Question
Construct △ ABC, in which side BC = 7 cm, ∠B = 40° and AC - AB = 3 cm.
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Construct ∆XYZ, in which ∠Y = 58°, ∠X = 46° and perimeter of triangle is 10.5 cm.
In the adjoining figure, ABCD is a parallelogram in which $\angle\text{A}=60^{\circ}.$ If the bisectors of $\angle\text{A}$ and $\angle\text{B}$ meet DC at P, prove that
→- $\angle\text{APB}=90^{\circ},$
- AD = DP and PB = PC = BC,
- DC = 2AD.
If $\frac{a}{b}=\frac{b}{c}$ and $a, b, c>0$, then show that, : $(a+b+c)(b-c)=a b-c^2$
→In the adjoining figure, ABCD is a parallelogram in which $\angle\text{BAO}=35^{\circ},\angle\text{DAO}=40^{\circ}$ and $\angle\text{COD}=150^{\circ}.$ Calculate
→- $\angle\text{ABO},$
- $\angle\text{ODC},$
- $\angle\text{ACB},$
- $\angle\text{CBD}.$
In the neighbouring figure, percentage bar-diagram is given. Percentage expenses on different items of two families are given.
Answer the following questions based on it :
(i) Write the percentage expenses of every component for each family.
(ii) Which family spends more percent of expenses on food as compared to the other and by how much ?
(iii) What are the percentage expenses on other items ?
(iv) Which family shows more percentage expenses on electricity?
(v) Which family's percentage expense is more on education ?
Answer the following questions based on it :
(i) Write the percentage expenses of every component for each family.
(ii) Which family spends more percent of expenses on food as compared to the other and by how much ?
(iii) What are the percentage expenses on other items ?
(iv) Which family shows more percentage expenses on electricity?
(v) Which family's percentage expense is more on education ?
The investments (in ten crores of rupees) of Life Insurance Corporation of India in different sectors is given below:
Represent the above data with the help of a bar graph.
|
Sectors
|
Investment (in ten crores of rupess)
|
|
Central government securities
|
45
|
|
State government securities
|
11
|
|
Securities guaranteed by the government
|
23
|
|
Private sectors
|
18
|
|
Socially oriented sectors (plan)
|
46
|
|
Socially oriented sectors (Non–plan)
|
11
|
In a $\triangle\text{ABC},\angle\text{ABC}=\angle\text{ACB}$ and the bisectors of $\angle\text{ABC}$ and $\angle\text{ACB}$ intersect at O such that $\angle\text{BOC}=120^\circ.$ Show that $\angle\text{A}=\angle\text{B}=\angle\text{C}=60^\circ.$
→i. Write the subset relation between the sets.
P is the set of all residents in Pune.
M is the set of all residents in Madhya Pradesh.
I is the set of all residents in Indore.
B is the set of all residents in India.
H is the set of all residents in Maharashtra.
P is the set of all residents in Pune.
M is the set of all residents in Madhya Pradesh.
I is the set of all residents in Indore.
B is the set of all residents in India.
H is the set of all residents in Maharashtra.
ii. Which set can be the universal set for above sets ?
Kailash used to spend 85% of his income. When his income increased by 36% his expenses also increased by 40% of his earlier expenses. How much percentage of his earning he saves now ?
The diagonals of a quadrilateral ABCD are equal. Prove that the quadrilateral formed by joining the midpoints of its sides is a rhombus.