Commerce (English Medium) Class 11 - CBSE Question Bank Solutions

Find z if |z| = 4 and arg(z) = `(5pi)/6`.

Find principal argument of `(1 + i sqrt(3))^2`.

|z₁ + z₂| = |z₁| + |z₂| is possible if ______.

The value of arg (x) when x < 0 is ______.

Find the linear inequalities for which the shaded region in the given figure is the solution set.

Solve the following system of inequalities `(2x + 1)/(7x - 1) > 5, (x + 7)/(x - 8) > 2`

Find the linear inequalities for which the shaded region in the given figure is the solution set.

Show that the following system of linear inequalities has no solution x + 2y ≤ 3, 3x + 4y ≥ 12, x ≥ 0, y ≥ 1

Solve the following system of linear inequalities:

3x + 2y ≥ 24, 3x + y ≤ 15, x ≥ 4

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