Maths

Area of the region bounded by x = 0, y = 0, x = 2, y = 2, y ≤ e? and y ≥ ln x, is:

The lines L₁ : x = y = z, L₂ : x = $\frac{y}{2}=\frac{z}{3}$  and a line L₃ is passing through (1, 1, 1) form a triangle of area $\sqrt[]{6}$  units, (1, 1, 1) being one of the vertices of the triangle. Then the point of intersection of the L₃ with L₂ is

If dy/dx = (eʸ – x)⁻¹ where y(0) = 0, then y is equal to:

Two teachers are taking 6 students to a zoo. The teachers decide to split up. Each student must choose one of the teachers, with the condition that each teacher must take at least one student. Number of possible ways of doing this is:

The series of natural numbers is divided into groups as (1), (2, 3, 4), (3, 4, 5, 6, 7), (4, 5, 6, 7, 8, 9, 10) …………. . If sum of elements in the 20^th group is $\mathcal{l},then\mathcal{l}$  is equal to

A variable line passing through the point P(2, 3/2) meets co-ordinate axes at points A and B, then locus of the foot of perpendicular from origin on the line is:

The remainder when 5²²²² is divided by 7 is:

Coefficient of variation of two distributions are 50% and 60% and their arithmetic means are 30 and 25 respectively. Difference of standard deviation is:

The tangent at a point where eccentric angle 60° on the ellipse x²/a² + y²/b² = 1(a > b) meet the auxiliary circle at L and M. If LM subtends a right angle at the centre, then eccentricity of the ellipse is:

Set of all possible values of k for which f(x) = sin x – cos x – kx + b decreases for all real values of x, is: