If the Universal set U = {x: x is a natural number and 1 ≤ x ≤ 9}
P = {x: 1 ≤ x ≤4}
Q = {2, 4, 6, 8}

Find (P ∪ Q)'

The table below shows the masses to the nearest kg of a group of market women.

The mode of the distribution is

The table below shows the frequency distribution of marks obtained by 40 students in a test


If a student is selected at random, find the probability that he scored 6 marks

Find the sum to infinity of the sequence 
 3, 2, 4/3, 8/9 , ...

Consider a cylinder of height h cm and radius <span id="MathJax-Element-70-Frame" class="mjx-chtml MathJax_CHTML" style="line-height: 0;text-indent: 0px;text-align: left;text-transform: none;font-style: normal;font-weight: 400;font-size: 18.72px;letter-spacing: normal;float: none;direction: ltr;max-width: none;max-height: none;min-width: 0px;min-height: 0px;border: 0px;margin: 0px;padding: 1px 0px;color: #4c4c4c;font-family: 'Open Sans', sans-serif;background-color: #ffffff" role="presentation" data-mathml="r=2π">r=2πr=2π cm as shown in the figure (not drawn to scale). A string of a certain length, when wound on its cylindrical surface, starting at point A and ending at point B, gives a maximum of n turns (in other words, the string’s length is the minimum length required to wind n turns).

The same string, when wound on the exterior four walls of a cube of side n cm, starting at point C and ending at point D, can give exactly one turn (see figure, not drawn to scale). The length of the string is

The points of intersection of the graphs of y = x² + 2 and y = 2x + 5 when drawn on the same set of axes are

Evaluate, without using calculator/tables,

(0.35 × 0.84) ÷ 0.0105

Cards are drawn from a pack of 52 playing cards one at a time.
Calculate the probability of drawing without replacement 3 diamonds

The  journey from Southampton to London usually takes a motorist 1 hour 30 minutes.
By increasing his average speed by 20km/hr, the motorist saves 15 minutes.
His usual speed in km/hr is

In the diagram, PQR and RST are two semicircles with diameters 7 cm and 3.5 cm respectively and PT = 3.5 cm respectively and PT = 3.5 cm.



The perimeter of the figure is

If x varies directly as the square root of n, and x = 9 when n = 9,
the value of x when n = 16/9 is

On a semicircle with diameter AD, chord BC is parallel to the diameter. Further, each of the chords AB and CD has length 2, while AD has length 8. What is the length of BC?

Change the given logarithmic expressions into exponential expressions: 
log_b (2x + 1) = 3

If B be a 4x5 type matrix, then what is the number of elements in the third column

Solve for x
(1 / 3) ^{x/2 - 2} = 9

How long will it take for a sum of money invested at 8% simple interest to double the original sum?

The real numbers m which satisfy the inequality
(3/5)m + 3 > (2/3 )m - 4 are

The average age of 4 children is 15 years. If the ages of their parents are added, the average age is 25.
What is the age of the father if he is 4 years older than his wife?

One of the two parallel sides of a trapezium is one-half the length of the other.
If the height of the trapezium is 7 cm and its area is 52.5 cm²,
the length of the parallel sides are

What is the common factor to the binomial expressions 4x²-9y², 8x³+27y³ and (4x+6y)²