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

The set (A - B) U(B - A) is ___________

The length and breadth of a rectangular plot are 5 \(\times\) 10⁵ and 4 \(\times\) 10⁴ metres respectively. Its area is ______.

Rationalising the denominator \(\cfrac { 1 }{ \sqrt [ 3 ]{ 3 } } \)  ___________

The value of the polynomial f(x) = 6x - 3x²+9 when x = -1 is _____________________

The linear equation in one variable is __________

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

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

In what ratio does the y-axis divides the line joining the points (−5, 1) and (2, 3) internally ______.

A particular observation which occurs maximum number of times in a given data is called its _______.

The mean of 5, 9, x, 17,and 21 is 13 then find the value of x ___________

The value of 2tan30° tan60° is

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

A number between 0 and 1 that is used to measure uncertainty is called _______.

If U = {a, b, c, d, e, f, g, h}, A = {b, d, f, h} and B = {a, d, e, h}, find the following sets. A′\(\cup \) B′

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

Write the following in the form of 5ⁿ
\(\sqrt{5}\)

The mass of the Earth is 5.97 \(\times\) 10²⁴ kg and that of the Moon is 0.073 \(\times\) 10²⁴ kg. What is their total mass?

Factorise the following expressions: pr+qr+pq+p²

Which ones are not quadrilaterals?

Find the distance between the following pairs of points. (3,4) and (– 7, 2)

If A (10, 11) and B (2 ,3) are the coordinates of end points of diameter of circle. Then find the centre of the circle.

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.

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

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

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

Find the volume of a cube whose surface are is a 96 cm².

A manufacturer tested 7000 LED lights at random and found that 25 of them were defective. If a LED light is selected at random, what is the probability that the selected LED light is a defective one.

Given that A = {1,3,5,7} B = {1,2,4,6,8}. Find
(i) AΔB and
(ii) BΔA

If K = {a,b,d e f }  L = {b,c,d,g} and M = {a,b,c,d,h}, then find the following:
(i) K \(\cup \)(L \(\cap \) M)
(ii) K \(\cap \)(L \(\cup \) M)
(iii) (K\(\cup \)L)\(\cap \)(K\(\cup \)M)
(iv) (K\(\cap \)L)\(\cup \)(K\(\cap \)M)

Express the following decimal expression into rational numbers. \(2.\overline { 327 } \)

(i) Add 3\(\sqrt{7}\) and 5\(\sqrt{7}\) . Check whether the sum is rational or irrational.
(ii) Subtract 4\(\sqrt{5}\) from 7\(\sqrt{5}\) . Is the answer rational or irrational?

Write in scientific notation ;(60000000)³

Find quotient and the remainder when f(x) is divided by g(x) x⁴ – 3x³ + 5x² – 7 is divided by x² + x + 1 

Show that x+4 is a factor of x³ + 6x² - 7x - 60

Draw and locate the centroid of the triangle ABC where right angle at A, AB = 4cm and AC = 3cm

Determine whether the given set of points in each case are collinear or not (a, –2), (a, 3), (a, 0)

If (x, 3), (6, y), (8, 2) and (9, 4) are the vertices of a parallelogram taken in order, then find the value of x and y.

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.

For the measures in the figure, compute sine, cosine and tangent ratios of the angle \(\theta \)

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

Team I and Team II play 10 cricket matches each of 20 overs. Their total scores in each match are tabulated in the table as follows:

What is the relative frequency of Team I winning?

Factorise the following:
(i) (p - q²) - 6(p - q) -16
(ii) m² + 2mm - 24n²
(iii) \(\sqrt{5}a^2+2a-3\sqrt5\)
(iv) a⁴- 3a²+ 2
(iv) 8m³- 2m²n -15mn²
(v) \({1\over x^2}+{1\over y^2}+{2\over xy}\)

Find the quotient and remainder when 5x³ + 7x² + 3x + 2 is divided by 3x + 2

Draw ΔPQR with sides PQ = 7 cm, QR = 8 cm and PR = 5 cm and construct its Orthocentre.

Find the angle of the given cyclic quadrilateral ABCD in the figure.