HSC Commerce Class 12 - Tamil Nadu Board of Secondary Education Question Bank Solutions for Business Mathematics and Statistics

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The complementary function of (D² + 4) y = e^2x is

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The particular intergral of the differential equation `("d"^2y)/("d"x^2) - 8 ("d"y)/("d"x) + 16y = 2"e"^(4x)`

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The integrating factor of `x ("d"y)/("d"x) - y = x^2` is

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The particular integral of the differential equation f(D) y = e^ax where f(D) = (D – a)² 

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The complementary function of `("d"^2y)/("d"x^2) - ("d"y)/("d"x) = 0` is

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The P.I of (3D² + D – 14)y = 13e^2x is

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The general solution of the differential equation `("d"y)/("d"x) = cos x` is

Suppose that Q_d = `30 - 5"P" + 2 "dP"/"dt" + ("d"^2"P")/("dt"^2)` and Q_s = 6 + 3P. Find the equilibrium price for market clearance

What is null hypothesis? Give an example

Define alternative hypothesis

Define critical region

Define critical value

Define the level of significance

What is a type I error?

What is single tailed test

A sample of 100 items, draw from a universe with mean value 4 and S.D 3, has a mean value 63.5. Is the difference in the mean significant at 0.05 level of significance?

A sample of 400 individuals is found to have a mean height of 67.47 inches. Can it be reasonably regarded as a sample from a large population with a mean height of 67.39 inches and standard deviation of 1.30 inches?

The average score on a nationally administered aptitude test was 76 and the corresponding standard deviation was 8. In order to evaluate a state’s education system, the scores of 100 of the state’s students were randomly selected. These students had an average score of 72. Test at a significance level of 0.05 if there is a significant difference between the state scores and the national scores

The mean breaking strength of cables supplied by a manufacturer is 1,800 with a standard deviation of 100. By a new technique in the manufacturing process it is claimed that the breaking strength of the cables has increased. In order to test this claim a sample of 50 cables is tested. It is found that the mean breaking strength is 1,850. Can you support the claim at 0.01 level of significance?

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Errors in sampling are of