Mathematics Tes...

When 5⁹⁹ is divided by 13 then the remainder is

The equation of the diameter of the circle x² + y² - 6x + 2y = 0 which passes thro' the origin is

If the lines 3x - 4y - 7 = 0 and 2x - 3y - 5 = 0 are two diameters of a circle of area 49 π square units, the equation of the circle is

If z₁ and z₂ are two non-zero complex numbers such that |z₁ + z₂| = |z₁| + |z₂|, then argz₁ - argz₂ is equal to

If (1 + i√3)/[(1 + i√3)ⁿ] is an integer ,then n is equal to

The interval in which y=x²e^x is increasing with respect to x, is

If f(x) = 1 + αx, α ≠ 0 is the inverse of itself, then the value of α is

The line y=mx+c touches the parabola x²=4ay if

If ⁿP_r=840, ⁿC_r=35, then n=

If the integers m and n are chosen at random between 1 and 100, then the probability that a number of the form 7^m + 7ⁿ is divisible by 5 equals