Maths

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:

The term independent of 'x' in the expression of [(x+1)/(x²/³ - x¹/³ + 1) - (x-1)/(x-x¹/²)]¹?, where x ≠ 0, 1 is equal to…….

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:

Let p = 2i + 3j + k and q = i + 2j + k be two vectors. If a vector r = (αi + βj + γk) is perpendicular to each of the vectors (p + q) and (p - q), and |r| = √3, then |α| + |β| + |γ| is equal to……

There are 5 students in class 10, 6 students in class 11 and 8 students in class 12. If the number of ways, in which 10 students can be selected from them so as to include at least 2 students from each class and at most 5 students from the total 11 students of class 10 and 11 is 100k, then k is equal 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: