A cartwheel rolls along a straight line. If the distance covered is equal to the diameter of the wheel, what is the angle through which the wheel has turned?

• 90°

• between 90° and 120°

• between 120° and 150°

• between 150° and 180°

In a class of 10 students, 3 failed in History, 6 failed in Geography and 2 failed in both. How many passed in both the subjects?

• 1

• 2

• 7

• 0

3.

As shown in the diagram above, a sphere is placed on the top of an incline. It rolls down the incline without slipping in exactly 50 turns. The radius of the sphere is

• $\left(\frac{5}{\mathrm{\pi }}\right)\mathrm{cm}$

• $\left(\frac{5}{\mathrm{\pi }}\right)\mathrm{m}$

• $\left(\frac{10}{\mathrm{\pi }}\right) \mathrm{cm}$

• 10 cm

A set of concentric circles if integer radii 1, 2, ...., N is shown in the figure above. An ant starts at point A₁, goes around the first circle, returns to A₁, moves to A₂, goes round the second circle, returns to A₂, moves to A₃ , and repeats this until it reaches A_N. the distance covered by the ant is

• N(N + 1)$\mathrm{\pi }$

• 2N$\mathrm{\pi }$ + N

• $\mathrm{\pi }$(N + 1) N + N - 1

• $\mathrm{\pi }$(N - 1) N + N - 1

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

The distribution of heights and weights in a population is shown above in a 2-parameter scatter plot. The size of the square is proportional to the number of persons having a particular combination of weight and height. Which statement best describes the trend in the population?

• Height and weight are strongly correlated.

• Height and weight are anticorrelated.

• Large heights do not imply proportionately large weights.

• Height and weight are independent characteristics.

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

• 104

• 105

• 106

• 107