Math Answers

The following data represents the sale (Rs. 1,000) per month of 3 brands of a
toilet soap allocated among 3 cities:
Cities
Brands A B C
I 42 48 30
II 42 54 57
III 29 42 29
At 5% level of significance, test whether the mean sales of 3 brands are equal.

Compute the Riemann integral of the function f (x) = x on the interval [−1, 1].

If your regular output for your pivot is .375 per /24 hours and you need to put down .8what % speed should you set your pivot to?

Verify Inverse function theorem for finding the derivative at a point y of the 0
domain of the inverse function of the function f (x) = cosx, x ∈[0,π].Hence, find
the derivative of the inverse function aty

Verify the second mean value theorem of integrability for the functions f and g
defined on [1,2] by f (x) = 3x and g(x) = 5x.

Let V = R2. Define addition + on V by (x1, y1) + (x2, y2) = (x1 + x2, y1 + y2) and
scalar multiplication · by r · (a, b) = (ra,0). Check whether V satisfies all the
conditions for it to be a vector space over R with respect to these operations.

Let V be a vector space over a field F and let T : V → V be a linear operator. Show
T(W) ⊂ W for any subspace W of V if and only if there is a λ ∈ F such that Tv = λv
for all v ∈ V .

Let T : P2 → P1 be defined by
T(a+bx+cx2) = b+c+(a−c)x.
Check that T is a linear transformation. Find the matrix of the transformation with
respect to the ordered bases B1 = {x2,x2+x,x2+x+ 1} and B2 = {1,x}. Find the
kernel of T .

Reduce the conic x2 − 6xy+y2 − 4 = 0 to standard form. Hence the given conic.

Find the orthogonal canonical reduction of the quadratic form
−x2+y2+z2+ 2xy− 2xz+ 2yz. Also, find its principal axes