Question
Write the step of construct the tangents to a circle from an external point.
✓
Answer
Steps of construction:
- Take given circle and a point P outside the circle. O is centre of the circle.
- Joint OP.
- Bisect OP and get its mid-point M.
- Draw circle with centre M and radius = PM = MO.
- Circle drawn meets the given circle at Q above PO and at Q’ below PO.
- Join PQ and PQ’.
- PQ and PQ’ are the required tangents drawn to the circle from the point P.
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If $(\tan\theta+\sin\theta)=\text{m}$ and $(\tan\theta-\sin\theta)=\text{n},$ prove that $\big(\text{m}^2-\text{n}^2\big)^2=16\text{mn}.$
→The angle of elevation of the top Q of a vertical tower PQ from a point X on the ground is 60°. At a point Y, 40m vertically above X, the angle of elevation is 45°. Find the height of tower. $\big[\text{Take}\sqrt{3}=1.732\big]$
→A number consisting of two digits is seven times the sum of its digits. When 27 is subtracted from the number, the digits are reversed. Find the number.
Short-Answer Question:
Write the zeros of the quadratic polynomial $f(x) = 6x^2 - 3$
→Write the zeros of the quadratic polynomial $f(x) = 6x^2 - 3$
Solve for x and y:
$\frac{3}{\text{x}}-\frac{1}{\text{y}}+\text{9}=0,$
$\frac{2}{\text{x}}+\frac{3}{\text{y}}=\text{5}$ $(\text{x}\neq0,\ \text{y}\neq0).$
→$\frac{3}{\text{x}}-\frac{1}{\text{y}}+\text{9}=0,$
$\frac{2}{\text{x}}+\frac{3}{\text{y}}=\text{5}$ $(\text{x}\neq0,\ \text{y}\neq0).$
Find the roots of the following equations, if they exist, by applying the quadratic formula:
$3x^2 - 2x + 2 = 0$
→$3x^2 - 2x + 2 = 0$
Solve the following quadratic equation:
$\frac{1}{\text{x}-2}+\frac{2}{\text{x}-1}=\frac{6}{\text{x}}$ $\text{x}\neq0,\ 1,\ 2$
→$\frac{1}{\text{x}-2}+\frac{2}{\text{x}-1}=\frac{6}{\text{x}}$ $\text{x}\neq0,\ 1,\ 2$
From the following frequency distribution, prepare the 'More Then Ogive'.
Also find the median.
|
Score
|
Number of candidates
|
|
400-450
|
20
|
|
450-500
|
35
|
|
500-550
|
40
|
|
550-600
|
32
|
|
600-650
|
24
|
|
650-700
|
27
|
|
700-750
|
18
|
|
750-800
|
24
|
|
Total
|
230
|
Prove that $\frac{2}{\sqrt7}$ is an irrational number.
HINT: $\frac{2}{\sqrt7}=\Big(\frac{2}{\sqrt7}\times\frac{\sqrt7}{\sqrt7}\Big)=\frac{2}{7}.\sqrt7$
→HINT: $\frac{2}{\sqrt7}=\Big(\frac{2}{\sqrt7}\times\frac{\sqrt7}{\sqrt7}\Big)=\frac{2}{7}.\sqrt7$
Prove the following identities:
$\frac{(\sin\text{A}-\sin\text{B})}{(\cos\text{A}+\cos\text{B})}+\frac{(\cos\text{A}-\cos\text{B})}{(\sin\text{A}+\sin\text{B})}=0$
→$\frac{(\sin\text{A}-\sin\text{B})}{(\cos\text{A}+\cos\text{B})}+\frac{(\cos\text{A}-\cos\text{B})}{(\sin\text{A}+\sin\text{B})}=0$