Solve your IGNOU Doubts

Question:

Ripple marks

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Question:

Lithification and diagenesis

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Question:

Discuss the classification of sedimentary rocks based on size and shape of grains

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Question:

Describe palimpsest textures present in the metamorphic rocks.

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Question:

Explain briefly the secondary sedimentary structures.

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Question:

Discuss the IUGS Classification of Igneous rocks.

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Question:

Discuss the megascopic and microscopic characters of granite and basalt with the help of neat well labelled diagrams.

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Question:

Describe various mechanisms of magmatic differentiation.

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Question:

Discuss the different types of textures found in igneous rocks with the help of neat well labelled diagrams.

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Question:

Phase Rule

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Question:

Extraterrestrial Rocks

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Question:

State whether the following statements are True or False. Justify your answers.
a) The sequence $\left \{ \left ( \frac{1}{n},\frac{1}{n} \right ) : n \in N \right \}$ is convergent in $R^2$ under the discrete metric on $R^2$ .
b) A subset in a metric space is compact if it is closed.
c) Continuous image of a path connected space is path connected.
d) The second derivative of a linear map from $R^n$ to $R^m$ never vanishes.
e) If $\int_{A}f dm = \int_{A}g dm$ for all $A \in M$ , then $f = g$ .

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Question:

Find the fourier series of the function $f$ defined by

$f(x) = \begin{Bmatrix} -x^2, -\pi <x\leq 0\\ x^2, 0<x < \pi \end{Bmatrix}$

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Question:

Verify Bounded Convergence Theorem for the sequence of functions $\left \{ f_n \right \}$ where

$f_n (x) = \frac{1}{\left ( 1 + \frac{x}{n} \right )^n } , 0\leq x \leq 1, n \in N$

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Question:

Show that if f is measurable, then the function $f^a(x)$ given by

$f^a(x) = \begin{Bmatrix} a &if \: f(x)>a \\ f(x) & if \: f(x) \leq a \end{Bmatrix}$
is also measurable.

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Question:

Find the measure of the following sets.

i) $E = \bigcap_{n=1}^{\infty }\left ( a-\frac{1}{n}, b \right )$
ii) $E = Q \cup \left \{ 1 ,2 ,3,4 \right \}$
iii) $E = ]5,7[ \cup [7,7.5]$ .

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Question:

Let A be any set in R , show that $m^*(A) = m^*(A+x)$ where $m^*$ denotes the outer measure.

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Question:

Consider Z and let $F_1$ denote the class of subsets of Z , given by $F_1 = A \subset Z$ either A is finite or $A^c$ is finite}. Check whether $F_1$ is a $\sigma$ algebra or not.

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Question:

Which of the following sets are connected sets in 2 R with the metric given against it?
Justify your answer.
i) $A ={( x,y) : 0\leq x \leq 1, 0 \leq y \leq 2}$ under the standard metric.
ii) $A = \left \{ ( x,y) : x^2 + y^2 = 1\right \}$ under the discrete metric.

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Question:

Which of the following sets are totally bounded? Give reasons for your answer. Are they compact?
i) 2N in (N,d) where d is the discrete metric.
ii) $[0,2] \cup [5,10]$ in (R,d) where d is the Euclidean metric.