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$\lambda = 1$
if $\lambda > \frac{a}{m} = \frac{1}{{2.2}} = \frac{1}{4}$
==> $\lambda > \frac{1}{4}$.
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$(i)$ Let $\alpha_1$ be the total number of ways in which the committee can be formed such that the committee has $5$ members, having exactly $3$ boys and $2$ girls.
$(ii)$ Let $\alpha_2$ be the total number of ways in which the committee can be formed such that the committee has at least $2$ members, and having an equal number of boys and girls.
$(iii)$ Let $\alpha_3$ be the total number of ways in which the committee can be formed such that the committee has $5$ members, at least $2$ of them being girls.
$(iv)$ Let $\alpha_4$ be the total number of ways in which the committee can be formed such that the committee has $4$ members, having at least $2$ girls and such that both $M _1$ and $G _1$ are $NOT$ in the committee together.
| $LIST I $ | $LIST I $ |
| $P$ The value of $\alpha_1$ is | $1$ $136$ |
| $Q$ The value of $\alpha_2$ is | $2$ $189$ |
| $R$ The value of $\alpha_3$ is | $3$ $192$ |
| $S$ The value of $\alpha_4$ is | $4$ $200$ |
| $5$ $381$ | |
| $6$ $461$ |
The correct option is: