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

Draw Venn diagram for \(A\cap B\cap C\)

Verify \(n\left( A\cup B\cup C \right) \) = n(A) + n(B) +n(C) - \(n\left( A\cap B \right) -n\left( B\cap C \right) -n\left( A\cap C \right) -n\left( A\cap C \right) +\left( A\cap B\cap C \right) \) for the following A = {1,3,5,6,8} C = {1,2,3,6}

In an examination 50% of the students passed in Mathematics and 70% of students passed in Science while 10% students failed in both subjects. 300 students passed in atleast one subject. Find the total number of students who appeared in the examination, if they took examination in only two subjects.

Represent the following irrational numbers on the number line \(\sqrt { 6.5 } \)

Consider the ten real numbers
\(\sqrt { 2 } ,\frac { 7 }{ 9 } \),-1.32,\(\frac { 6 }{ 9 } ,-\sqrt { 3 } \) , 2.151155 .....,\(\frac { 23 }{ 6 } ,\frac { 48 }{ 5 } \), -3.010010001... and 12.353553555.
(i) Arrange the ten real numbers in the given boxes in ascending order.

(ii) Arrange the same numbers in the boxes given below in descending order

Find any three rational numbers between \(\frac { 1 }{ 2 } \) and \(\frac { 1 }{ 5 } \)

Represent \(-\frac { 2 }{ 11 } ,-\frac { 5 }{ 11 } and-\frac { 9 }{ 11 } \)on the number line.

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

Find the quotient and remainder when  5x³ - 9x² + 10x + 2 is divided by x + 2 using synthetic division

Factorise  2x³- x² - 12x - 9 into linear factors
 

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

Construct the right triangle PQR whose perpendicular sides are 4.5 cm and 6 cm. Also locate its circumcentre and draw the circumcircle.

Draw ΔABC, where AB = 6 cm, ㄥB = 110⁰ and BC = 5 cm and construct its Orthocentre.

Construct  \(\triangle\)ABC in which AB = BC = 8cm and \(\angle \)B =70^o. Locate its in centre and draw the incircle
 

Construct the centroid of \(\triangle\)PQR such that PQ = 9 cm, PQ = 7cm, RP = 8 cm.

Find the value of ‘a’ such that PQ = QR where P, Q, and R are the points whose coordinates are (6, –1), (1, 3) and (a, 8) respectively

Show that the given points (1, 1), (5, 4), (-2, 5) are the vertices of an isosceles right angled triangle.

Show that the point A (3,7) B (6, 5) and C (15, -1) are collinear.

The mid-points of the sides of a triangle are (5, 1), (3, −5) and (−5, −1). Find the coordinates of the vertices of the triangle.

Calculate the median for the following data:

Height (cm)	160	150	152	161	156	154	155
No. of Students	12	8	4	4	3	3	7

Find the mode for the following data

Marks	1-5	6-10	11-15	16-20	21-25
No. of students	7	10	16	32	24

In the class, weight of students is measured for the class records. Caculate mean weight of the students using direct method.

Weight in kg	15-25	25-35	35-45	45-55	55-65	56-75
No.of students	4	11	19	14	0	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 \(\theta\) 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°.

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.