Given
One angle of an isoceles triangle is 70.
Two angles are same.
Therefore the possibilities for the other two angles are 70, 40 (or) 55, 55.

No, It is not possible with angles 90°, 90°, 0°.
Because there cannot be two right angles in a triangle

All angles are right angles two triangles formed.
Both are Isoceles right angled triangle.

Isoceles right angled Triangle
Two angles are equal and one angle is right angle.
Therefore the three angles are 45^o, 45^o, 90^o.

i)

3 angles are acute and 2 sides are equal.
Type: Isoceles acute angled triangle.
ii)

Three sides are different and one angle is right angle.
Type: Scalene right angled triangle.
iii)

Two sides are equal and one angle is obtuse.
Type: Isoceles obtuse angled triangle.
iv)

Two sides are equal and one angle is right angle.
Type: Isoceles acute angled triangle.
v)

Three sides are equal and Three angles are acute.
Type: Equilateral right angled triangle.
vi)

All sides are different and one angle is obtuse.
Type: Scalene obtuse angled triangle.

i)
 
All sides are equal.
Type: Equilateral triangle.
ii) 

Three sidesare different lengths,
Type: Scalene triangle .
iii)

Two sides are equal,
Type : Isoceles triangle.
iv)
 
Three sides are different lengths.
Type: Scalene triangle.

c.p T.V. = Rs. 12,000
He spent = Rs. 1,000
= Rs. 13,000
m.p = Rs. 15,000
Discount = Rs. 1,000
c.p Fridge = Rs. 11,000
Painting Charges = Rs. 1,500
= Rs. 12,500
m.p = 15,500
Discount = Rs. 1,000
c.p of tv and fridge
= 13,000 + 12,500
c.p = Rs. 25,500
m.p = Rs. 15,000 + 15,500 = Rs. 30,500
Discount = Rs. 1,000 + Rs. 1,000 =
= Rs. 2000
Therefore s.p = m.p - Discount
= 30,500 - 2,000 = Rs. 28,500
s.p = Rs. 28,500
Here, s.p > c.p
Therefore profit = s.p - c.p
= 28,500 - 25,500
Therefore Profit = Rs. 3,000

Given
Profit = Rs. 50
1 dozen Pens Rs. 216
Therefore 12 pens = 216
He paid = 48
c.p = Rs. 274
s.p = c.p + profit
= Rs. 274 + Rs. 50
s.p = Rs. 324
Discount = Rs. 2
1 dozen = 2 \(\times\)12 = Rs. 24
m.p = s.p + discount
= Rs. 324 + Rs. 24
12 pens = Rs. 348
Therefore 1 pen = 348 / 12 = 29
Therefore the m.p of each pen = Rs. 29

Given
Cost of Scientific Calculator = Rs. 750.
Battery = Rs. 100
He had spent = Rs. 50
Total = Rs. 900
Therefore c.p = Rs. 900
s.p = Rs. 850
Here, c.p > s.p
Therefore Loss = c.p - s.p
= Rs. 900 - Rs. 850
= Loss = Rs. 50

Given
m.p = Rs. 300
s.p = Rs. 275
Discount = m.p - s.p
= Rs. 300 - Rs. 275 = Rs. 25

Given
Sugan bought a Jeans Pant = Rs. 750
c.p = Rs. 750
s.p = Rs. 710
Here, c.p > s.p
Loss = c.p - s.p = Rs.750 - 710
Therefore Loss = Rs. 40

C.P. = Rs. 55,000
Profit = Rs. 5,500
Profit = S.P. - C.P.
\(\Rightarrow\) Rs. 5,500 = S.P. - Rs. 55,000
\(\Rightarrow\) S.P.= Rs. 5,500 + Rs. 55,000 = Rs. 60,500

Given
Lunch Break = 1 hour
From 10 a.m. to 5.45 p.m = 12.00 - 10:00 = 2.00 +  5.45 = 7.45
lunch break - 1.00 = 6.45
Also given, the post office works for 6 days a week.
Total duration of working hours in a week = 6.45 \(\times\) 6
= 6 hours 45 min \(\times\) 6 = 36 hours 270 minutes
= 270/60 = 4 30/60 = 4 1/2 hr.
= (36 + 4) hours 30 min.
Total Working hours = 40 hours 30 min.

Length of the line segments are
AB = 2 cm, BC = 2.5 cm, CD = 2.5 cm DE = 2 cm.
1^st way distance = AB + BC + CD + DE = [2 + 2.5 + 2.5 + 2]cm = 9 cm
2^nd way distance = AG = 2.5 cm, GF = 1.7 cm, F to E = 1.7 + 2.8 = 4.5 cm
= (2.5 + 1.7 + 4.5) cm = 8.7 cm
3^rd way distance = AH = 3 cm, HI = 2.3 cm, IJ = 1 cm, JE = 3.2cm
= [3 + 2.3 + 1 + 3.2] cm = 9.5cm
Therefore the shortest way to reach the grains = 2^nd way (middle way 8.7 cm distance)

The saplings are planted at a distance = 2 m 50 cm = 2 m 50 cm
The road of length = 5 km = 5000 m
= 5000 \(\times\) 100
= 500000 cm
No. of Saplings = 2560

= 2000 saplings will be planted by him.
Therefore 560 saplings are left.

Republic day = January 26^th 
Kalvi Valarchi day = July 15^th

(31 -25) (2020 is leap year)
Number of days between Republic day and Kalvi Valarchi day = 172 days. 

(i) 2.00 hours
Answer: 2 a.m.
(ii) 08.45 hours
Answer: 8.45 a.m.
(iii) 21.10 hours - 12.00
Answer: 9.10 p.m.
(iv) 11.20 hours
Answer: 11.20 a.m.
(v) 00.00 hours
Answer: 12.midnight

weight of a tablet = 650 mg
\(=650.0\times \frac { 1 }{ 1000 } g\)      (1 g = 1000 mg)
 (\(\frac { 1 }{ 1000 } \)g = 1 mg)

Given: the statement is Every even number greater than 2 can be expressed as the sum of two prime numbers.
To verify : This statement for every even number upto 16.
Even numbers are 4, 6, 8, 10, 12, 14, 16
Now 4 = 2 + 2, 6 = 3 + 3,
8 = 3 + 5,
10 = 3 + 7 (or) 5 + 5
12 = 5 + 7
14 = 7 + 7 (or) 3 + 11
16 = 5 + 11 (or) 3 + 13
\(\therefore\) "Every even number greater than 2 can be expressed as the sum of two prime number" is true.

Given LCM = 210, HCF = 14
Let the two numbers be x and y.
x * y = HCF(x,y) x LCM(x,y) = 210 \(\times\) 14
Product of 2 given numbers == 2940
Therefore two pairs possible,

Given Sum of my digits is 10.
Factors of 57 are 1, 3, 19, 57
Here, 19 and 57 are two digit prime numbers.
Therefore 19 = 1 + 9 = 10.
Therefore I am 19.

Answer : Given statement is True.
Example : Let the composite number be 4.
4 has 3 factors namely, 1, 2 and 4.
Now, let 6 be the another composite.number,
6 has ⇾ 1, 2, 3, 6 4 factors.
Therefore Each of the composite numbers has atleast three factors.

The given prime number 13 can be reversed
to get another prime number 31.
Similarly, other any such pairs are (17, 71), (37, 73) and (79, 97)

The smallest 3 digit composite number = 100
The biggest three digit composite number = 999

31 = 5+7+19 (find another way, if possible)
55 = 3 + 23+29