H K Dass, Rama Verma and, Bhagwat Swarup Sharma Solutions for Chapter: Model Test Paper, Exercise 1: SECTION

In a $\mathrm{\Delta ABC}, \mathrm{AB}=\mathrm{BC}=\mathrm{AC}$ and $\mathrm{D}$ is a point on $\mathrm{BC}$ such that $\mathrm{BD}=\frac{1}{3}\mathrm{BC}$. Prove that $9{\mathrm{AD}}^2=7{\mathrm{AB}}^2$.

In a $∆\mathrm{ABC}$ as shown in figure $AC\Vert XY$. Also given that area of $\Delta BXY$ is same as area of trapezium $AXYC$. Prove that $AX:AB=(2-\sqrt{2}):2$.

 

In figure, $AB$ and $CD$ are two parallel tangents to a circle with centre $O$. $ST$ is tangent segment between the two parallel tangents touching the circle at $Q$. Show that $\angle SOT=90°$.


 

The following table gives the number of participants in a yoga camp:

The mean of the following frequency distribution is $50$ and the sum of all the frequencies is $120.$ Find the missing frequencies $x$ and $y$.

In a game, the entry fee is $₹5.$ The game consists of tossing a coin $3$ times. For one head or two heads, Sweta gets her entry fee back. If she throws $3$ heads, she receives double the entry fees. Otherwise, she will lose. For tossing a coin three times, if the probability that she loses the entry fee is $\frac{1}{k}$, then find the value of $k$.

In a game, the entry fee is $₹5.$ The game consists of a tossing a coin $3$ times. If one or two heads show, Sweta gets her entry fee back. If she throws $3$ heads, she receives double the entry fees. Otherwise, she will lose. For tossing a coin three times, find the probability that she gets double entry fee. (Write the final answer in its simplest fraction form)

In a game, the entry fee is $₹ 5$. The game consists of a tossing a coin a $3$ times. If one or two heads show, Sweta gets her entry fee back. If she throws $3$ heads, she receives double the entry fees. Otherwise, she will lose. For tossing a coin three times, if the probability that she just gets her entry fee is $\frac{k}{4}$, then find $k$.