Solve your IGNOU Doubts

Question:

Any finite set is a subset of $\mathbb{Z}.$

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Question:

c) Fit a straight line for regression of Y on X from the following table.

x	0	1	2	3	4	5	6
y	2	1	3	2	4	3	5

Find the value of y when $x=10.$

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Question:

The geometrical representation of the set $\left \{ ix\mid x\mid \in \mathbb{R} \right \}$ is a point.

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Question:

b) If $y=e^x+e^{-x},$ prove tha $\sqrt{y^{2}-4.}$

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Question:

a) A and B are two events which are independent. The probability that both A and B occur is $\frac{1}{2}$ and the probability that neither of them occurs is $\frac{1}{3}.$ Find the probability of the occurrences of A and B.

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Question:

For any $x,\,y\in \mathbb{R},\left | x-y \right |\geq \left | \left | x \right | - \left | y \right | \right | .$

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Question:

c) The difference of mean and variance of a binomial distribution of 9 trails is 4. Find the probability p of success of the binomial distribution. Also find the probability of (i) exactly two successes and (ii) less than 2 successes.

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Question:

b) Obtain $\int tan ^{-1\left ( \frac{2x}{1-x^2} \right )}dx.$

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Question:

a) If $f:R\rightarrow R$ is defined by $f(x)=4x+1$ then show that f is a bijection. Find the formula that defines $f^-1.$

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Question:

c) Find the sum of the first n terms of the series log 2 + log6 + log18 + log54 + .....

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Question:

b) Show that sin x 1( + cos x) has a maximum at $x=\frac{\pi }{3}.$

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Question:

a) It is known that 10 men out of every 100 men and 30 women out of every 1000 women are color blind. In a community, half the population is male. Using Baye’s theorem find the probability that a color blind person chosen at random from among all color blind persons in the community is male.

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Question:

c) A garden pea plant is genetically mixed for the gene pair Tt, where the gene T (for tall) is dominant over the gene t (for short). The plant produced 40 tall and 20 short offspring. Using $x^2-$ test find out whether the plant was self fertilized or fertilized by a short plant at 5% level of significance.

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Question:

If A and B are two sets such that $(A\cup B)^{c}$ is empty, then either A or = $\O$ B . = $\O$

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Question:

b) Solve the differential equation cos $x\frac{dy}{dx}+sin xy=xe^{2x}cos^2x.$

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Question:

a) Find (a × b)⋅ c where

$a=2i+3j-k,b=i-2j+k,c=3i+4j+5k.$

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Question:

Given any n positive numbers in R , the product of their harmonic mean and their arithmetic mean is 1.

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Question:

$\left ( \sqrt{2} ,1,\frac{3}{5}\right )\in \mathbb{Q}\times\mathbb{Z}\times\mathbb{R}.$

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Question:

The roots of $x^{3}-8x-3=0$ are given by $x=\frac{8\pm\sqrt{64+12}}{2}.$

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Question:

c) Two groups of 10 plants each were grown on two different fertilizers. The average height of first group of plants was 92.44 cm, with a standard deviation of 4 cm. For the second group, the average height was 90 cm with a standard deviation of 2 cm. At 5% level of significance test the hypothesis that first fertilizer is better than the second in terms of the plant growth. $[Give:t_{0.05.18}=1.734,t_{0.0.20}=1.729,t_{0.05.22}=1.721]$