Domain exclusion omitted

Questions that set this trap

8 published questions

• mathematicsLet $y=f(x)$ represent a parabola with focus $\left(-\frac{1}{2}, 0\right)$ and directrix $y=-\frac{1}{2}$. Then…
• mathematicsLet R be a relation on $\mathbb{N} \times \mathbb{N}$ defined by $(a, b)\text{R}(c, d)$ if and only if $ad(b - c) = bc(a - d)$. Then R is
• mathematicsThe number of real roots of the equation $\sqrt{x^2 - 4x + 3} + \sqrt{x^2 - 9} = \sqrt{4x^2 - 14x + 6}$, is :
• mathematicsThe equation $\mathrm{e}^{4 x}+8 \mathrm{e}^{3 x}+13 \mathrm{e}^{2 x}-8 \mathrm{e}^{x}+1=0, x \in \mathbb{R}$ has :
• mathematicsLet $(a, b) \subset (0, 2\pi)$ be the largest interval for which…
• mathematicsIf an unbiased die, marked with $-2,-1,0,1,2,3$ on its faces, is thrown five times, then the probability that the product of the outcomes i…
• mathematicsThe plane $2x - y + z = 4$ intersects the line segment joining the points $\text{A}(a, -2, 4)$ and $\text{B}(2, b, -3)$ at the point…
• mathematicsLet the function $f(x) = 2x^3 + (2p - 7)x^2 + 3(2p - 9)x - 6$ have a maxima for some value of $x < 0$ and a minima for some value of…