Insert the appropriate symbol ∈ (belongs to) or ∉ (does not belong to) in the blanks.

Verify A∩(B∪C)=(A∩B)∪(A∩C) using Venn diagrams.

If A = {11,13,14,15,16,18}, B = {11,12,15,16,17,19}, and C = {13,15,16,17,18,20}, then verify \(A\cap (B\cup C)=(A\cap B)\cup (A\cap C)\).

Verify A -(BUC) = (A-B)∩(A-C) using Venn diagrams.

Express the following decimal expression into rational numbers -\(21.21\overline {37}\)

Find the value of a and b if \(\frac { \sqrt { 7 } -2 }{ \sqrt { 7 } +2 } \) = a\(\sqrt{7}\) + b

If p(x) = 4x²-3x+2x³+5 and q(x) = x²+2x+4 find p(x)+q(x)

Rewrite the following polynomial in standard form.
\(\sqrt { 2 } x^{ 2 }-\frac { 7 }{ 2 } { x }^{ 4 }+x-5{ x }^{ 3 }\)

Rewrite the following polynomial in standard form.
\({ y }^{ 2 }+\sqrt { 5 } { y }^{ 3 }-11-\frac { 7 }{ 3 } y+{ 9y }^{ 4 }\)

Subtract the second polynomial from the first polynomial and find the degree of the resultant polynomial
p(x) = 7x²+ 6x -1 q(x) = 6x - 9

Subtract the second polynomial from the first polynomial and find the degree of the resultant polynomial
h(z) = z⁵-6z⁴+z f(z) = 6z²+10z-7

What must be subtracted from 2x⁴+4x²-3x+7 to get 3x³-x²+2x+1?

Find the quotient and the remainder when (5x²-7x+2) ÷ (x-1)

Find quotient and the remainder when f(x) is divided by g(x)
f(x) = x³ + 1, g(x) = x+1

Find the quotient and remainder of the following. (4x³ + 6x² – 23x +18)÷(x+3)

Find the quotient and remainder of the following.
(–18z + 14z² + 24z³ +18)÷(3z+4)

What is the remainder when x²⁰¹⁸ + 2018 is divided by x–1

Find the remainder when f(x) = x³ + 3x² + 3x + 1  is divided by x+1.

Write the following polynomials in standard form.

S.No	Polynomial	Standard form
1	5m4 -3m + 7m2 + 8
2	\(\frac { 2 }{ 3 } y+{ 8y }^{ 3 }-12+\sqrt { 5 } { y }^{ 2 }\)
3	12p2 -8p5 -10p4 -7

(i) Prove that (x - 1) is a factor of x³- 7x² + 13x - 7
(ii) Prove that (x + 1) is a factor of x³ + 7x² + 13x + 7

Solve the system of linear equations x + 3y = 16 and 2x − y = 4 by substitution method.

Solve by cross-multiplication method
(i) 8x − 3y = 12 ; 5x = 2y + 7
(ii) 6x + 7y −11 = 0 ; 5x + 2y = 13
(iii) \(\frac { 2 }{ x } +\frac { 3 }{ y } =5;\frac { 3 }{ x } -\frac { 1 }{ y } +9=0\)

In the figure, AB is parallel to CD, find x

Consider the given pairs of triangles and say whether each pair is that of congruent triangles. If the triangles are congruent, say ‘how’; if they are not congruent say ‘why’ and also say if a small modification would make them congruent:

Show that the following points A(3, 1), B(6,4) and C(8, 6) lies on a straight line.