Draw Venn diagram and shade the region representing the following sets
(A – B)′

Find A∪B, A∩B, A–B and B–A for the following sets.
A = Set of all letters in the word “mathematics” and
B = Set of all letters in the word “geometry”

In a class of 50 students, each of the students passed either in mathematics or in science or in both. 10 students passed in both and 28 passed in science. Find how many students passed in mathematics only

Represent U= {1,2,3,4,5,6,7,8,9,10} A = {1,2,4,6,8,10} and B = {3,6,1,10} in venn-diagram, then find
(i) (A UB)'
(ii) (A ∩ B)'

Without actual division classify the decimal expansion of the following numbers as terminating or non-terminating and recurring.
\(-{11\over 75}\)

Divide \(\sqrt [ 9 ]{ 8 } \) by \(\sqrt [ 6 ]{ 6 } \).

Express the surds in the simple form \(\sqrt [ 3 ]{ 128 } \)

Can we write 0.25 as 0.250000 ...? Can a terminating decimal be written as a recurring decimal?

Write the coefficient of x² and x in each of the following polynomials \(\sqrt { 3 } { x }^{ 2 }+\sqrt { 2 } x+0.5\)

Expand the following using identities: (3x + 4y)²

Factorise the following : 25m^-2-16n²

Solve \(\cfrac { 1 }{ 3 } x-\cfrac { 5 }{ 2 } =6\)

Identify which ones are trapeziums and which are not.

In the given figure, AC is the diameter of the circle with centre O. If ㄥADE = 30°; ㄥDAC = 35° and ㄥCAB = 40°. Find
(i) ㄥACD 
(ii) ㄥACB 
(iii) ㄥDAE

The chord of length 32 cm is drawn at the distance of 12 cm from the centre of the circle. Find the radius of the circle

Find the value of X^o

Find the distance between the following pairs of points. (1, 2) and (4, 3)

The vertices of a triangle are (1, 2), (h, −3) and (−4, k). If the centroid of the triangle is at the point (5, −1) then find the value of \(\sqrt { { (h+k) }^{ 2 }+{ (h+3k) }^{ 2 } } \)

Find the coordinates of the point which divides, the line segment joining the point A (3,7) and B (-11, -2) in the ratio 5 : 1.

If the centroid of a triangle is at (10, -1) and two vertices are (3, 2) and (5, -11). Find the third vertex of a triangle.

Find the mode for the set of values 17, 18, 20, 20, 21, 21, 22, 22.

A set of numbers consists of five 4’s, four 5’s, nine 6’s,and six 9’s. What is the mode.

In a week, temperature of a certain place is measured during winter are as follows 26^oC, 24^oC, 28^oC, 31^oC, 30^oC, 26^oC, 24^oC. Find the mean temperature of the week.

In a class test in mathematics,10 students scored 75 marks,12 students scored 60 mark, 8 students scored 40 marks and 3 students scored 30 marks. Find the mean of their score.

Verify the following equalities :
sin²60⁰ + cos²60⁰ = 1

Find the area of a right triangle whose hypotenuse is 10cm and one of the acute angle is 24⁰24'

Find the six trigo'nometric ratios of the angle 0 using the diagram

From the given figure, find all the trigonometric ratios of angle \(\theta\).

The perimeter of a triangular plot is 600 m. If the sides are in the ratio 5:12:13, then find the area of the plot

A metallic cube with side 15 cm is melted and formed into a cuboid. If the length and height of the cuboid is 25 cm and 9 cm respectively then find the breadth of the cuboid

Using Heron's formula, find the area of a triangle whose sides are 41 m, 15 m, 25 m.

The outer dimensions of a closed wooden box are 10 cm by 8 cm by 7 cm, Thickness of the wood is 1 cm³. Find the total cost of wood required to make box if 1 cm³ of wood costs Rs. 2.00?

Frame two problems in calculating probability, based on the spinner shown here.

The probability of guessing the correct answer to a certain question is \(\frac { x }{ 3 } \). If the probability of not guessing the correct answer is \(\frac { x }{ 5 } \), then find the value of x.

Find the probability that a leap year selected at random will contain 53 Sundays.

A bag contains 3 red and 2 blue marbles. A marble is drawn at random. What is the probability of drawing a blue marble?