Arun Sharma Solutions for Exercise 2: Level of Difficulty

If the equation $5x+9y+17z=a$, $4x+8y+12z=b$, and $2x+3y+8z=c$ have at least one solution for $x$, $y$, and $z$ and $a$, $b$, and $c\ne 0$, then which of the following is true?

If $\left[x\right]$ represents the greatest integer less than or equal to $x$, then the value of $\left[{315}^{\frac{1}{3}}\right]+\left[{316}^{\frac{1}{3}}\right]+\left[{317}^{\frac{1}{3}}\right]+....+\left[{515}^{\frac{1}{3}}\right]$ is:

If ' $\mathrm{x}$ ' is $\mathrm{a}$ real number then what is the number of solutions for the equation: ${\left({\mathrm{x}}^8+12\right)}^{\frac{1}{2}}={\mathrm{x}}^4-2$

If $f\left(x\right)=4x—\sqrt{7}$, which of the following statements is true about the roots of the equation $f\left(x\right) = 2.$

If the equation $a{x}^2+bx+a=0(a > 0)$ has real and positive roots then which of the following is always true?

If $p, q, r$ are real and $(x-p)(x-q)+(x-q)(x-r)+(x-r)(x-p)=0$ if $p\ne q\ne r$ then which of the following options is true?

If $f\left(x\right)=p{x}^2+qx+r \& g\left(x\right)=r{x}^2+qx+p.$ If one root of $f\left(x\right)=0$ is $2$ and one root of $g\left(x\right)=0$ is $\frac{1}{4}$, then find the sum of the roots of $f\left(x\right)$ and $g\left(x\right)$.

The number of distinct points at which the curve $y^3—4y^2+x^2—5x+3y=0$ intersects either the y-axis or the x-axis is _____.