Q1. The side of a triangle are in the ratio of 1/2:1/3:1/4 if the perimeter is 104 cm. What is the sum of the largest side & smallest side?
Ratio of side = 1/2:1/3:1/4
= 6 : 4 : 3
Let the side of triangle is 6x , 4x and 3x respectively.
Given that perimeter = 104 cm
6x + 4x + 3x = 104
x = 104/13
x = 8
sides are = 48 cm, 32 cm and 24 cm
Required answer = 48 cm + 24 cm
= 72 cm
Q2. The exterior angle of a polygon is 1/5 of the its interior angle. How many sides does the polygon have
Interior angle of polygon having n sides
Exterior angle = 2π/n
According to question,
(interior angle)/(exterior angle)=((n-2)π)/2π=5
n – 2 = 10
n = 12
Q3. What is (in unit square) the area at a triangle with side length 4 unit, 6 unit and 10 unit?
(d) None of these
The triangle is not possible (since sum of length of two sides > length of third side
Q4. If the perimeter of right angle triangle is 30 cm and its hypotenuse is 13 cm. What is the radius of the circle inscribed in a triangle?
(a) 2 cm
(b) 5 cm
(c) 1 cm
(d) None of these
In a right angle triangle,
In radius = semi perimeter-hypotenuse
= 15 – 13 = 2 cm
Q5. What is the relation between the circum radius and in radius in any triangle?
(a) R ≥ 2r
(b) R = 2r
(c) R ≤ 2r
(d) R < 2r
When R = circum radius
r = in radius
d = distance between circum centre and in centre
From equation (1) be obtain the inequality
R ≥ 2r
Q6. A seller fixes the marked price 50% more than cost price and gives a discount of 15%, and so he gets a profit of Rs. 165. Find the marked price of that article.
(a) Rs. 900
(b) Rs. 800
(c) Rs. 700
(d) Rs. 1000
Let the cost price = 100
Mark price = 150 Selling price = 150 × 85/100 = 127.5
Profit = 27.5
In a mark price of 150 profit = 27.5
Mark price for profit of 165 = (150 × 165)/27.5 = 900
Q7. If the area of a square is increased by 100%, then the percentage increase in the length of its diagonal is
Assume some values and solve the question.
Assume original area = 100 ⇒ Diagonal = 2√10
New area = 200 ⇒ Diagonal = 20
Percentage increase = 41.4%
Q8. On Independence Day, if 30 children were made to stand in a column, 16 columns could be formed. If 24 children were made to stand in a column, how many columns could be formed?
Let the number of column =x, when 24 student stands in one column.
Total students = 30 × 16 = 480 children
24 × x = 480
x = 20 column
Q9. At the start of seminar, the ratio of the number of male participants to the number of female participants was 3:1. During the tea break, 16 participants left and 6 more female participants registered. The ratio of the male to the female participants became 2 : 1. What was the total number of participants at the start of the seminar?
Let the number of male participants and the number of female participants is 3n and n respectively
During the tea break number of participants left,
And female participants=n+6
so total number of participants=4*28=112
Q10. Each edge of a cube is increased by 40%. What is the percentage increase in its volume?
Volume of cube = a3 (where a = length of a edge)
When each edge is increased by 40%
⇒ Length of the new edge = 1.4a
⇒ Volume of new cube = (1.4a)3 = 2.744a3
⇒ Required % increase = [(2.744a3 – a3)/a3] × 100%