Find the number of cubes in the base layer of the following figure In the above figure, if only the shaded cubes are visible from the top, draw the visible layer.

Here, we observe that in the base layer of the given figure, there are 3 cubes in one row, 2 cubes in the middle row and only 1 cube in the third row. Hence, there are 3 + 2 + 1 = 6 cubes in the base layer of the given figure. Now, we know that top view is the view of a figure as it appears when we look at the figure from its top. It is given that only shaded cubes are visible from the top. Hence, the top view of the given figure will look like the following:

Using Euler's formula, find the value of unknown x , y , z , p , q and r . Faces 7 y 9 p 6 8 Vertices 10 12 z 6 q 11 Edges x 18 16 12 12 r

We know that Euler's formula is F + V - E = 2 , where F is the number of faces, V is the number of vertices, E is the number of edges. In the first set, F = 7 , V = 10 , E = x . Upon substituting the given values, we get, F + V - E = 2 ⇒ 7 + 10 - x = 2 ⇒ 17 - x = 2 ⇒ x = 15 . In the second set, F = y , V = 12 , E = 18 . Upon substituting the given values, we get, F + V - E = 2 ⇒ y + 12 - 18 = 2 ⇒ y - 6 = 2 ⇒ y = 8 . In the third set, F = 9 , V = z , E = 16 . Upon substituting the given values, we get, F + V - E = 2 ⇒ 9 + z - 16 = 2 ⇒ z - 7 = 2 ⇒ z = 9 . In the fourth set, F = p , V = 6 , E = 12 . Upon substituting the given values, we get, F + V - E = 2 ⇒ p + 6 - 12 = 2 ⇒ p - 6 = 2 ⇒ p = 8 . In the fifth set, F = 6 , V = q , E = 12 . Upon substituting the given values, we get, F + V - E = 2 ⇒ 6 + q - 12 = 2 ⇒ q - 6 = 2 ⇒ q = 8 . In the last set, F = 8 , V = 11 , and E = r . Upon substituting the given values, we get, F + V - E = 2 ⇒ 8 + 11 - r = 2 ⇒ 19 - r = 2 ⇒ r = 17 . So, the values are x = 15 , y = 8 , z = 9 , p = 8 , q = 8 , r = 17 .

Look at the map given below. Now, answer the following question. Name the roads that meet at roundabout.

Observe the map carefully and find the roads that meet at the roundabout. The roads that meet at round about are Mall Road, Khel Marg, Sneha Marg and Flower Road.