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If the median of $33, 28, 20, 25, 34, x$ is $29$, find the maximum possible value of $x.$
→Marks scored by $40$ students of class $IX$ in mathematics are given below: $81, 55, 68, 79, 85, 43, 29, 68, 54, 73, 47, 35, 72, 64, 95, 44, 50, 77, 64, 35, 79, 52, 45, 54, 70, 83, 62, 64, 72, 92, 84, 76, 63, 43, 54, 38, 73, 68, 52, 54$. Prepare a frequency distribution with class size of $10$ marks.
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In a quadrilateral $ABCD, CO$ and $DO$ are the bisectors of $\angle\text{C}\ \text{and}\ \angle\text{D}$ respectively. Prove that $\angle\text{COD} = \frac{1}{2} (\angle\text{A}\ \text{and}\ \angle\text{B})$.
→ Using factor theorem, factorize the following polynomials: $2y^3 - 5y^2 - 19y + 42$
→In $\triangle\text{ABC},$ if $\angle\text{A}=40^\circ$ and $\angle\text{B}=60^\circ.$ Determine the longest and shortest sides of the triangle.
→Find the area of a parallelogram $ABCD$ in which $AB = 14\ cm, BC = 10\ cm$ and $AC = 16\ cm$. $\big(\text{Given},\sqrt{3}=1.73\big)$
→In the following, using the remainder theorem, find the remainder when $f(x)$ is divided by $g(x)$ and verify the by actual division: $f(x) = 9x^3 - 3x^2 + x - 5$, $\text{g(x)}=\text{x}-\frac{2}{3}$
→The height of an equilateral triangle measures $9\ cm$. Find its area, correct to places of decimal. $\big(\text{Take}\sqrt{3}=1.732\big)$
→Find the value of the following correct to three place of decimals, it begin that $\sqrt2=1.4142, \sqrt3=1.732,\ \sqrt5=2.2360,\ \sqrt6=2.4495$ and $\sqrt{10}=3.162.$ $\frac{3-\sqrt5}{3+2\sqrt5}$
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