IGNOU MST-001 PGDAST Solved Assignment 2024 cover page

IGNOU MST-001 Solved Assignment 2024 | PGDAST

Solved By – Narendra Kr. Sharma – M.Sc (Mathematics Honors) – Delhi University

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IGNOU MST-001 Assignment Question Paper 2024

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1. State whether the following statements are True or False and also give the reason in support of your answer.

a) Collection of rich persons in India forms a set.

b) Following rule is a function from \(A\) to \(B\).

c) \(\frac{d}{d x}(9-7 x)^5=45(9-7 x)^4\)

d) In exclusive method, upper limit of a class is included in the same class.

e) The order of the matrix \(\left[\begin{array}{lll}2 & 5 & 6 \\ 4 & 3 & 1\end{array}\right]\) is \(3 \times 2\).

2. If four cards are chosen from a pack of 52 playing cards then find the number of ways that all four cards are:
a) of same suit
b) red
c) face cards
d) king
e) of different suit

3. Arrange the numbers 49, 36, 42, 19, 22, 27, 14, 13, 24, 48, 23, 28, 17, 42, 39, 45, 22, 24, 17, \(41,18,42,38,43,11,27,36,13,40,30,24,10,18,47,18,19,23,12,27\) in stretched stemand-leaf display that has single-digit starting parts and leaves, but has stem width of 5. 

4. If the universal set is \(\mathrm{U}=\{1,2,3,4,5,6,7,8\}\) and \(\mathrm{A}=\{2,3,6,7\}, \mathrm{B}=\{4,6,8\}, \mathrm{C}=\{6,7,8\}\) are the subsets of \(U\), then verify
a) De-Morgan’s laws
b) left distributive law

5. Evaluate the following:
a) \(\quad \int x^{2} e^{2 x} d x\)
b) \(\frac{d y}{d x}\), where \(y=(4 x+5)^{4}(9 x+4)^{5}\)

6. a) Prove that \(\left|\begin{array}{lll}\text { a } & \text { b } & c \\ b & c & a \\ c & a & b\end{array}\right|=(a+b+c)\left(a b+b c+c a-a^{2}-b^{2}-c^{2}\right)\)

b) What do you mean by primary data and secondary data? Also give an example in each case.

7. Draw a box plot with whisker, \(+\) ve sign and outliers for the following data:

\(42,37,28,23,32,25,26,39,38,41,22,38,21,31,26,36,42,52,50,47,24,53,28\)

8. a) Find the values of \(\mathbf{a}\) and \(\mathbf{b}\), if the function \(\mathbf{f}\) given below is continuous at \(x=2\)

\[
f(x)= \begin{cases}a+b, & x<2 \\ a+b x+4, & x=2 \\ 5, & x>2\end{cases}
\]

b) Draw a histogram for the following data:

Wages40−4950−6970−99100−109110−119
No of workers22060354

Also draw frequency polygon in the same graph.

\(sin\:3\theta =3\:sin\:\theta -4\:sin^3\:\theta \)

MST-001 Sample Solution 2024

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1(a) False.

Reason: –  A collection of rich persons in India does not form a set as it does not satisfy the mathematical definition of a set, which requires that its elements are well-defined and distinct objects. The wealth of a person is a subject to change and is not a well-defined characteristic, hence the collection of rich persons cannot be considered as a set in mathematics.

Hence, Given statement is false.

1(b) 

1(d) 

False.

Reason: –     In exclusive method, the upper limit of a class is not included in the same class. Exclusive method, also known as the left-open right-closed method, defines a class interval by specifying the lower limit (included) and the upper limit (excluded) of the interval. This means that an object with the upper limit value does not belong to the class interval defined by the lower and upper limits.

Hence Given statement is False.

1 (e) False

Reason: –    The order of a matrix is given as the number of rows followed by the number of columns. The given matrix  has 2 rows and 3 columns, so its order is 2×3.

Hence Given statement is False.

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\(cos\:2\theta =cos^2\theta -sin^2\theta\)

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