Mathemagic! Trivia Quiz

Answer: 204

This one may seem easy to you, but it is not that easy!

Many may know that number of squares in a chessboard is 64. But, the question is "total number of squares in a chessboard".
We only count the single squares, But not the combined ones. Let me explain(please draw a chessboard in a paper for your convenience to understand it).
First, as usual, count the single squares on the chessboard. There are 8 horizontally and 8 vertically, i.e,
8 x 8 = 64 in total.

Then, count the squares, made by combining 4 single squares. There are 7 horizontally and 7 vertically, i.e,
7 x 7 = 49 in total.

Then, count the squares, made by combining 9 single squares. There are 6 horizontally and 6 vertically, i.e,
6 x 6 = 36 in total.

Then, count the ones, made by combining 16 single squares. There are
5 x 5 = 25 in total

Continue in this pattern.

It may appear:

8 square + 7 square + 6 square + 5 square + 4 square + 3 square + 2 square + 1,
which makes a total of 204 squares, which is the answer.

Answer: 6 : 1

When the cylinder of volume V is cut into half, the volume of the half cylinder obtained becomes V/2, i.e, half the volume of the full cylinder.

The volume of the cone made from the half cylinder, with the dimensions of the half cylinder, is 1/3rd of the volume of the half cylinder.

Hence, volume of the cone = 1/3 x V/2 = V/6
= 1/6 V

Therefore, the ratio is 6 : 1, which is the answer.

Answer: Rs. 8

Cost of 12(1 dozen) apples = Rs.12
Cost of 1 apple = 12/12 = Rs.1
Hence, cost of 2 apples = 1 x 2 = Rs.2

Cost of 10 bananas = Rs.20
Cost of 1 banana = 20/10 = Rs.2
Hence, cost of 3 bananas = 2 x 3 = Rs.6

Therefore, Rs.6 + Rs.2 = Rs.8, which is the answer.

Answer: area(PQB) = 3/8 area(ABCD)

This question is a tricky one, but not so difficult. Let me explain (you may want to draw the figure to see more clearly).

area(APB) = 1/4 area(ABCD) = 2/8 area(ABCD)
area(BQC) = 1/4 area(ABCD) = 2/8 area(ABCD)

Join A and C to make the diagonal AC.
According to the midpoint theorem,
area(PDQ) = 1/4 area(ACD)
Hence, areaPDQ) = 1/8 area(ABCD)

Hence, area(APB) + area(BQC) + area(PDQ) = 2/8 + 2/8 + 1/8 = 5/8.
1 - 5/8 = 3/8.

Hence, the answer is area(PQB) = 3/8 area(ABCD).

Answer: 2 (l + b) x h + l x b

Side surface area of a cuboid = 2(l + b) x h
Area of the ceiling = l x b

Hence, the answer is 2(l + b) x h + l x b.

Answer: 12.8

40% of 4000 = 40/100 x 4000 = 1600
40% of 1600 = 40/100 x 1600 = 640
20% of 640 = 20/100 x 640 = 128
10% of 128 = 10/100 x 128 = 12.8

Hence, the answer is 12.8.

Answer: All of these

According the trigonometric identity,
(sin x)² + (cos x)² = 1

the number which is neither prime nor composite is 1.

Also, the other trigonometric identities are (sec x)² - (tan x)² = (cosec x)² - (cot x)² = 1


Hence, As all the options equal to 1, the answer is 'All of these".

Answer: 1 / square root of 2

This is a trigonometric problem, using compound formulas of trigonometry. It is very easy. Let me explain.

sin 135 degree
= sin(90 + 45)
Using the formula, sin(A + B) = sin A cos B + cos A sin B

Therefore,
sin(90° + 45°)
= sin 90° cos 45° + cos 90° sin 45°
= 1 x 1/square root of 2 + 0 x 1/square root of 2
= 1/square root of 2 + 0
= 1/square root of 2

Hence, 1/square root of 2 is the required answer.

Quite easy right?

Answer: 1, 3, 3, 3, 5, 3

Mode = the data which occurs maximum number of times value = 3.
Median = average of the central values = 3 + 3 / 2 = 3.
Mean = Average of all the values = 1 + 3 + 3 + 3 + 5 + 3 = 18 / 6 = 3.

Hence, the mean, median and mode are same.

Answer: 2

2 is the only even prime number!