Download App

4.2 Quadratic equations and inequations — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS4.2 Quadratic equations and inequations1 Mark
MCQ
Let $\lambda \neq 0$ be in $R$. If $\alpha$ and $\beta$ are the roots of the equation, $x^{2}-x+2 \lambda=0$ and $\alpha$ and $\gamma$ are the roots of the equation, $3 x^{2}-10 x+27 \lambda=0$ then $\frac{\beta \gamma}{\lambda}$ is equal to
  • A
    $36$
  • B
    $27$
  • C
    $9$
  • ✓
    $18$
✓

Answer

Correct option: D.
$18$
d
$\alpha+\beta=1, \alpha \beta=2 \lambda$

$\alpha+\beta=\frac{10}{3}, \quad \alpha \gamma=\frac{27 \lambda}{3}=9 \lambda$

$\gamma-\beta=\frac{7}{3}$

$\frac{\gamma}{\beta}=\frac{9}{2} \Rightarrow \gamma=\frac{9}{2} \beta=\frac{9}{2} \times \frac{2}{3} \Rightarrow \gamma=3$

$\frac{9}{2} \beta-\beta=\frac{7}{3}$

$\frac{9}{2} \beta=\frac{7}{3} \Rightarrow \beta=\frac{2}{3}$

$\alpha=1-\frac{2}{3}=\frac{1}{3}$

$2 \lambda=\frac{2}{9} \Rightarrow \lambda=\frac{1}{9}$

$\frac{\beta \gamma}{\lambda}=\frac{\frac{2}{3} \times 3}{\frac{1}{9}}=18$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "MCQ" from 4.2 Quadratic equations and inequations→4.2 Quadratic equations and inequations — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

A square is inscribed in the circle ${x^2} + {y^2} - 2x + 4y + 3 = 0$, whose sides are parallel to the coordinate axes. One vertex of the square is
→
$\mathop {\lim }\limits_{x \to a} \frac{{{{(x + 2)}^{5/3}} - {{(a + 2)}^{5/3}}}}{{x - a}} = $
→
If ${{({e^x} + 2)} \over {({e^x} - 1)\,(2{e^x} - 3)}} = - {3 \over {{e^x} - 1}} + {B \over {2{e^x} - 3}}$, then $B = $
→
The number of numbers between $2,000$  and $5,000$  that can be formed with the digits $0, 1, 2, 3, 4,$ (repetition of digits is not allowed) an are multiple of $3$ is?
→
Total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants is equal to:
​​​​​​
→
The value of $\cos 52^\circ + \cos 68^\circ + \cos 172^\circ $ is
→
Let $\alpha, \beta, \gamma, \delta \in \mathrm{Z}$ and let $\mathrm{A}(\alpha, \beta), \mathrm{B}(1,0), \mathrm{C}(\gamma, \delta)$ and $D(1,2)$ be the vertices of a parallelogram $\mathrm{ABCD}$. If $\mathrm{AB}=\sqrt{10}$ and the points $\mathrm{A}$ and $\mathrm{C}$ lie on the line $3 y=2 x+1$, then $2(\alpha+\beta+\gamma+\delta)$ is equal to
→
Given $(1 - 2x + 5x^2 - 10x^3) (1 + x)^n = 1 + a_1x + a_2x^2 + ....$ and that $a_1^2\,= 2a_2$ then the value of $n$ is
→
If $|z + 4|\, \le \,3,$ then the greatest and the least value of $|z + 1|$ are
→
The complex numbers $z = x + iy$ which satisfy the equation $\left| {\frac{{z - 5i}}{{z + 5i}}} \right| = 1$ lie on
→