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Two dice are thrown together. What is the probability that,
i) Sum of the numbers is divisible by 3 or 4?
ii) Sum of the numbers is neither divisible by 3 nor 5?
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Suppose $f(x)=p x+3$ for $a \leq x \leq b$
$=5 x^2-q \text { for } b<x \leq c$
Find the condition on $p, q$, so that $f(x)$ is continuous on $[a, c]$, by filling in the boxes
→$=5 x^2-q \text { for } b<x \leq c$
Find the condition on $p, q$, so that $f(x)$ is continuous on $[a, c]$, by filling in the boxes
If A∪B∪C = S (the sample space) and A, B and C are mutually exclusive events, can the
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ii) P(A) = 0.4, P(B) = 0.6, P(C) = 0.2
following represent probability assignment?
i) P(A) = 0.2, P(B) = 0.7, P(C) = 0.1
ii) P(A) = 0.4, P(B) = 0.6, P(C) = 0.2
If $A$ and $B$ are two independent events and $P(A)=\frac{3}{5}, P(B)=\frac{2}{3}$, find
i) $\mathrm{P}(\mathrm{A} \cap \mathrm{B})$ ii) $\mathrm{P}\left(\mathrm{A}^{\prime} \cap \mathrm{B}^{\prime}\right)$ iii) $\mathrm{P}\left(\mathrm{A}^{\prime} \cap \mathrm{B}\right)$ iv) $P\left(A^{\prime} \cap B^{\prime}\right)$ v) $P(A \cup B)$
→i) $\mathrm{P}(\mathrm{A} \cap \mathrm{B})$ ii) $\mathrm{P}\left(\mathrm{A}^{\prime} \cap \mathrm{B}^{\prime}\right)$ iii) $\mathrm{P}\left(\mathrm{A}^{\prime} \cap \mathrm{B}\right)$ iv) $P\left(A^{\prime} \cap B^{\prime}\right)$ v) $P(A \cup B)$
The letters of the word STORY be arranged randomly. Find the probability that
a) T and Y are together.
b) arrangment begins with T and end with Y.
a) T and Y are together.
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Find the length of transverse axis, length of conjugate axis, the eccentricity, the co-ordinates of foci, equations of directrices and the length of latus rectum of the hyperbola
$\frac{x^2}{4}-\frac{y^2}{12}=1$
$\frac{y^2}{9}-\frac{x^2}{16}=1$
→$\frac{x^2}{4}-\frac{y^2}{12}=1$
$\frac{y^2}{9}-\frac{x^2}{16}=1$