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prove the theorem : In a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of remaining two sides.
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→Find the area of the major segment APB of a circle of radius 35cm and $\angle\text{AOB}=90^\circ$ as shown in the given figure.
→Water is flowing at the rate of $6$km/hr through a pipe of diameter $14\ cm$ into a rectangular tank which is $60m$ long and $22m$ wide. Determine the time in which the level of water in the tank Will rise by $7\ cm.$
→The point A divides the join of$ P(-5, 1)$ and $Q(3, 5)$ in the ratio $k : 1$. Find the two values of k for which the area of $\triangle ABC$ where $B$ is $(1, 5)$ and $C(7, -2)$ is equal to $2$ units.
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→If the median of the following frequency distribution is 28.5 find the missing frequencies:
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Class interval
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0-10
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10-20
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20-30
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30-40
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40-50
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50-60
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Total
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|
Frequency
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5
|
$f_1$
|
20
|
15
|
$f_2$
|
5
|
60
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Find the ratio in which the point $\text{P}\Big(\frac{3}{4},\frac{5}{12}\Big)$ divides the line segment joining the points $\text{A}\Big(\frac{1}{2},\frac{3}{2}\Big)$ and B(2, -5).
→If first term of an A.P. is a, second term is b and last term is c, then show that sum of all terms is $\frac{(a+c)(b+c-2 a)}{2(b-a)}$.
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