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How many outcomes are obtained from rollings n indistinguishable dice ?


Suppose the temperature of a COVID positive patient is recorded as Tbody = 40ยฐC.



Determine the wavelength at which the radiation emitted from the body reaches its peak.

a. The points ๐ด,๐ต and ๐ถ have co-ordinates (โˆ’1,2),(1,1) and (2,3) respectively. Sketch the triangle ๐ด๐ต๐ถ .By calculating the lengths of the sides of this triangle, determine if it is scalene, isosceles, or equilateral.

b. Find the distance ๐‘€๐ต, where ๐‘€ is the midpoint of ๐ด๐ถ, and hence find the area of the triangle ๐ด๐ต๐ถ.


a. The points ๐ด,๐ต and ๐ถ have co-ordinates (โˆ’1,2),(1,1) and (2,3) respectively. Sketch the triangle ๐ด๐ต๐ถ. By calculating the lengths of the sides of this triangle, determine if it is scalene, isosceles, or equilateral.


1. Consider the following data to answer the question below


What is the command to convert the above dictionary into a dataframe named โ€˜df_stateโ€™?

2. List 3 commands to display the columns of the above dataframe df_state.

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3. Correlation between two variables X&Y is 0.85. Now, after adding the value 2 to all the values of X, the correlation co-efficient will be______

4. A) Read the given dataset โ€œTips.csvโ€ as a dataframe โ€œDataโ€. Give 3 commands to extract the columns in the following sequence - Time, TotalBill, Tips?

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B)ย ย ย ย ย Read the given excel sheet โ€˜Tips1.xlsxโ€™ as a dataframe โ€˜Data1โ€™. What command should be given to merge the two data frames โ€˜Dataโ€™ and โ€˜Data1โ€™ by columns?

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C)ย ย ย ย ย Copy the 'Data1' dataframe as 'Data2'ย (Data2 = Data1.copy()) and identify the command to find the total tips received across Dayโ€™s from the dataframe โ€˜Data2โ€™?

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The line joining the point ๐ด (4,6) ๐‘ก๐‘œ ๐ต (๐‘,โˆ’3) has a gradient of 3. Find the value of ๐‘.


๐‘ƒ and ๐‘„ are the points (3,1) and (โˆ’2,โˆ’9) respectively. Calculate:

a. The distance ๐‘ƒ๐‘„

b. The midpoint of the line joining ๐‘ƒ to ๐‘„

c. The gradient of the line ๐‘ƒ๐‘„

d. The gradient of a line perpendicular to ๐‘ƒ๐‘„



Artificial Mouse population satisfying the following conditions :

i. Two mouses are born one by one in 1st and 2nd months respectively. This newly born pair of mice build the initial population.

ii. These mice can mate at the age of 2nd month such that this mice pair brings another pair of mice in the 3rd month. So, in this way the mouses produced in a particular month will be equal to sum of mouses produced in the previous 2 months.

iii. If the a and b are produced in the 1st and 2nd months to form an initial population there will be a + b mouses in the 3rd month.

iv. These mice are immortal. They will not die.


Write a python function population-series(a, b, n) which takes the population as a ,b and a

positive integer number 'n' as number of months and returns no. of mouses produced in each month till the nth month in string format using recursion.


How many strings of length n can be formed from the English alphabet ?


In how many ways can a committee of 5 teachers and 4 students be chosen from 9 teachers and 15 students ?


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