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

Two finite sets have m and n elements. The number of subsets of the first set is 112 more than that of the second set. The values of m and n are, respectively ______.

If A and B are finite sets such that A ⊂ B, then n (A ∪ B) = ______.

Which of the following is not correct?

Solve the equation `z^2 = barz`, where z = x + iy.

If |z² – 1| = |z|² + 1, then show that z lies on imaginary axis.

If a complex number z lies in the interior or on the boundary of a circle of radius 3 units and centre (–4, 0), find the greatest and least values of |z + 1|.

The conjugate of the complex number `(1 - i)/(1 + i)` is ______.

If a complex number lies in the third quadrant, then its conjugate lies in the ______.

If z₁ = `sqrt(3) + i  sqrt(3)` and z₂ = `sqrt(3) + i`, then find the quadrant in which `(z_1/z_2)` lies.

What is the conjugate of `(sqrt(5 + 12i) + sqrt(5 - 12i))/(sqrt(5 + 12i) - sqrt(5 - 12i))`?

If z₁, z₂ and z₃, z₄ are two pairs of conjugate complex numbers, then find arg`(z_1/z_4)` + arg`(z_2/z_3)`.

Solve the system of equations Re(z²) = 0, z = 2.

State True or False for the following:

If z is a complex number such that z ≠ 0 and Re(z) = 0, then Im(z²) = 0.

What is the conjugate of `(2 - i)/(1 - 2i)^2`?

If `(a^2 + 1)^2/(2a - i)` = x + iy, what is the value of x² + y²?

sinx + icos2x and cosx – isin2x are conjugate to each other for ______.

If z = x + iy lies in the third quadrant, then `barz/z` also lies in the third quadrant if ______. 

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

State which of the following statement is True or False.

If x < y and b < 0, then `x/"b" < y/"b"`

State which of the following statement is True or False.

If xy > 0, then x > 0 and y < 0