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Permutations an...

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  • Question 1
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    Find the area of the triangle whose vertices are $$(a, b + c), (a, b - c)$$ and $$(-a, c)$$.

  • Question 2
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    Find the area of the right-angled triangle whose vertices are $$(2, -2)$$ , $$(-2, 1)$$ and $$(5, 2).$$

  • Question 3
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    The  triangle with vertices A(4, 4), B(-2, -6) and C(4, -1) is shown in the diagram. The area of $$\Delta$$ ABC is _______

  • Question 4
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    The coordinates of $$A$$ for which area of triangle, whose vertices are $$A(a, 2a),\  B(-2, 6)$$ and $$C(3, 1)$$ is $$10$$ square units, are:

  • Question 5
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    The number of positive fractions $$\dfrac{m}{n}$$ such that $$\dfrac{1}{3}< \dfrac{m}{n}<1 $$ and having the property that the fraction remains the same by adding some positive integer to the numerator and multiplying the denominator by the same positive integer is:

  • Question 6
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    $$(3, 1), (-3, 2)$$ and $$\displaystyle (0,2-\sqrt{3})$$ are the vertices of __________ triangle of area ___________.

  • Question 7
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    Three points A, B and C have coordinates $$(a, b + c), \ (b, c + a)$$ and $$(c, a + b)$$, respectively. The area of the triangle ABC will be:

  • Question 8
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    If the area of a triangle formed by the points (k, 2k) (-2, 6) and (3, 1) is 20 square units. Find the value of k.

  • Question 9
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    If the coordinates of two points A and B are $$(3, 4)$$ and $$(5, -2)$$, respectively, then the coordinates of any point P if $$PA = PB$$ and area of $$\displaystyle \Delta PAB=10$$ is

  • Question 10
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    Find pair of consecutive odd natural numbers, both of which are larger than 13 such that their sum is less than 40

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