The straight line y = 2x + does not meet the parabola y^2 = 2x, i… - Vidyadip

MCQ

The straight line $y = 2x + \lambda $ does not meet the parabola ${y^2} = 2x$, if

A
$\lambda < \frac{1}{4}$
✓
$\lambda > \frac{1}{4}$
C
$\lambda = 4$
D
$\lambda = 1$

✓

Answer

Correct option: B.

$\lambda > \frac{1}{4}$

b
(b) $y = 2x + \lambda $ does not meet,

if $\lambda > \frac{a}{m} = \frac{1}{{2.2}} = \frac{1}{4}$

==> $\lambda > \frac{1}{4}$.

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

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

$\int_0^{\pi /6} {\frac{{\sin x}}{{{{\cos }^3}x}}\,dx = } $

Two sides of a triangle are to have lengths $'a'$ cm & $'b'$ cm. If the triangle is to have the maximum area, then the length of the median from the vertex containing the sides $'a'$ and $'b'$ is

Let $ABC$ be a triangle such that $\overrightarrow{ BC }=\overrightarrow{ a }, \overrightarrow{ CA }=\overrightarrow{ b }$, $\overrightarrow{ AB }=\overrightarrow{ c },|\overrightarrow{ a }|=6 \sqrt{2}, \quad|\overrightarrow{ b }|=2 \sqrt{3}$ and $\overrightarrow{ b } \cdot \overrightarrow{ c }=12$ Consider the statements.

$( S 1):|(\overrightarrow{ a } \times \overrightarrow{ b })+(\overrightarrow{ c } \times \overrightarrow{ b })|-|\overrightarrow{ c }|=6(2 \sqrt{2}-1)$

$( S 2): \angle ABC =\cos ^{-1}\left(\sqrt{\frac{2}{3}}\right)$. Then

The value of $\mathop {\lim }\limits_{x \to 0} \frac{{\sqrt {1 - \cos {x^2}} }}{{1 - \cos x}}$ is

If the mean and variance of the data $65,68,58,44$, $48,45,60, \alpha, \beta, 60$ where $\alpha>\beta$ are $56$ and $66.2$ respectively, then $\alpha^2+\beta^2$ is equal to

If $\alpha ,\beta $are the roots of ${x^2} - ax + b = 0$ and if ${\alpha ^n} + {\beta ^n} = {V_n}$, then

Which of the following is correct?

A line passes through the point $(3, 4)$ and cuts off intercepts from the coordinates axes such that their sum is $14.$ The equation of the line is

Let $\alpha $ and $\beta $ be the roots of the equation $x^2 + x + 1 = 0.$ Then for $y \ne 0$ in $R,$ $\left| {\begin{array}{*{20}{c}}
{y\, + \,1}&\alpha &\beta \\
\alpha &{y\, + \,\beta }&1\\
\beta &1&{y\, + \,\alpha }
\end{array}} \right|$ is equal to

A light ray emits from the origin making an angle $30^{\circ}$ with the positive $x$-axis. After getting reflected by the line $x + y =1$, if this ray intersects $x$-axis at $Q$, then the abscissa of $Q$ is