -2, 1, 5, 0, 4. Also check the following.
engineering mathematics updated 10 months ago by sagarkolekar ★ 10k
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Find fourier series for $f(x) =\dfrac {3x^2 6\pi x + 2\pi^2}{12}, (0,2\pi) $ Hence deduce that $\dfrac 1{1^2}+\dfrac 1{2^2}+\dfrac 1{3^2} + --- =\dfrac {\pi^2}6$
engineering mathematics updated 11 months ago by sagarkolekar ★ 10k
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The pyramid defined by the coordinates A(0,0,0), B(1,0,0), C(0,1,0) and D(0,0,1) is rotated $45^o$ about the line L that has the direction V = J + K and passing through point C(0,1,0).
engineering mathematics updated 12 months ago by pedsangini276 • 4.7k
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Given the three points $P_{1}=(10,-8,3), P_{2}=(8,-4,3.2)$ and $P_{3}=(8,4,3.2),$ Derive the equation of the triangle defined by them.
engineering mathematics updated 13 months ago by pedsangini276 • 4.7k
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The voltage in an electric circuit are related by following equations : $V_{1}+V_{2}+V_{3}= 9;V_{1}-V_{2}+V_{3} = 1find V_{1},V_{2} and V_{3} by using cramer's rule.$
engineering mathematics updated 13 months ago by pedsangini276 • 4.7k
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1] Closure Axiom. 2] Associative prop. 3] Identity element property. 4] Inverse element property.
engineering mathematics updated 13 months ago by pedsangini276 • 4.7k
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$ \text { Find the Fourier series of }f(x)=x \text { in the interval }(0,2 \pi) \text {. } $
engineering mathematics updated 13 months ago by prajapatijaimin • 2.9k
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