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Mathematics · 2022 · 3 marks
CBSE 2022 · Region 3 · Set 2 · Q7
A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle of $\displaystyle 30$° with it. The height of the breaking point from the ground is $\displaystyle 2$ m . Find the total height of the tree.
Marking-scheme solution
Modal class is $\displaystyle 45$-$\displaystyle 55$
Mode $\displaystyle =45+10 \times \frac{23-22}{46-22-14}$
$\displaystyle =46$
For what value of ' n ', are the $\displaystyle \mathrm{n}^{\text {th }}$ terms of the APs : $\displaystyle 9$, $\displaystyle 7$, 5..... and $\displaystyle 15$, $\displaystyle 12$, 9..... the same ?
$\displaystyle n$th terms are $\displaystyle 9+(n-1)(-2)$ and $\displaystyle 15+(n-1)(-3)$
Thus, $\displaystyle 9-2(n-1)=15-3(n-1)$ gives $\displaystyle n=7$
Pag
(a)
$\displaystyle 150$ spherical marbles, each of diameter $\displaystyle 1.4$ cm , are dropped in a cylindrical vessel of diameter $\displaystyle 7$ cm containing some water, and are completely immersed in water. Find the rise in the level of water in the cylindrical vessel.
Let $\displaystyle h \mathrm{~cm}$ be the rise in the water level. Then
\[\begin{array}{l}
\pi(3 \cdot 5)^{2} h=\frac{4 \pi}{3}(0 \cdot 7)^{3}(150) \\
\Rightarrow h=5 \cdot 6 \mathrm{~cm}
\end{array}
\]
Or
(b) Three cubes of side $\displaystyle 6$ cm each, are joined as shown in Figure 1. Find the total surface area of the resulting cuboid.
Figure $\displaystyle 1$
Length of cuboid=18cm
Total surface area of solid $\displaystyle =2(18 \times 6+6 \times 6+6 \times 18)$
\[=504 \mathrm{~cm}^{2}
\]
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CBSE Class 10 Mathematics past-paper question from the 2022board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.