11.

My birthday is in January. What would be a sufficient number of questions with 'Yes/ No' answers that will enable one to find my birth date?

• 6

• 3

• 5

• 2

A square is drawn with one of its sides as the hypotenuse of a right-angled triangle as shown in the figure. What is the area of the shaded circle?

• $\frac{25\mathrm{\pi }}{3} {\mathrm{cm}}^2$

• $\frac{25\mathrm{\pi }}{4}{\mathrm{cm}}^2$

What should be added to the product of the two numbers 983713 and 983719 to make it a perfect square?

• 9

• 13

• 19

• 27

In $∆$ABC, AB = AC and angle BAC = 90°; EF $\parallel$AB and DF $\parallel$ AC.

The total area of the shaded region is

• AF²/ 2

• AF²

• BC²/ 2

• BC²

Consider a circle of radius r. Fit the largest possible square inside it and the largest possible circle inside the square. What is the radius of the innermost circle?

• r/ $\sqrt{2}$

• $\mathrm{\pi r}/ \sqrt{2}$

• $\frac{\mathrm{r}}{2\mathrm{\pi }\sqrt{2}}$

• r/ 2

In how many ways can you place N coins on a board with N rows and N columns such that every row and every column contains exactly one coin?

• N

• N (N - 1) (N - 2)...... 2 × 1

• N²

• N^N

Two identical wheels B and C move on the periphery of circle A. Both start at the same point on A and return to it, B moving inside A and C outside it. Which is the correct statement?

• B wears out $\mathrm{\pi }$ times C

• C wears out $\mathrm{\pi }$ times B

• B and C wear out about equally.

• C wears out two times B

Which of the following is the odd one out?

• Isosceles triangle

• Square

• Regular hexagon

• Rectangle

Find the missing word: A, AB, .........., ABBABAAB

• AABB

• ABAB

• ABBA

• BAAB

A 100 m long train crosses a 200 m long and 20 m wide bridge in 20 seconds. What is the speed of the train in km/hr?

• 45

• 36

• 54

• 57.6