Exercise

In a $△\mathrm{PQR}$, $\mathrm{L}$ and $\mathrm{M}$ are two points on base $\mathrm{QR}$, such that $\angle \mathrm{LPQ}=\angle \mathrm{QRP}$ and $\angle \mathrm{RPM}=\angle \mathrm{RQP}$.

Then, which of the following are true:

(i) $△\mathrm{PQL}~△\mathrm{RPM}$

(ii) $\mathrm{QL}\times \mathrm{RM}=\mathrm{PL}\times \mathrm{PM}$

(iii) ${\mathrm{PQ}}^2=\mathrm{QR}·\mathrm{QL}$

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A boy of height $90 \mathrm{cm}$ is walking away from the base of a lamp-post at a speed of $1.2 \mathrm{m}/\mathrm{s}$. If the lamp is $3.6 \mathrm{m}$ above the ground, then the length of his shadow after $6 \mathrm{s}$ is

In $△\mathrm{s}$ $ABC$ and $DEF$, $\angle A=\angle E=40°$, $AB:ED=AC:EF$ and $\angle F=65°$, then $\angle B$is 

In the figure, $DE\parallel BC, AD=4 \mathrm{cm}, DB=6 \mathrm{cm}$ and $AE=5 \mathrm{cm}$, then measure of $EC$ will be:

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In the given figure, $DE\Vert \mathrm{BC}$ and $AD=2 \mathrm{cm}, DB=3 \mathrm{cm},$ $AC=6 \mathrm{cm},$ then $AE=$