The figure above shows an infinite series of triangles, in which r₁ > r₂ > r₃ .... What is the total length of the solid line segments in the figure?

• $\frac{{\mathrm{r}}_1}{{\mathrm{r}}_2} + \frac{{\mathrm{r}}_2}{{\mathrm{r}}_3} + .....$

• $\frac{{\mathrm{r}}_1^2}{{\mathrm{r}}_1 - {\mathrm{r}}_2}$

• $\frac{{\mathrm{r}}_2^2}{{\mathrm{r}}_1 + {\mathrm{r}}_2}$

• $\frac{{\mathrm{r}}_1 - {\mathrm{r}}_2}{{\mathrm{r}}_1^2}$

If a_i, b_i, and c_i are distinct, how many terms will the expansion of the product (a₁ + a₂ + a₃) (b₁ + b₂ + b₃ + b₄) (c₁ + c₂ + c₃ + c₄ + c₅) contain?

• 12

• 30

• 23

• 60

The above plot depicts the number of research publications of a scientist along with the number of citations.

Which of the following statements is not correct?

• In the year 2012, 50% more papers were published but citations decreased by 25%.

• In the year 2012, 100% more papers were published but citations were 75% of the number of papers in that year.

• The papers published in the year 2011 are 33.33% of the total number of papers in both years.

• The total number of citations for both years is 16.66% more than the total number of papers.

The next number of the sequence 1, 5, 14, 30, 55, ..., is

• 85

• 90

• 91

• 95

What is the maximum sum of the numbers of Saturdays and Sundays in a leap year?

• 104

• 105

• 106

• 107

Two trains of lengths 150 m and 250 m pass each other with constant speeds on parallel tracks in opposite directions. The drivers and guards are at the extremities of the trains. The time gap between the drivers passing each other and first driver-guard pair passing each other is 30 s. How much later will the other driver-guard pair pass by?

• 10 s

• 20 s

• 30 s

• 50 s

In a room, we have one grandfather, two fathers, two sons and a grandson. the age of one father is seven times the age of his son. The age of the other father is twice his son's age. Assuming that there are only3 people in the room and the grandfather is 70 years old, how old is the grandson?

• 1

• 2

• 5

• Cannot be determined

A hemispherical bowl is being filled with water at a constant volumetric rate. the level of water in the bowl increases

• in direct contact to time

• in inverse proportion to time

• faster than direct proportion to time

• slower than direct proportion to time

Equal masses of two liquids of densities 6 kg/m³ and 4 kg/m³ are mixed thoroughly. The density of the mixture is

• 4.8 kg/ m³

• 5.0 kg/ m³

• 5.2 kg/ m³

• 5.4 kg/ m³

180.

Two points A and B on the surface of the Earth have the following latitude and longitude coordinates.

A : 30° N, 45° E

B : 30° N, 135° W

If R is the radius of the Earth, the length of the shortest path from A to B is

• $\frac{\sqrt{3}}{2}\mathrm{\pi R}$

• $\frac{\mathrm{\pi R}}{3}$

• $\frac{\mathrm{\pi R}}{6}$

• $\frac{2\mathrm{\pi R}}{3}$