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

If a, b, c are in G.P. and a^1/x = b^1/y = c^1/z, then xyz are in

The coordinates of the focus of the parabola y² − x − 2y + 2 = 0 are 

Solve the following problem.

Obtain a derivative of the following function: x sin x

Two finite sets have m and n elements respectively. The total number of subsets of first set is 56 more than the total number of subsets of the second set. The values of m and n respectively are ______.

If A and B are two finite sets, then n(A) + n(B) is equal to ______.

If A is a finite set containing n element, then number of subsets of A is ______.

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.