Science (English Medium) कक्षा ११ - CBSE Question Bank Solutions

Draw the Venn diagrams to illustrate the following relationship among sets E, M and U, where E is the set of students studying English in a school, M is the set of students studying Mathematics in the same school, U is the set of all students in that school.

Not all students study Mathematics, but every students studying English studies Mathematics.

Let U be the set of all boys and girls in a school, G be the set of all girls in the school, B be the set of all boys in the school, and S be the set of all students in the school who take swimming. Some, but not all, students in the school take swimming. Draw a Venn diagram showing one of the possible interrelationship among sets U, G, B and S.

If for real values of x, cosθ = `x + 1/x`, then ______.

Find the derivative of 2x⁴ + x.

Find the derivative of x² cosx.

Find the derivative of f(x) = tan(ax + b), by first principle.

(ax² + cot x)(p + q cos x)

`(a + b sin x)/(c + d cos x)`

Let f(x) = x – [x]; ∈ R, then f'`(1/2)` is ______.

The frequency distribution:

where A is a positive integer, has a variance of 160. Determine the value of A.

For the frequency distribution:

Find the standard deviation.

There are 60 students in a class. The following is the frequency distribution of the marks obtained by the students in a test.

where x is a positive integer. Determine the mean and standard deviation of the marks.

The weights of coffee in 70 jars is shown in the following table:

Determine variance and standard deviation of the above distribution.

Following are the marks obtained, out of 100, by two students Ravi and Hashina in 10 tests.

Who is more intelligent and who is more consistent?

An urn contains twenty white slips of paper numbered from 1 through 20, ten red slips of paper numbered from 1 through 10, forty yellow slips of paper numbered from 1 through 40, and ten blue slips of paper numbered from 1 through 10. If these 80 slips of paper are thoroughly shuffled so that each slip has the same probability of being drawn. Find the probabilities of drawing a slip of paper that is blue or white

An urn contains twenty white slips of paper numbered from 1 through 20, ten red slips of paper numbered from 1 through 10, forty yellow slips of paper numbered from 1 through 40, and ten blue slips of paper numbered from 1 through 10. If these 80 slips of paper are thoroughly shuffled so that each slip has the same probability of being drawn. Find the probabilities of drawing a slip of paper that is numbered 1, 2, 3, 4 or 5

An urn contains twenty white slips of paper numbered from 1 through 20, ten red slips of paper numbered from 1 through 10, forty yellow slips of paper numbered from 1 through 40, and ten blue slips of paper numbered from 1 through 10. If these 80 slips of paper are thoroughly shuffled so that each slip has the same probability of being drawn. Find the probabilities of drawing a slip of paper that is red or yellow and numbered 1, 2, 3 or 4

An urn contains twenty white slips of paper numbered from 1 through 20, ten red slips of paper numbered from 1 through 10, forty yellow slips of paper numbered from 1 through 40, and ten blue slips of paper numbered from 1 through 10. If these 80 slips of paper are thoroughly shuffled so that each slip has the same probability of being drawn. Find the probabilities of drawing a slip of paper that is numbered 5, 15, 25, or 35

An urn contains twenty white slips of paper numbered from 1 through 20, ten red slips of paper numbered from 1 through 10, forty yellow slips of paper numbered from 1 through 40, and ten blue slips of paper numbered from 1 through 10. If these 80 slips of paper are thoroughly shuffled so that each slip has the same probability of being drawn. Find the probabilities of drawing a slip of paper that is white and numbered higher than 12 or yellow and numbered higher than 26.

In a leap year the probability of having 53 Sundays or 53 Mondays is ______.