Question
Draw $\triangle A B C$ with side $B C=6 cm, A B=5 cm$, and $\angle A B C=60^{\circ}$. Also, construct $\triangle X Y Z$ whose sides are $\frac{3}{4}$ of the corresponding sides of $\triangle X Y Z$.
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In the following data, find the values of p and q. Also, find the median class and modal class.
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Class
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Frequency (f)
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Cumulative frequency (cf)
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100-200
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11
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11
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200-300
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12
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p
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300-400
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10
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33
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400-500
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q
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46
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500-600
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20
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66
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600-700
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14
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80
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In the given figure, D is the midpoint of side BC and $\text{AE}\perp\text{BC}.$ If BC = a, AC = b, AB = c, ED = x, AD = p and AE = h, prove that.
$\text{c}^2=\text{p}^2-\text{ax}+\frac{\text{a}^2}{4}$
→$\text{c}^2=\text{p}^2-\text{ax}+\frac{\text{a}^2}{4}$
If the roots of the equation $(a^2 + b^2)x^2 - 2(ac + bd)x + (c^2 + d^2) = 0$ are equal prove that $\frac{\text{a}}{\text{b}}=\frac{\text{c}}{\text{d}}.$
→If $\triangle\text{ABC}\sim\triangle\text{DEF}$ such that 2AB = DE and BC = 6cm, find EF.
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Class
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$0-20$
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$20-40$
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$40-60$
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$60-80$
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$80-100$
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Frequency
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$25$
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$20$
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$5$
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The $17^{\text {th }}$ term of an A.P. is 5 more than twice its $8^{\text {th }}$ term. If the $11^{\text {th }}$ term of the A.P. is 43 . find the $n ^{\text {th }}$ term.
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Class
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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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$60-70$
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Frequency
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$25$
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$40$
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$42$
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$33$
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$10$
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Write the set of values of a and b for which the following system of equations has infinitely many solutions.
2x + 3y = 7
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