Evaluate \(\int \sqrt{2 x+1} \ d x\)

Evaluate \(\int { \left( { x }^{ 3 }+7 \right) \left( x-4 \right) dx } \)

Integrate the following with respect to x.
\(\frac { 8x+13 }{ \sqrt { 4x+7 } } \)

Evaluate \(\int { \frac { \cos2x }{ { \sin }^{ 2 }{ x \cos }^{ 2 }x } dx } \) 

Evaluate ഽ\(\sqrt { { x }^{ 2 }-16 } \)dx

If \(\int _{ 1 }^{ a }{ { 3 }x^{ 2 } } \) dx = -1, then find the value of a ( a ∈ R ).

Evaluate the following using properties of definite integrals:
\(\int _{ -\frac { \pi }{ 4 } }^{ \frac { \pi }{ 4 } }{ { x }^{ 3 }{ cos }^{ 3 }xdx } \)

Find the area of the region bounded by the line x − 2y − 12 = 0 , the y-axis and the lines y = 2, y = 5.

Using Integration, find the area of the region bounded the line 2y + x = 8, the x axis and the lines x = 2, x = 4.

Find the area bounded by the lines y − 2x − 4 = 0, y = 1, y = 3 and the y-axis

If MR = 14 − 6x + 9x², find the demand function.

Solve: \(\frac { dy }{ dx } ={ ae }^{ y }\)

Solve the following differential equations
\(\frac { { d }^{ 2 }y }{ d{ x }^{ 2 } } -6\frac { dy }{ dx } +8y=0\)

Find the differential equation of the following
xy = c²

The number of cars in a household is given below.

No. of cars	0	1	2	3	4
No. of Household	30	320	380	190	80

Estimate the probability mass function. Verify p(x_i ) is a probability mass function.

Define discrete random variable.

Explain the distribution function of a random variable.

The following information is the probability distribution of successes.

No. of Successes	0	1	2
Probability	\(\frac{6}{11}\)	\(\frac{9}{22}\)	\(\frac{1}{22}\)

Determine the expected number of success.

What do you understand by Mathematical expectation?

Define Mathematical expectation in terms of discrete random variable.

State the definition of Mathematical expectation using continuous random variable.

Verfy the following statement:
The mean of a Binomial distribution is 12 and its standard deviation is 4.

In a book of 520 pages, 390 typo-graphical errors occur. Assuming Poisson law for the number of errors per page, find the probability that a random sample of 5 pages will contain no error.

Write down the conditions for which the binomial distribution can be used.

A pair of dice is thrown 4 times. If getting a doublet is considered a success, find the probability of 2 successes.

Determine the binomial distribution for which the mean is 4 and variance 3. Also find P(X=15).

Write the conditions for which the poisson distribution is a limiting case of binomial distribution.

Define Standard normal variate.

Using the following Tippett’s random number table,

2952	6641	3992	9792	7969	5911	3170	5624
4167	9524	1545	1396	7203	5356	1300	2693
2670	7483	3408	2762	3563	1089	6913	7991
0560	5246	1112	6107	6008	8125	4233	8776
2754	9143	1405	9025	7002	6111	8816	6446

Draw a sample of 15 houses from Cauvery Street which has 83 houses in total.

What is sample?

What is standard error?

State any two demerits of systematic random sampling.

What is an estimate?

What is interval estimation?

Define critical region.

What is single tailed test.

Mention the components of the time series.

Explain cyclic variations.

Discuss about irregular variation

Define seasonal index.

Mention the classification of Index Number.

State the test of adequacy of index number.

Define Statistical Quality Control.

Define Assignable Cause.

What do you mean by process control?

Name the control charts for variables.

Write the control limits for the R chart.

Write mathematical form of transportation problem.

What is the Assignment problem?

What is the difference between Assignment Problem and Transportation Problem?