Maths NCERT Exemplar Solutions Class 11th Chapter Four

The region represented by {z = x+iy∈C: |z|-Re(z)≤1} is also given by the inequality:

Which of the following points lies on the locus of the foot of perpendicular drawn upon any tangent to the ellipse, x²/4 + y²/2 = 1 from any of its foci?

A ray of light coming from the point (2,2√3) is incident at an angle 30° on the line x=1 at the point A. The ray gets reflected on the line x=1 and meets x-axis at the point B. Then, the line AB passes through the point:

Out of 11 consecutive natural numbers if three numbers are selected at random (without repetition), then the probability that they are in A.P. with positive common difference, is:

If I₁=∫₀¹(1-x⁵⁰)¹⁰⁰dx and I₂=∫₀¹(1-x⁵⁰)¹⁰¹dx such that I₂=αI₁, then α equals to:

If f(x+y)=f(x)f(y) and Σₓ₌₁^∞ f(x)=2, x,y∈N where N is the set of all natural numbers, then the value of f(4)/f(2) is:

Let L₁ be a tangent to the parabola y²=4(x+1) and L₂ be a tangent to the parabola y²=8(x+2) such that L₁ and L₂ intersect at right angles. Then L₁ and L₂ meet on the straight line:

The general solution of the differential equation √(1+x²+y²+x²y²) + xy(dy/dx)=0 is: (where C is a constant of integration)

The area (in sq. units) of the region A={(x,y): |x|+|y|≤1, 2y²≥|x|} is:

If α and β be two roots of the equation x² - 64x + 256 = 0. Then the value of (α³/β⁵)¹/⁸ + (β³/α⁵)¹/⁸ is: