Solve your IGNOU Doubts

Question:

Show that the area A of a rectangle with a given perimeter S is maximum when it is a square.

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Question:

Determine the standard derivation of the random variable X whose values are given below:

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Question:

(a) The probability that a man will get the contract A is $\frac{2}{3}$ and the probability that the will not get the contract B is $\frac{5}{9}$ If the probability of getting at least one contract is what is $\frac{4}{5}$ the probability that he will get both the contracts?

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Question:

(a) (i) Given f : $\mathbb{R}$ → $\mathbb{R}$ , f (x) = 3x + ,1 x ∈ $\mathbb{R}$ , show that f is bijective.

(ii) Given f : $\mathbb{R}$ → $\mathbb{R}$ , f (x) = x² +2 ,x ∈ $\mathbb{R}$ 2 and g : $\mathbb{R}$ → $\mathbb{R}$ , g(x) = 3x + ,5 x ∈ $\mathbb{R}$ . Is fog = gof ? Justify.

Is fog = gof ? Justify.

(b) Evaluate $\int_{1}^{2}\frac{dx}{x(1+2x)^{2}}$

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Question:

State whether the following statements are true or false. Justify your answer with the help of a short proof or a counter-example.

(i) The best measure of tendency for the data 10,8,6,4,2 98, ,100 is its mean.

(ii) | a×b | is maximum when a and b are parallel.

(iii) $f(x)=\left\{\begin{matrix} 0.02(10-x);0\leq x\leq 10 & \\ 0, otherwise & \end{matrix}\right.$

is a p.d.f. of a random variable X.

(iv) Function f define by f (x)= $x+\tfrac{1}{x}$ is increasing for 0 < x ≤ 1.

(v) Total 5³ simple random samples of size 3 can be drawn without replacement from a population of size 5.

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Question:

Which of the following statements are true and which are false? Justify your answer with a short proof or a counterexample.

i) The Row Reduced Echelon form of any invertible square matrix is the identity matrix

dim(W₁) $>$ dim(v)/2,dim(W₂) $>$ dim(v) /2 ,the W₁ ∩ W₂ $\neq$ {0}.

iii) If See Answer →

Question:

a) Let See Answer →

Question:

a) Check whether the matrices See Answer →

Question:

b) Let See Answer →

Question:

a) Consider the following system of equations:

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Question:

a) For the vector space See Answer →

Question:

Let See Answer →

Question:

a) Which of the following are subspaces of R³? Justify your answer.

i) { $S={(x,y,z)\in R^{3}\left | x+z=2y \right |}$ }

ii) { $S={(x,y,z)\in R^{3}\left | x+yz=0 \right |}$ }

For those subsets which are subspaces, find a basis.

b) Check that See Answer →

Question:

Let $u=\frac{2i+2j+k}{3}, V=\frac{i-j}{\sqrt{2}}$ and $W=\frac{-\sqrt{2(i+j-4k)}}{6}.$ Compute the scalar products See Answer →

Question:

Find the vector equation of the plane determined by the points (1, 0,−1), (0, 1, 1) and (−1, 1, 0). Also find the point of intersection of the line See Answer →

Question:

Which of the following are binary operations on $\mathbb{R}$ ? Justify your answer.

i) The operation ▽ defined by See Answer →

Question:

(a) Evaluate $\int_{0}^{2}[x] dx.$