If U = {x | x ∈ N, x < 10} and A = {x | x ∈ N, 2 ≤ x < 6} then (A′)′ is –––––––––.

The number of elements of the set {x : x ∈ Z, x² = I} is ________

if \(\frac { 1 }{ 7 } \) = \(0.\overline { 142857 } \) then the value of \(\frac { 5 }{ 7 } \) ________.

If \(\frac { 1 }{ 7 } \)= 0.142857, then the value of is______________.

The type of the polynomial 4–3x³ is  ________.

(a-b) (a²+ab+b²)=_________

The perpendicular line from the centre of the circle to the chord divided the chord in the ratio________

The point whose ordinate is 4 and which lies on the y-axis is ______.

The distance between the points (4, -1) and the origin is___________

The mean of a, b, c, d and e is 28. If the mean of a, c and e is 24, then mean of b and d is _______.

The mean of the square of first 11 natural number is ___________

The value of \(\frac { 2tan\ 30° }{ 1-{ tan }^{ 2 }30° } \) is equal to ________.

The perimeter of an equilateral triangle is 30 cm. The area is _______.

The six faces of the dice are called equally likely if the dice is _______.

Find the number of subsets and the number of proper subsets of the following sets.
X = { x² : x ∈ N, x² ≤ 100}.

Without actual division classify the decimal expansion of the following numbers as terminating or non-terminating and recurring.
\(7\over 16\)

Find any five rational numbers between
(i) \(\frac { 1 }{ 4 } \) and \(1\over 5\)
(ii) 0.1 and 0.11
(iii) -1 and -2

Give any two rational numbers lying between 0.5151151115…. and 0.5353353335…

Simplify: (x-2y+3z) (x²+4y²+9z²+2xy+6yz-3xz)

Draw the circumcircle for, An isosceles right triangle having 6 cm as the length of the equal sides.

Show that the line segment joining the mid-points of two sides of a triangle is half of the third side
(Hint: Place triangle ABC in a clever way such that A is (0, 0), B is (2a, 0) and C to be (2b, 2c). Now consider the line segment joining the mid-points of AC and BC. This will make calculations simpler).

Using section formula, show that the points A (7, -5), B (9, -3) and C (13, 1), are collinear.

A car travels, at an uniform speed. At 2 pm it is at a distance of 5 km at 6 pm it is at a distance of 120 km. Using section formula, find at what distance it will reach 2 midnight.

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

Find the value of sin 3x. sin 6x. sin 9x when x = 10°

Find the value of cot 15°. cot 30°. cot 45°. cot 60°. cot 75°

Find the surface area of a cube whose edge is
(i) 27 cm
(ii) 3 cm
(iii) 6 cm
(iv) 2.1 cm

1500 families were surveyed and following data was recorded about their maids at homes

A family is selected at random. Find the probability that the family selected has
(i) Both types of maids
(ii) Part time maids
(iii) No maids

From the venn-diagram, list the following:

(i) A
(ii) B
(iii) A ∩ B
(iv) AU B
(v) A-B
(vi) B-A
(vii) (A - B) ∩ (B - A)

Draw: Venn diagram for each of the following:
(i) \(A\cup (B\cap C)\)
(ii) \(A\cap (B\cup C)\)
(iii) \((A\cup B)\cap C\)
(iv) \((A\cap B)\cup C\)

Express the following decimal expression into rational numbers -\(21.21\overline {37}\)

Represent the following numbers in scientific notation:
(i) (300000)² \(\times\) (20000)⁴
(ii) (0.000001)¹¹ ÷ (0.005)³
(iii) \( \{ (0.00003 ) ^{ 6 }\times (0.00005)^{ 4 }\} \div \{ (0.009)^{ 3 }\times (0.05)^{ 2 }\} \)

Subtract \(6\sqrt { 7 } \) from \(9\sqrt { 7 } \). Is the answer rational or irrational?

Multiply the following polynomials and find the degree of the resultant polynomial:
p(x) = x²-9 q(x) = 6x²+7x-2

Expland the following using identities :(7x+2y)²

Construct the ΔLMN such that LM = 7.5cm, MN = 5cm and LN = 8cm. Locate its centroid.

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.

Find the points which divide the line segment joining A(−11, 4) and B(9, 8) into four equal parts.

The median of observation 11,12,14,18, x+12, x+4, 30, 32, 35, 41 arrenged in ascending order is 24. Find the values of x.

Find the value of sin 64⁰34'.

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

When a dice is rolled, find the probability to get the number greater than 4?