A tells only lies on Monday, Tuesday, and Wednesday and speaks only the truth for the rest of the week. B tells only lies on Thursday, Friday and Saturday and speaks only the truth for the rest of the week. If today both of them state that they have lied yesterday, what day is it today?

• Monday

• Thursday

• Sunday

• Tuesday

A fair die was thrown three times and the outcome was repeatedly six. If the die is thrown again what is the probability of getting six?

• 1/6

• 1/216

• 1/1296

• 1

Which is the odd one out based on a divisibility test?

154, 286, 363, 474, 572, 682

• 474

• 572

• 682

• 154

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

415.

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?

• $\frac{25\mathrm{\pi }}{1} {\mathrm{cm}}^2$

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

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

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

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