If A, B and C are overlapping sets, then draw Venn diagram for the following sets:
(i) (A-B)\(\cap \)C
(ii) (A\(\cup \)C)-B
(iii) A-(A\(\cap \)C)
(iv) (B\(\cup \)C)-A
(v) A\(\cap \)B\(\cap \)C

If A = {y : y =\(\frac { a+1 }{ 2 } \), a \(\in \) W and a ≤ 5}, B = {y : y =\(\frac { 2n-1 }{ 2 } \), n\(\in \)W and n < 5} and C =\(\left\{ -1,-\frac { 1 }{ 2 } ,1,\frac { 3 }{ 2 } ,2 \right\} \), then show that \(A-(B\cup C)=(A-B)\cap (A-C)\).

A survey of 1000 farmers found that 600 grew paddy, 350 grew ragi, 280 grew corn, 120 grew paddy and ragi, 100 grew ragi and corn, 80 grew paddy and corn. If each farmer grew atleast any one of the above three, then find the number of farmers who grew all the three.

A survey was conducted among 200 magazine subscribers of three different magazines A, B and C. It was found that 75 members do not subscribe magazine A, 100 members do not subscribe magazine B, 50 members do not subscribe magazine C and 125 subscribe atleast two of the three magazines. Find
(i) Number of members who subscribe exactly two magazines.
(ii) Number of members who subscribe only one magazine

In a party of 45 people, each one likes tea or coffee or both. 35 people like tea and 20 people like coffee. Find the number of people who
(i) like both tea and coffee.
(ii) do not like Tea.
(iii) do not like coffee

A and B are two sets such that n(A – B) = 32 + x, n(B – A) = 5x and n(A∩B) = x. Illustrate the information by means of a Venn diagram. Given that n(A) = n(B), calculate the value of x.

Express the rational number \(\frac { 1 }{ 33 } \) in recurring decimal form by using the recurring decimal expansion of \(\frac { 1 }{ 11 } \). Hence write \(\frac{71}{33}\) in recurring decimal form

Arrange surds in descending order:
(i) \(\sqrt [ 3 ]{ 5 } ,\sqrt [ 9 ]{ 4 } ,\sqrt [ 6 ]{ 3 } \)
(ii) \(\sqrt [ 2 ]{ \sqrt [ 3 ]{ 5 } } ,\sqrt [ 2 ]{ \sqrt [ 3 ]{ 5 } } ,\sqrt [ 3 ]{ \sqrt [ 4 ]{ 7 } } ,\sqrt { \sqrt { 3 } } \) 

Express the following rational numbers into decimal and state the kind of decimal expansion
(i) \(\frac { 2 }{ 7 } \)
(ii) \(-5\frac { 3 }{ 11 } \)
(iii) \(\frac { 22 }{ 3 } \)
(iv) \(\frac { 327 }{ 200 } \)

Find the product (4x – 5), (2x² + 3x – 6).

Without actual division , prove that f(x) = 2x⁴- 6x³ + 3x² + 3x - 2  is exactly divisible by x² – 3x + 2

The polynomial ax³ - 3x² + 4 and 2x³ - 5x +a when divide by (x - 2) leave the remainders p and q respectively if p - 2q = 4 ; find the value of a.

If both (x - 2) and \(\left( x-\frac { 1 }{ 2 } \right) \) are the factors of ax²+ 5x + b, then show that a = b.

Verify x³+y³+z³-3xyz = \(\frac{1}{2}\)[x+y+z][(x-y)²+(y-z)²+(z-x)²]

Factorise the following:
(i) x²+10x + 24
(ii) z²+ 4z -12
(iii) p²- 6p -16
(iv) t²+72 -17t
(v) y²-16 - 80
(vi) a²+10a - 600

Draw the graph for the following
(i) y = 3x - 1
(ii) \(y=\left( \frac { 2 }{ 3 } \right) x+3\)

Solve 2x = −7y + 5; −3x = −8y −11 by cross multiplication method.

ΔABC and ΔDEF are two triangles in which AB = DF, ∠ACB = 70°, ∠ABC = 60°, ∠DEF = 70° and ∠EDF = 60°. Prove that the triangles are congruent.

ABCD is a parallelogram Fig such that ∠BAD = 120^o and AC bisects ∠BAD show that ABCD is a rhombus.

Construct the circumcentre of the ΔABC with AB = 5 cm, ㄥA = 60⁰ and ㄥB = 80⁰. Also draw the circumcircle and find the circumradius of the ΔABC.

Let A(2, 2), B(8, –4) be two given points in a plane. If a point P lies on the X- axis (in positive side), and divides AB in the ratio 1: 2, then find the coordinates of P.

Verify that the following points taken in order form the vertices of a rhombus.
A (1, 1), B(2, 1),C (2, 2) and D(1, 2)

Find the values of the following:
(i) (cos 0⁰ + sin 45⁰ + sin 30⁰)(sin 90⁰ - cos 45⁰ + cos 60⁰)
(ii) tan²60⁰ - 2tan²45⁰ - cot²30⁰ +2sin²30⁰ + \(\frac { 3 }{ 4 } \) cosec² 45⁰

Find the value of the following: 
\(\frac { cos70° }{ sin20° } +\frac { cos59° }{ sin31° } +\frac { cos\theta }{ sin\left( 90°-\theta \right) } -8 \cos^{ 2 }60°\)

A farmer has a field in the shape of a rhombus. The perimeter of the field is 400 m and one of its diagonal is 120 m. He wants to divide the field into two equal parts to grow two different types of vegetables. Find the area of the field.