Solve your IGNOU Doubts

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

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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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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. $[Give:t_{0.05.18}=1.734,t_{0.0.20}=1.729,t_{0.05.22}=1.721]$

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Question:

b) Verify Euler’s theorem for the function $f(x,y)=\frac{x+y}{x-y}.$

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Question:

a) Find the radius of the sphere which passes through the points ),1,0,0( ),,0,0,1( )0,1,0( and ).1,0

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Question:

c) A club has 9 member having ages 21, 28, 23, 29, 52, 43, 32, 37 and 30 years. One has to be at least 30 years of age to be eligible for the presidentship of the club. A simple random sample of size 5 is selected to provide an estimate of the population proportion eligible for presidentship. Find the mean and the standard error of this estimate

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Question:

b) Find the mean and the standard deviation of a random variable with the following probability density function:

$f(x)=e^-^{x},x\geq 0.$

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Question:

a) Integrate $\int ^1_0tan^1\left ( \frac{2x}{i-x^2} \right )dx..$

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Question:

c) In a certain Poisson distribution the probability of 3 successes is exactly equal to the probability of 4 successes. Find its mean and standard deviation. Also find the probability of more than 1 success for the given distribution.

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