WBJEE Maths Test - 6 - JEE MCQ

The coordinates of the point from which equal tangents are drawn to the circle x²+y²=1, x²+y²+8x+15=0 and x²+y²+10y+24=0 are

(1 − ω + ω²)⁷ + (1 + ω − ω²)⁷ =

Circles x²+y²+2gx+2fy=0 and x²+y²+2g'x+2f'y=0 touch externally, if

is equal to

If a ≠ 6, b, c satisfy = 0 then abc =

The differential equation dy/dx+sin 2y=x³cos²y is reduced to linear from dv/dx+Pv=Q where P and Q are function of x alone, by changing the variable as :

The derivative of is

If f (x)   = (x − x₀) φ (x) and φ (x) is continuous at x = x₀ , then f ′(x) 0 is equal to

The eccentricity of the ellipse 9x² + 5y² − 30y = 0 is

The roots of the equation = 0 are

The solution of differential equation

The sum of distances of any point on the ellipse 3x² + 4y² = 24 from its foci is

The locus of the middle points of chords of the hyperbola 3x² − 2y² + 4x − 6^y = 0 parallel to y = 2x is

The eccentricity of the conic 9x² - 16y² = 144 is

If f(x) = x³ + 4x² + λx + 1 is a monotonically decreasing function of x in the largest possible interval (- 2, -2/3) then

If cos⁻¹x+cos⁻¹y+cos⁻¹z = 3π then xy + yz + zx is equal to

The maximum area of the rectangle that can be inscribed in a circle of radius r is

If |z₁|=|z₂| and amp. z₁+amp.z₂=0, then

If A and B are any 2 x 2 matrics, then det (A + B) = 0 implies

The parabola with directrix x + 2y − 1 = 0 and focus (1, 0) is

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