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2
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Apply Cayley-Hamilton theorem for $A = \begin{bmatrix} \ 1 & 2 \\ \ 2 & -1 \\ \end{bmatrix}$ and deduce that $A^8=625I$
engineering mathematics updated 4.3 years ago by teamques10 ★ 70k
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Using Cauchy's Integral formula evaluate $\int_{c}\frac{sin^6z}{(z-\pi/6)^3}dz$ where c is |z|=1
engineering mathematics updated 4.3 years ago by teamques10 ★ 70k
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Using Residue theorm evaluate $ \int_{0}^{2 \pi} \frac{d \theta}{5+4cos \theta} $
engineering mathematics updated 4.3 years ago by teamques10 ★ 70k
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show that the vector F = (y+z)i +(z+x)j +(x+y)k is solenoidal
engineering mathematics updated 4.3 years ago by yerasylmakulbe671 • 10
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In a sampling a large number of parts manufactured by a machine , the mean number of defectives in a sample of 20 is 2.
engineering mathematics updated 4.3 years ago by teamques10 ★ 70k
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Seven dice are thrown 729 times.How many times do you expect at least four dice to show three or five?
engineering mathematics updated 4.3 years ago by teamques10 ★ 70k
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The probability of a man hitting the target is 1/4.How many times must he fire so that the probability of his hitting the target atleast once is greater than 2/3.
engineering mathematics updated 4.3 years ago by teamques10 ★ 70k
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Verify Cauchy-Schwartz inequality for u=(2, 3, 1) and v=(3,0, 4).Also find the angle between u and v.
engineering mathematics updated 4.3 years ago by teamques10 ★ 70k
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If one root of quadratic equation is $2\sqrt{3}-4$ then what is the form the quadratic equation.
engineering mathematics updated 4.3 years ago by teamques10 ★ 70k
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Check whether the set of all pairs of real numbers of the form (1,x) with operations $(1,y) +(1+y^{'})=(1,y+y^{'}) and k(1,y)=(1,ky)$ is a vector space.
engineering mathematics updated 4.3 years ago by teamques10 ★ 70k
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Show that every square matrix can be uniquely expressed as sum of a symmetric and Skew-symmetric matrix.
engineering mathematics updated 4.3 years ago by yerasylmakulbe671 • 10
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Explain different fuzzy membership function
engineering mathematics updated 4.3 years ago by yerasylmakulbe671 • 10
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473
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Show that \[ \int_0^{\infty}e^{-t} \sin \left( \frac{t}{2}\right) \sin h{\ \left(\frac{\sqrt{3}t}{2}\right)}\ dt=\ \frac{\sqrt{3}}{2} \]
engineering mathematics updated 4.3 years ago by yerasylmakulbe671 • 10
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Marks obtained by students in an examination follow the normal distribution.If 30% of students got below 35 marks and 10% got above 60 marks.Find mean and standard deviation
engineering mathematics updated 4.4 years ago by teamques10 ★ 70k
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Show that the set V of positive real numbers with operations Addition: $x + y = xy$ Scalar Multiplication: $kx = x^k$ is a vector space where x, y are any two real numbers and k is any scalar.
engineering mathematics updated 4.4 years ago by teamques10 ★ 70k
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Let G be the set of real numbers and let G be the set of real numbers and let a * b=ab/2. Show that (G, *) is a abelian group.
engineering mathematics updated 4.4 years ago by teamques10 ★ 70k
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Find moment generating function of Binomial distribution & hence find mean and variance.
engineering mathematics updated 4.4 years ago by teamques10 ★ 70k
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Evaluate \[ i) \ \lim_{x\to 0} \dfrac {\sin x. \sin^{-1} x-x^2}{x^6} \] ii) Fit straight line to the following data (x,y)= (-1, -5), (1,1), (2,4), (3,7), (4, 10) Estimate y when x=7.
engineering mathematics updated 4.4 years ago by pg1118329 • 0
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Test the consistancy of the following equations and solve them if they are consistent. 2x-y+z=8, 3x-y+z=6 4x-y+2z=7, -x+y-z=4
engineering mathematics updated 4.4 years ago by pg1118329 • 0
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Fit a curve y=ax+bx2 for the data; | x : | 1 | 2 | 3 | 4 | 5 | 6 || y : | 2.51 | 5.82 | 9.93 | 14.84 | 20.55 | 27.06 |
engineering mathematics updated 4.4 years ago by pg1118329 • 0
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Solve the equation x6-i=0.
engineering mathematics updated 4.4 years ago by pg1118329 • 0
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Fit a straight line to following data and also estimate the production in 1957. | Year | 1951 | 1961 | 1971 | 1981 | 1991 || Production in Thousand Tones | 10 | 12 | 8 | 10 | 13 |
engineering mathematics updated 4.4 years ago by pg1118329 • 0
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Fit a second degree parabolic curve to following data:- | X | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 || Y | 2 | 6 | 7 | 8 | 10 | 11 | 11 | 10 | 9 |
engineering mathematics updated 4.4 years ago by pg1118329 • 0
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Expand log (1+sinx) = (x - x2/2 + x3/6 +...)
engineering mathematics updated 4.4 years ago by pg1118329 • 0
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Test for consistency and solve if consistent - x1-2x2+x3-x4=2; x1+2x2+2x4=1; 4x2-x3+3x4=-1.
engineering mathematics updated 4.4 years ago by pg1118329 • 0
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