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Study the following information to answer the given questions
(i) Eight friends $A, B, C, D, E, F, G$ and $H$ are seated in a circle facing centre.
(ii) $D$ is between $B$ and $G$ and $F$ is between $A$ and $H$
(iii) $E$ is second to the right of $A$.
(a) Determine the position of $A$ ?
(b) Which of the informations statement are not required to ascertain the position of $C$ ?
(c) Determine the position of $C$ ?
→(i) Eight friends $A, B, C, D, E, F, G$ and $H$ are seated in a circle facing centre.
(ii) $D$ is between $B$ and $G$ and $F$ is between $A$ and $H$
(iii) $E$ is second to the right of $A$.
(a) Determine the position of $A$ ?
(b) Which of the informations statement are not required to ascertain the position of $C$ ?
(c) Determine the position of $C$ ?
A die is rolled. If $E=\{1,3,5\}, F=\{2,3\}$ and $G=$ $\{2,3,4,5\}$, find (a) $P((E \cup F) / G)$, (b) $P((E \cap F) / G)$
→If $f(x)=x-\frac{1}{x}$, prove that
$[f(x)]^3=f(x)^3+3 f\left(\frac{1}{x}\right)$
→$[f(x)]^3=f(x)^3+3 f\left(\frac{1}{x}\right)$
$(645)_{10}$
→Find the domain and range of the real function \[f(x)=\frac{x^2-9}{x-3}\]
A girl throws a die. If she gets a 5 or 6, she tosses a coin three times and notes the number of heads. If she gets 1, 2, 3, or 4, she tosses a coin two times and notes the number of heads obtained. If she obtained exactly two heads, what is the probability that she threw 1, 2, 3, or 4 with the die?
If $2 x^2+\lambda x y+2 y^2+(\lambda-4) x+6 y-5=0$ is the equation of the circle, then find its radius.
→Calculate the electricity bill amount for a month of April, if 4 bulbs of 40 W for $5 \text{ h, } 4$ tube lights of 60 W for 5 h, a TV of 100 W for 6 h, a washing machine of 400 W for 3 h are used per day. The cost per unit is ₹ 1.80.
→Find the foot of the perpendicular from the point (3, 8) to the line x + 3y = 7.
If $x \sqrt{1+y}+y \sqrt{1+x}=0$ and $x \neq y$ prove that $\frac{d y}{d x}=-\frac{1}{(x+1)^2}$.
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