1.
The average yield of a product in different years is shown in the histogram. If the vertical bars indicate variability during the year, then during which year was the percent variability over the average of that year the least?
2.
A rectangular sheet ABCD is folded in such a way that vertex A meets vertex C, thereby forming a line PQ.Assuming AB = 3 and BC = 4, find PQ. Note thatAP = PC and AQ = QC.
3.
The density of a rice grain is 1.5 g/cc and the bulk density of the rice heap is 0.80 g/cc. If a 1-liter container is completely filled with rice, what will be the approximate volume of pore space in the container?
Using allegation Formula: Quantity of Cheaper/ Quantity of dearer = (high value-mean value)/(mean value-low value) volume of pour Space/Volume of rice = 1.5-0.80.8-0 = 78So volume of pour space = 1000/15?7 = 466.66 approximately 465.
4.
A peacock perched on the top of a 12 m high tree spots a snake moving towards its hole at the base of the tree from a distance equal to thrice the height of the tree. The peacock flies towards the snake in a straight line and they both move at the same speed. At what distance from the base of the tree will the peacockcatch the snake?
5.
The map given below shows a meandering river following a semi-circular path, along which two villages arelocated at A and B. The distance between A and B along the east-west direction in the map is 7 cm. What isthe length of the river between A and B in the ground?
Distance of river on ground = perimeter of semi circle
= ? x r = 3.14 x 3.5 = 11 cm
According to Scale = 11 x 50,000 cm = 5,50,000 cm or 5.5 km
6.
How many nine-digit positive integers are there, the sum of squares of whose digits is 2?
7.
A bird leaves its nest and flies away. Its distance x from the nest is plotted as a function of time t. Which ofthe following plots cannot be right?
Given that
y = x
y = 1 - x and x = 0AB = BC
& y = x = m1 = 1
y = -x + 1 = m2 = -1
so m1 m2 = -1 , triangle is right - angled.
8.
What is the next number in the following sequence?39, 42, 46, 50, ...
The given sequence will follow the pattern 3, 4 4, 3 ..........
These are the difference between two consecutive numbers of the sequence.
So.
9.
A solid cylinder of basal area A was held dipped in water in a cylindrical vessel of basal area 2A verticallysuch that a length h of the cylinder is immersed. The lower tip of the cylinder is at a height h from the waterin the vessel when the cylinder is taken out?
Volume of vessel upto height 2h is equal to 2a * 2h ...(1)
Volume of vessel after removing cylinder = 2A * h? ...(2)
where h? = new height of water level.
Volume of water =Volume of vessel =Volume of solid
after removing upto height 2h Cylinder upto height cylinder h
? 2A * h? = 2A * 2h ? A.hh? = h
10.
How many pairs of positive integers have gcd 20 and lcm 600?(gcd = greatest common divisor; lcm = least common multiple)
gcd = 20lcm = 600
lcm =
x * y = 600 ? 20
x * y = 2
5
? 3
1
? 5
3
x y
5
1
? 2
2
5
2
? 2
3
? 3
5
2
? 2
2
5
1
? 2
3
? 3
5
2
? 2
3
5
1
? 2
2
? 3
5
2
? 2
2
? 3 5
1
? 2
3