A polygon is convex if, for every pair of points inside the polygon, the line segment joining them lies completely inside or on the polygon. Which one of the following is NOT a convex polygon?
A circular sheet of paper is folded along the lines in the directions shown. The paper, after being punched in the final folded state as shown and unfolded in the reverse order of folding, will look like \(\underline{\hspace{2cm}}\)
Details of prices of two items P and Q are presented in the above table. The ratio of cost of item P to cost of item Q is 3:4. Discount is calculated as the difference between the marked price and the selling price. The profit percentage is calculated as the ratio of the difference between selling price and cost, to the cost. The formula for Profit Percentage is: \[ \text{Profit \%} = \frac{\text{Selling Price} - \text{Cost}}{\text{Cost}} \times 100 \] The discount on item Q, as a percentage of its marked price, is:
A function, \( \lambda \), is defined by \[ \lambda ( p,q ) = \begin{cases} (p - q)^2, & \text{if } p \geq q, \\ p + q, & \text{if } p < q. \end{cases} \] The value of the expression \( \dfrac{\lambda ( -(-3 + 2), (-2 + 3) )}{( -(-2 + 1) )} \) is:
Five line segments of equal lengths, PR, PS, QS, QT and RT are used to form a star as shown in the figure above. The value of \( \theta \), in degrees, is
Statement: Either P marries Q or X marries Y Among the options below, the logical NEGATION of the above statement is:
Given two operators \( \oplus \) and \( \odot \) on numbers \( p \text{ and } q \) such that \[ p \oplus q = \frac{p^2 + q^2}{pq} \text{and} p \odot q = \frac{p^2}{q}, \] if \( x \oplus y = 2 \odot 2 \), then \( x = \)
The mirror image of the above text about the x-axis is
Corners are cut from an equilateral triangle to produce a regular convex hexagon as shown in the figure above. The ratio of the area of the regular convex hexagon to the area of the original equilateral triangle is
The number of minutes spent by two students, X and Y, exercising every day in a given week are shown in the bar chart above. The number of days in the given week in which one of the students spent a minimum of 10\% more than the other student, on a given day, is