Mathematics Test - 2

At present, a firm is manufacturing 2000 items. It is estimated that the rate of change of production P w.r.t. additional number of workers x is given by dP/dx = 100 - 12√x If the firm employs 25 more workers, then the new level of production of items is

All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of 10 to each of the students. Which of the following statistical measures will not change even after the grace marks were given ?

Let T_n be the number of all possible triangles formed by joining vertices of an n-sided regular polygon. If T_n+1 − T_n = 10, then the value of n is

The intercepts on x-axis made by tangents to the curve, y= ₀∫^x |t| dt, x ∈ R, which are parallel to the line y = 2x, are equal to

If α, β ∊ C are the distinct roots, of the equation x² −x+1=0, then α ¹⁰¹+β¹⁰⁷ is equal to :

If the system of linear equations

x+ky+3z=0

3x+ky−2z=0

2x+4y−3z=0

has a non-zero solution (x, y, z), then xz/y² is equal to :

A ray of light along x + √3y = √3 gets reflected upon reaching x-axis, the equation of the reflected rays is