Question : If $(2 x+3 y+4)(2 x+3 y-5)$ is equivalent to $\left(a x^2+b y^2+2 h x y+2 g x+2 f y+c\right)$, then what is the value of $\frac{g + f - c}{abh}$?
Option 1: $\frac{37}{216}$
Option 2: $\frac{35}{432}$
Option 3: $\frac{19}{108}$
Option 4: $\frac{19}{216}$
Correct Answer: $\frac{35}{432}$
Solution : According to the question $(2x + 3y + 4)(2x + 3y - 5) = (ax^2 + by^2 + 2hxy + 2gx + 2fy + c)$ ⇒ $4x^2 + 6xy - 10x + 6xy + 9y^2 - 15y + 8x + 12y - 20 = (ax^2 + by^2 + 2hxy + 2gx + 2fy + c)$ ⇒ $4x^2 + 12xy - 2x + 9y^2 - 3y - 20 = (ax^2 + by^2 + 2hxy + 2gx + 2fy + c)$ On comparing, ⇒ $a = 4, h = 6, g = -1, b = 9, f =\frac{-3}{2}$ and $c = -20$ Now, $\frac{g + f - c}{abh}$ $=\frac{-1 - \frac{3}{2} + 20}{4 × 9 × 6}$ $=\frac{\frac{-2 - 3 + 40}{2}}{4 × 6 × 9}$ $=\frac{\frac{35}{2}}{216}$ $=\frac{35}{432}$ Hence, the correct answer is $\frac{35}{432}$.
Result | Eligibility | Application | Selection Process | Cutoff | Admit Card | Preparation Tips
Question : What is $\frac{\left (x^{2}-y^{2} \right)^{3}+\left (y^{2}-z^{2} \right )^{3}+\left (z^{2}-x^{2} \right )^{3}}{\left (x-y \right)^{3}+\left (y-z \right )^{3}+\left (z-x \right)^{3}}?$
Question : What is the simplified value of: $\frac{1}{8}\left\{\left(x+\frac{1}{y}\right)^2-\left(x-\frac{1}{y}\right)^2\right\}$
Question : The value of $\frac{(x-y)^3+(y-z)^3+(z-x)^3}{\left(x^2-y^2\right)^3+\left(y^2-z^2\right)^3+\left(z^2-x^2\right)^3}$, where $x \neq y \neq z$, is:
Question : If $\left(5 \sqrt{5} x^3-3 \sqrt{3} y^3\right) \div(\sqrt{5} x-\sqrt{3} y)=\left(A x^2+B y^2+C x y\right)$, then the value of $(3 A+B-\sqrt{15} C)$ is:
Question : If $\left(5 \sqrt{5} x^3-3 \sqrt{3} y^3\right) \div(\sqrt{5} x-\sqrt{3} y)=\left(A x^2+B y^2+C x y\right)$, then what is the value of $(3 A-B-\sqrt{15} C)$?
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile