Arts (English Medium) कक्षा ११ - CBSE Question Bank Solutions for Mathematics

18 mice were placed in two experimental groups and one control group, with all groups equally large. In how many ways can the mice be placed into three groups?

A sports team of 11 students is to be constituted, choosing at least 5 from Class XI and atleast 5 from Class XII. If there are 20 students in each of these classes, in how many ways can the team be constituted?

At the end of each year the value of a certain machine has depreciated by 20% of its value at the beginning of that year. If its initial value was Rs 1250, find the value at the end of 5 years.

If a, b, c, d are in G.P., prove that a² – b², b² – c², c² – d² are also in G.P.

If a, b, c, d are four distinct positive quantities in G.P., then show that a + d > b + c

In a G.P. of positive terms, if any term is equal to the sum of the next two terms. Then the common ratio of the G.P. is ______.

Let S be the sum, P be the product and R be the sum of the reciprocals of 3 terms of a G.P. Then P² R³ : S³ is equal to ______.

In a G.P. of even number of terms, the sum of all terms is 5 times the sum of the odd terms. The common ratio of the G.P. is ______.

If the p^th and q^th terms of a G.P. are q and p respectively, show that its (p + q)^th term is `(q^p/p^q)^(1/(p - q))`

If p^th, q^th, and r^th terms of an A.P. and G.P. are both a, b and c respectively, show that a^b–c . b^{c – a} . c^{a – b} = 1

The third term of G.P. is 4. The product of its first 5 terms is ______.

If x, 2y, 3z are in A.P., where the distinct numbers x, y, z are in G.P. then the common ratio of the G.P. is ______.

The lengths of three unequal edges of a rectangular solid block are in G.P. The volume of the block is 216 cm³ and the total surface area is 252cm². The length of the longest edge is ______.

For a, b, c to be in G.P. the value of `(a - b)/(b - c)` is equal to ______.

The third term of a G.P. is 4, the product of the first five terms is ______.

The sum or difference of two G.P.s, is again a G.P.

Find the distance between the lines 3x + 4y = 9 and 6x + 8y = 15.

Show that the locus of the mid-point of the distance between the axes of the variable line x cosα + y sinα = p is `1/x^2 + 1/y^2 = 4/p^2` where p is a constant.

The distance of the point P(1, – 3) from the line 2y – 3x = 4 is ______.

A point moves such that its distance from the point (4, 0) is half that of its distance from the line x = 16. The locus of the point is ______.