The sum of (5a+ 6c) and(3a+9c)=5a+6c+3a+9c=8a+15c

The difference of (5a+ 6c) and(3a+9c)=(5a+6c)-(3a+9c)=5a+6c-3a-9c=2a-3c

The sum of (5a+ 6c) and(3a+9c)=5a+6c+3a+9c=8a-15c

Sets A and B are overlapping sets

.Sets A and B are disjoint sets.

n(A)= N(B)=3

$$A\sim B$$  but  $$A\ne B$$  

Sets P and Q are Overlapping sets.

n(P)=4 ,n(Q)=5 ,so $P\ne Q$

Sets P and Q are disjoint sets.

Complementary angle of 80 degree =90-80=10 degree

Supplementary angles of 30 degrees =180-30=150 degree.

40 and 50 degree are complementary of each other's.

120 and 60 degree are Supplemetary of each other

0 degree and 90 degree are supplemeary.

if lines are Parallel corresponding angles must equal.

if lines are Parallel Alternate angles must equal.

if lines are Parallel sum of cointerior angles must 180.

if lines are Parallel corresponding angles mustnot equal.

Factors of 15={1,3,5,15}

Factors of 18={1,2,3,6,9,18}

common factors of 15 and 18={1,3}

H.C.F.=3

Factors of 15={1,3,5,15}

Factors of 18={1,2,3,6,9,18}

common factors of 15 and 18={1,3}

H.C.F.=1

Factors of 12={1,2,3,4,6,12}

Factors of 18={1,2,3,6,9,18}

common factors of 12 and 18={1,2,3,6}

H.C.F.=6

Factors of 30={1,2,3,5,610,15,30}

Factors of 24={1,2,3,4,6,8,12,24}

common factors of 30and 24={1,2,3,6}

H.C.F.=6

What is total surface area of above cuboid?

Solution:

lengh of cuboid (l)= 5 cm,

breadth of cuboid (b)= 3 cm

height of cuboid (h)= 4 cm

Total surface area of cuboid = ?

Total surface area of cuboid = 2(lb+bh+lh)

=2(5x3+3x4++5x4)cm²

= 2(15+12+20)cm²

= 2(47)cm²

=94 cm²

What is volume of above cuboid?

Solution:

lengh of cuboid (l)= 5 cm,

breadth of cuboid (b)= 3 cm

height of cuboid (h)= 4 cm

Volume of cuboid = ?

Volume of cuboid = lxbxh

= 5x3x4 cm³

= 60 cm³

What is base area of above cuboid? or what is area of rectangle CDEF

Solution:

lengh of cuboid (l)= 5 cm,

breadth of cuboid (b)= 3 cm

base area of cuboid(A) = ?

A= lxb

= 5 cm x 3 cm

= 15 cm²

What is base area of above cuboid? or what is area of rectangle CDEF

Solution:

lengh of cuboid (l)= 5 cm,

breadth of cuboid (b)= 4 cm

base area of cuboid(A) = ?

A= lxb

= 5 cm x 4 cm

= 20 cm²

The square root of 625 = $\sqrt{625\ }=\sqrt{5\times5\times5\times5}\ =5\times5=25$

The square root of 900 = $\sqrt{900}=\sqrt{2\times2\times3\times3\times5\times5}\ =2\times3\times5=30$

The square root of 121 = $\sqrt{121}=\sqrt{11\times11}=11$

The square root of 400= $\sqrt{400}=\sqrt{2\times2\times2\times2\times5\times5}=2\times5=10$

Q) What is cube of 4 ?

Solution : cube of 4= 4³= 64

Q) What is cube root of 64 ? Solution : cube root of 64 =4

Q) What is square root of 49 x 25 . Solution : square root of 49 x 25 = $$\sqrt{49\ }\times\sqrt{25}=\sqrt{7\times7}\ \times\sqrt{5\times5}\ =7\times5\ =35$$ 7X5=35

What is cube root of 125 ?

Solution : cube root of 125 =25

$$Cube\ root\ of\ 8\ =2$$

Cube of 2 = 8

Cube of 3 = 27

cube root of 27 =3

Cube of 4 =16

Convert $1010_2$ in decimal $solution:1010_2=1\times2^3+0\times2^2+1\times2^1+0\times2^0$ =1x8+0x4+1x2+0x1=8+0+2+0=10

Convert $1204_5\ into\ decimal\ number\ .$ $Solution:1204_5=1x5^3+2\times5^2+0\times5^1+4\times5^o=1\times125+2\times25+0\times5+4\times1=125+50+0+4=179$

Add : $1001_2+110_2=1111_2$

Add: $2_5+1_5=3_5$

Add: $3_5+2_5=5_5$

What is cube of 2?

Solution: cube of 2=2³ =2X2X2=8

What is cube of 1 ?

Solution: cube of 1=1³=1X1X1=1

What is cube root of 8?

Solution: cube root of 8 = 2

What is cube root of 27?

Solution: cube root of 27 = 9

सर्वव्यापक समूह (U) काे उपयुक्त  उपसमूहहरू:

(proper subsets of set U are:)

A={ a},B={a,o}

सर्वव्यापक समूह (U) काे अनुपयुक्त  उपसमूह:

(improper subsets of set U is:)

D={a,e,i,o,u}

सर्वव्यापक समूह (U) काे उपयुक्त  उपसमूहहरूकाे सङ्ख्या( Number of proper subsets of set U are): $$2^n$$  -1

$$=^{2^{5^{ }}}$$ -1 

=32-1=31

सर्वव्यापक समूह (U) काे उपयुक्त  उपसमूहहरूकाे सङ्ख्या( Number of proper subsets of set U are): $$2^n$$  +1

$$=^{2^{5^{ }}}$$ +1 

=32+1=33

Name of figure (I) is

Acute angle And ,

Name of figure (II) is

right angle.

Name of figure (II) is

Acute angle. And

Name of figure (III) is

reflex angle.

Name of figure (II) is

right angle .And,

Name of figure (Iv) is

straight angle.

Name of figure (III) is

Obtuse angle .And,

Name of figure (v) is

reflex angle.

$$\angle ABD\ \ and\ \angle\ DBC\ are\$$   $$Adjacent\ angles.$$  

$$\angle GHE\ and\ \angle GHF\ are$$  

$$Adjacent\ angles.$$  

Sum of complementary angles equal to $$180^o$$   .And

Sum of supplementary angles equal to $$90^o$$  

Solution:

lengh of figure= 5

lengh of figure= 4

Area of figure= 5x4

20

Solution:

lengh of figure= 5

lengh of figure= 4

Perimeter of figure= 2(5+4)=2X9

=18

Solution:

lengh of figure= 5

lengh of figure= 4

Area of figure= 5+4

9

Solution:

lengh of figure= 5

lengh of figure= 4

Perimeter of figure= (5X4)=20

Sum of three angles of any type of triangle is 180°.

Obtuse angle triangle has only one angle more than 90°other two acute angle.

Right angle triangle has one angle exactly 90°other two acute angle.

Acute angle triangle has only one angle more than 90°.