Using the suitable identities, evaluate the following :
(103) ²  .

5

(a)

Find the value of the following :
\(\frac { (151+149)^{ 2 }-(151-149)^{ 2 } }{ 151\times 149 } \)

5

(a)

Find the value of p,if 
px=\(\frac { 4{ x }^{ 2 }-7x-15 }{ x-3 } -5\)

5

(a)

if mean of some observations is (4x ²-9) and their sum is 16x⁴ -81. Then , find the number of observations

5

(a)

If perimeter of square 4x² -36 unit. Then, find the area of the square? Find the area, if x=2

5

(a)

Factorise p³-3p²+2p-6-6pq+3q

5

(a)

Factorise (m⁸-n⁸) and after this divide by (m⁴+n⁴)

5

(a)

Verify the following expressions:
(i) (ab + bc) (ab - bc) + (bc + ca) (bc - ca)+(ca + ab)(ca -ab) = 0
(ii) (a + b + c)(a² + b² + c² - ab - bc - ca)= a³ + b³ + c³ - 3abc

5

(a)

The product of two expressions is x⁵ + x³ + x. If one of them is x² + x + 1,find the other expression.

5

(a)

Factorise the following expressions:
p⁴+ q⁴ + p²q²

5

(a)

The curved surface area of a cylinder is 2\(\pi \) (y² + 7y + 12) and its radius is (y + 3). Find the height of the cylinder. (CSA of cylinder = 2\(\pi \)rh)

5

(a)

A farmer has squared field of area x² - 26x + 169 square units. He has one son and one daughter. He divides the field into two equal parts between his son and daughter. Then,
(a) find the side of the field in terms of x.
(b) find the perimeter of field, if x = 15.
(c) what type of value depicted by farmer?

5

(a)