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

Show that the solution set of the following system of linear inequalities is an unbounded region 2x + y ≥ 8, x + 2y ≥ 10, x ≥ 0, y ≥ 0.

Solution set of x ≥ 0 and y ≤ 0 is

Solution set of x ≥ 0 and y ≤ 1 is

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 ______.