Out of 500 car owners investigated, 400 owned car A and 200 owned car B, 50 owned both A and B cars. Is this data correct?

If A = {b,e,f,g} and B = {c,e,g,h}, then verify the commutative property of
(i) union of sets
(ii) intersection of sets.

In a group of 100 students, 85 students speak Tamil, 40 students speak English, 20 students speak French, 32 speak Tamil and English, 13 speak English and French and 10 speak Tamil and French. If each student knows atleast any one of these languages, then find the number of students who speak all these three languages.

If A = {-2,0,1,3,5}, B = {-1,0,2,5,6} and C = {-1,2,5,6,7} then show that A-(BUC) = (A-B)∩(A-C).

Identify the type of numbers needed to solve the simple equations given here. Question 1 and 2 are solved for you, as examples. (Perhaps -the number systems developed gradually depending on the needs of 'answers' during such problem solving!)

S.No	Equation	Solution	Type of number in the solution
1	x - 7 = 17	x = 24	Natural number
2	x + 5 = 5	x = 0	Whole number
3	x + 1 = 9
4	x + 9 = 1
5	7x = 19
6	5x = -3
7	x2 - 2 = 0

Rewrite the following polynomial in standard form.
\(7{ x }^{ 3 }-\frac { 6 }{ 5 } { x }^{ 2 }+4x-1\)

Find the quotient and remainder of the following.
(x³ + 3x² – 31x +12)÷(x–4)

Factorise x³+13x²+ 32x + 20 into linear factors.

Check the value of k for which the given system of equations kx + 2y = 3; 2x − 3y = 1 has a unique solution.

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:

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 points A(–4, –3), B(3, 1), C(3, 6), D(–4, 2) taken in that order form the vertices of a parallelogram.

Plot the following points on a graph sheet by taking the scale as 1cm = 1 unit.
Find how far the points are from each other?
A (1,0) and D (4, 0). Find AD and also DA.
Is AD = DA?
You plot another set of points and verify your Result.

For the data 11, 15, 17, x+1, 19, x–2, 3 if the mean is 14 , find the value of x. Also find the mode of the data.

Find the six trigonometric ratios of the angle \(\theta\) using the given diagram.

Find the values of
(i) tan7° tan23° tan60° tan67° tan83°  
(ii) \(\frac { cos35° }{ sin55° } +\frac { sin12° }{ cos78° } -\frac { cos18° }{ sin72° } \)

Find the value of sin 64⁰34'.

Find the value of
(i) sin 38⁰36' + tan 12⁰12'
(ii) tan 60⁰25' - cos 49⁰20'

The lengths of sides of a triangular field are 28 m, 15 m and 41 m. Calculate the area of the field. Find the cost of levelling the field at the rate of Rs. 20 per m²

The dimensions of a sweet box are 22 cm × 18 cm × 10 cm. How many such boxes can be packed in a carton of dimensions 1 m × 88 cm × 63 cm?

The total surface area of a cube is 864 cm². Find its volume

The probability that it will rain tomorrow is \(\\ \frac { 91 }{ 100 } \). What is the probability that it will not rain tomorrow?