Find a,b,c if \[ \bar{F}=(axy+bz^{3})\bar{i}+(3x^{2}-cz)\bar{j}+(3xz^{2}-y)\bar{k}\ \]is irrational.

Find \[A^{5}-4A^{4}-7A^{3}+11A^{2}-A=10 I \] in terms of A using Cayley-Hamilton theorem for \[A=\begin{bmatrix} 1 &4 \\ 2& 3 \end{bmatrix}\ \]

A continuous random variable x has the p.d.f defined by f(x)=A+Bx, 0≤ x ≤1 if the mean of the distribution is \(\dfrac{1}{3}\),Find A and B.

X | 10 | 12 | 18 | 18 | 15 | 40 |

Y | 12 | 18 | 25 | 25 | 50 | 25 |

between 60 & 75 (ii)more than 75.

Show that the matrix \[A=\begin{bmatrix} 8 & -6 & 2\\ -6& 7 &-4 \\ 2&-4 & 3 \end{bmatrix}\ \]Find the diagonal form and transforming matrix.

5,2,8,-1,3,0,6,-2,1,5,0,4.can it be concluded that the injection will be in general accompanied by an increase in blood pressure?

Optimize \(Z=x_{1}^{2}+x_{2}^{2}+x_{3}^{2}-6x_{1}-8x_{2}-10x_{3}\)

\[ \displaystyle \oint (x^{2}-y)dx+(2y^{2}+x)dy\] around the boundary of the region defined by \[ y =x^{2}\] and y=4.

Grades in Physics |
Grade in Maths | |||

High | Medium | Low | ||

High | 56 | 71 | 12 | |

Medium | 47 | 163 | 38 | |

Low | 14 | 42 | 81 |

X | 65,66,67,67,68,69,70,72 |

Y | 67.68,65,66,72,72,69,71 |

Diet A | 5,6,8,1,12,4,3,9,6,10gms |

Diet B | 2,3,6,8,1,10,2,8gms |

Find if the variances are significantly different?

If \(A=\begin{bmatrix} -1 & 4\\ 2& 1 \end{bmatrix}\)then prove that 3tan A=Atan3.

Using the Kuhn-Tucker condition solve the following N.L.P.P.

Maximize\( Z=x_{1}^{2}-x_{2}^{2}-x_{3}^{2}+4x_{1}+6x_{2}\)

Subject to \(x_{1}+x_{2}\leq 2\)

\(2x_{1}+3x_{2} \leq12\)

\(x_{1},x_{2} \geq 0.\)