A 15 metres high tower casts a shadow 24 metres long at a certain time and at the same time, a telephone pole casts a shadow 16 metres long. The height of the telephone pole is ____________ .

A 15 metres high tower casts a shadow 24 metres long at a certain…

In $\triangle ABC \sim \triangle DEF$, AB = 4 cm DE = 6 cm EF = 9 cm and FD = 12 cm then the perimeter of $\triangle ABC$ is ____________ .

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The ratio between the HCF and LCM of 5, 15 and 20 is __________.

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PA and PB are two tangents drawn from an external point P to a circle with centre O. If $\angle PBA = 65^{\circ}$ then $\angle APB$ = ____________ .

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Sum of the probabilities of each outcome in an experiment is ____________ .

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Two triangles are similar, if their corresponding sides are ........... (proportional, equal).

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The value of $\left(\sin 30^{\circ}+\cos 30^{\circ}\right)^2-\left(\sin 60^{\circ}-\cos 60\right)^2$ is ____________ .

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If the HCF and LCM of two a and b are x and y respectively, then $\frac{x^2 y^2}{a^2 b^2}$= __________.

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If $(k+1) x^2+\frac{3}{2} x=7$ is a quadratic equation, then k cannot be equal to __________.

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If the mean of x, y, z is y, then mean of x and z is ____________ .

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The area of the largest circle that can be drawn inside a rectangle of length a cm and breadth b cm $(a>b)$ is ____________ .

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