1 .
In one km race, A beats B by 50 meters and B beats C by 40 metres, Find, by how much distance, A beats C in a race of .5 kms ?

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2 .
If $x^2$ - x - 1 = 0 find value of $x^3$ - 2x + 1 = ?

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3 .
If $x^2$ + $y^2$ + $z^2$ + 4x + 4y + 8 = 0, Find the value of x + y - z = ?

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4 .
If x + y = 2z Find $x \over x - z$ + $z \over y - z$ = ?

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5 .
If Sin $\theta$ +Cos $\theta$ = 2 . Find The value of $\theta$ ?

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6 .
If tan ( A+B) = $1 \over 2$ and tan (A-B)= $1\over 3$ Find the value of tan 2 A = ?

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7 .
If Sin $\theta$ + $Sin^ 2$$\theta$ =1 Find the value if $Cos^ {12}$$\theta$ +3 $Cos^ {10}$$\theta$ +3 $ Cos^ 8$$\theta$ +$Cos^ 6$$\theta$ +2$Cos^ 4$$\theta$ +2 $Cos^ 2$$\theta$ -2 ?

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8 .
In a triangle, sides are in A.P. and biggest angle is twice of smallest. Then The ratio of sides is :

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9 .
The length of the perpendiculars drawn from a point in the interior of an equilateral triangle are 6 cm, 7cm, and 8 cm. What is the length of the side of triangle ?

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10 .
The side AB of rectangle ABCD has been divided in four equal parts by points x,y and z. Then $Ar(\Delta XYC) \over Ar(Rectangle ABCD)$ = ?

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