For the following questions answer them individually
Let $$C$$ be a circle with centre $$P_0$$ and $$AB$$ be a diameter of $$C$$. Suppose $$P_1$$ is the mid point of the line segment $$P_0B$$,$$P_2$$ is the mid point of the line segment $$P_1B$$ and so on. Let $$C_1,C_2,C_3,...$$ be circles with diameters $$P_0P_1, P_1P_2, P_2P_3...$$ respectively. Suppose the circles $$C_1, C_2, C_3,...$$ are all shaded. The ratio of the area of the unshaded portion of $$C$$ to that of the original circle is
Consider the sequence of numbers $$a_1, a_2, a_3$$....... to infinity where $$a_1 = 81.33$$ and $$a_2 = -19$$ and $$a_j = a_{j-1} - a_{j-2}$$ for $$j\ge3$$. What is the sum of the first 6002 terms of this sequence?
A sprinter starts running on a circular path of radius r metres. Her average speed (in metres/minute) is $$\pi$$ rĀ during the first 30 seconds, $$\pi$$ r/2Ā during next one minute, $$\pi$$ r/4Ā during next 2 minutes, $$\pi$$ r/8Ā during next 4 minutes, and so on. What is the ratio of the time taken for the nth round to that for the previous round?
Let $$u = ({\log_2 x})^2 - 6 {\log_2 x} + 12$$ where x is a real number. Then the equation $$x^u = 256$$, has
If the lengths of diagonals DF, AG and CE of the cube shown in the adjoining figure are equal to the three sides of a triangle, then the radius of the circle circumscribing that triangle will be?
In the adjoining figure, the lines represent one-way roads allowing travel only northwards or only westwards. Along how many distinct routes can a car reach point B from point A?
On a semicircle with diameter AD, chord BC is parallel to the diameter. Further; AD and BC are separated by 2cm, while AD has length 8. What is the length of BC?
A circle with radius 2 is placed against a right angle. Another smaller circle is also placed as shown in the adjoining figure. What is the radius of the smaller circle?
In the adjoining figure, chord ED is parallel to the diameter AC of the circle. If angle CBE = 65Ā°, then what is the value of angle DEC?
Incase of any issue contact support@cracku.in