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Verify Cayley-Hamilton theorem for following matrix and also find the following
engineering mathematics updated 23 months ago by sagarkolekar ★ 11k
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Evaluate $\int \frac{sin\pi z^2 + cos\pi z^2}{(z - 1)(z - 2)}dz$, where c is the circle $|z| = 3$
engineering mathematics updated 2.3 years ago by vikashkashu563 • 30
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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 2.8 years 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 2.9 years ago by sagarkolekar ★ 11k
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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 3.0 years ago by sagarkolekar ★ 11k
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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 3.0 years ago by sagarkolekar ★ 11k
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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 3.0 years ago by sagarkolekar ★ 11k
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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 3.0 years ago by sagarkolekar ★ 11k
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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 3.0 years ago by sagarkolekar ★ 11k
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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 3.0 years ago by sagarkolekar ★ 11k
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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 3.0 years ago by sagarkolekar ★ 11k
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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 3.0 years ago by sagarkolekar ★ 11k
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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 3.0 years ago by sagarkolekar ★ 11k
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Evaluate $\int(\overline z + 2z)dz$ along the circle $x^2+y^2 = 1.$
engineering mathematics updated 3.0 years ago by sagarkolekar ★ 11k
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Explain in detail a. The Multistage Algorithm b. The multihash Algorithm
engineering mathematics updated 3.0 years ago by sagarkolekar ★ 11k
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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 3.0 years 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 3.0 years ago by sagarkolekar ★ 11k
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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 3.1 years ago by sagarkolekar ★ 11k
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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 3.1 years ago by sagarkolekar ★ 11k
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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 3.1 years ago by sagarkolekar ★ 11k
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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 3.3 years ago by sagarkolekar ★ 11k
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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 3.5 years ago by sagarkolekar ★ 11k
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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 3.6 years ago by pedsangini276 • 4.8k
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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 3.6 years ago by pedsangini276 • 4.8k
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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 3.6 years ago by pedsangini276 • 4.8k
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