Each student in a class of 35 plays atleast one game among chess, carrom and table tennis. 22 play chess, 21 play carrom, 15 play table tennis, 10 play chess and table tennis, 8 play carrom and table tennis and 6 play all the three games. Find the number of students who play (Hint: Use Venn diagram)
(i) chess and carrom but not table tennis
(ii) only chess
(iii) only carrom.

In a village of 100 families, 65 families buy Tamil newspapers and 55 families buy English newspapers. Find the number of families who buy
(i) Both Tamil and English newspapers.
(ii) Tamil newspapers only
(iii) English newspapers only.

Find any two irrational numbers between \(\sqrt { 2 } \) and \(\sqrt { 3 } \)

Represent \(3.4\bar { 5 } \) on the number line Upto 4 decimal places

Simplify the following using multiplication and division properties of surds:
(i) \(\sqrt { 3 } \times \sqrt { 5 } \times \sqrt { 2 } \)
(ii) \(\sqrt { 35 } \div \sqrt { 7 } \)
(iii) \(\sqrt [ 3 ]{ 27 } \times \sqrt [ 3 ]{ 8 } \times \sqrt [ 3 ]{ 125 } \)
(iv) \((7\sqrt { a } -5\sqrt { b } )(7\sqrt { a } +5\sqrt { b } )\)
(v) \(\left[ \sqrt { \frac { 225 }{ 729 } } -\sqrt { \frac { 25 }{ 144 } } \right] \div \sqrt { \frac { 16 }{ 81 } } \)

Classify the numbers as rational or irrational
(i) \(\sqrt { 10 } \)
(ii) \(\sqrt { 49 } \)
(iii) 0.025
(iv) \(0.7\overline { 6 } \)
(v) 2.505500555...
(vi) \(\frac { \sqrt { 2 } }{ 2 } \)

The area of a rectangle is x² + 7x + 12. If its breadth is (x + 3), then find its length.

If the polynomials f(x) = ax³ + 4x² + 3x –4 and g(x) = x³ – 4x + a leave the same remainder when divided by x–3, find the value of a. Also find the remainder.

Subtract the following polynomials and find the degree of the polynomial.

Sl.No	Polynomial	Difference	Degree of the resultant polynomial
1	p(x) = 5x3 - 3x +x2 + 4 q(x) = 7x 4x2+ 2
2	p(m) = 6m - 7 q(m) = 7m2 - 12 + 4m
3	p(x) = 4x2 - 6x3 - 4x + 6 q(x) = 8x3 + 2x2 - 2
4	r(y) = 7y4 + 5y2 + 4y s(y) = 2y - 3y2
5	p(m) = 12m3 -10m2 -7 q(m) = 7m3 + 5m2 - 3

Expand the following:
(i) (x+5)(x+6)(x+4)
(ii) (3x-1)(3x+2)(3x-4)

Factorise the following:
(i) am + bm + cm
(ii) a³- a²b
(iii) 5a -10b - 4bc + 2ac
(iv) x+y-1-xy

Factorise 2x² + 15x - 27

Find the quotient and remainder for the following using synthetic division:
(i) (x³+x²-7x-3) ÷ (x - 3)
(ii) (x³+2x²-x-4) ÷ (x + 2)
(ii) (3x³-2x²+7x-5) ÷ (x + 3)
(iv) (8x⁴-2x²+6x+5) ÷ (4x + 1)

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

Solve 3x − 4y = 10 and 4x + 3y = 5 by the method of cross multiplication.

Draw a triangle ABC, where AB = 8 cm, BC = 6 cm and ㄥB = 70⁰ and locate its circumcentre and draw the circumcircle.

In a parallelogram ABCD, the bisectors of the consecutive angles ∠A and ∠B intersect at P. Show that ∠APB = 90^o.

Which type of quadrilateral satisfies the following properties?
(i) Both pairs of opposite angles are equal in size.
(ii) Both pairs of opposite sides are equal in length.
(iii) Each diagonal is an angle bisector.
(iv) The diagonals bisect each other.
(v) Each pair of consecutive angles is supplementary.
(vi) The diagonals are equal.
(vii) Can be divided into two congruent triangles.

ABCD is a parallelogram such that AB is parallel to DC and DA parallel to CB. The length of side AB is 20 cm. E is a point between A and B such that the length of AE is 3 cm. F is a point between points D and C. Find the length of DF such that the segment EF divides the parallelogram in two regions with equal areas.

Iron rods a, b, c, d, e, and f are making a design in a bridge as shown in the figure. If a || b , c || d , e || f , find the marked angles between
(i) b and c
(ii) d and e
(iii) d and f
(iv) c and f

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.

Plot the points A(2, 4), B(–3, 5), C(–4, –5), D(4, –2) in the Cartesian plane  

Find the points of trisection of the line segment joining (−2, −1) and (4, 8)

Find the value of \(\theta\) if
(i) sin \(\theta\) = 0.9858
(ii) cos\(\theta\) = 07656

Find the area of a quadrilateral ABCD whose sides are AB = 8cm, BC = 15 cm, CD = 12 cm, AD = 25 cm and = 90°.