The probability of a boy or a girl being born is $\frac{1}{2}$. For a family having only three children, what is the probability of having two girls and one boy ?
Person 1 and Person 2 invest in three mutual funds $A, B$, and C . The amounts they invest in each of these mutual funds are given in the table.
| Mutual found A |
Mutul fund B |
Mutul fund C |
|
|---|---|---|---|
| Person 1 | Rs. 10,000 |
Rs. 20,000 |
Rs. 20,000 |
| Person 2 | Rs. 20,000 |
Rs. 15,000 |
Rs. 15,000 |
At the end of one year, the total amount that Person 1 gets is Rs. 500 more than Person 2. The annual rate of return for the mutual funds $B$ and $C$ is $15 \%$ each. What is the annual rate of return for the mutual fund $A$ ?
Visualize two identical right circular cones such that one is inverted over the other and they share a common circular base. If a cutting plane passes through the vertices of the assembled cones, what shape does the outer boundary of the resulting cross-section make ?
If a real variable $x$ satisfies $3^{x^2}=27 \times 9^x$, then the value of $\frac{2^{x^2}}{\left(2^x\right)^2}$ is :
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