From the adjacent diagram n[P(AΔB)] is ________.

If U = {x : x\(\in \)W and x < 20}, A = {2,4,6,8}, B = {6,8,12,14} then\(\left[ n\left( A\cup B^{ ' } \right) \right] \)

Which one of the following is an irrational number.

Which of the following is not an irrational number?

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

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

What is the name of a regular polygon of six sides?

Point (0, –7) lies ________

A point on the y-axis is ________________

The mean of the first 10 prime numbers is ___________

If the mean of five observations x, x+2, x+4, x+6, x+8, is 11, then the mean of first three observations is __________

if sin 30⁰ = x and cos 60⁰ = y, then x²  + y² is________.

The lateral surface area of a cube of side 12 cm is _______.

The probability of an event cannot be _______.

Identify the following sets as null set or singleton set.
B = The set of all even natural numbers which are not divisible by 2

Express the following in the form 2ⁿ:
\(\frac{1}{4}\)

Use a fractional index to write \(\sqrt [ 3 ]{ 7 } \)

Find any 3 irrational numbers between 0.12 and 0.13.

Expand the following using identities: (2x - 3b)²

Draw a right triangle whose hypotenuse is 10 cm and one of the legs is 8 cm. Locate its incentre and also draw the incircle.

Plot the following points in the coordinate plane and join them. What is your conclusion about the resulting figure? 
(0, –4) (0, –2) (0, 4) (0, 5)

Find the centroid of the triangle whose vertices are (2, -5), (5, 11) and (9, 9)

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.

In a rice mill, seven labours are receiving the daily wages of Rs. 500, Rs. 600, Rs. 600, Rs. 800, Rs. 800, Rs. 800 and Rs. 1000, find the modal wage

If 3 (tan \(\theta\)) + 4 (sec \(\theta\) \(\times\) sin 6) = 24. Then find all the trigonometric ratios of the angle \(\theta\)

Find the value of \(\frac{\tan 25^{\circ}}{\cot 65^{\circ}}+\frac{\sin 40^{\circ}}{\cos 50^{\circ}}\)

Find the TSA and LSA of a cuboid whose length, breadth and height are 10 cm, 12 cm and 14 cm respectively.

In a survey of 400 youngsters aged 16-20 years, it was found that 191 have their voter ID card. If a youngster is selected at random, find the probability that the youngster does not have their voter ID card.

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

In the adjacent diagram, if n(U) = 125, y is two times of x and z is 10 more than x, then find the value of x,y and z.

Express the following decimal expression into rational numbers \(3.1\overline { 7 } \)

Can you reduce the following numbers to surds of same order :
(i) \(\sqrt{3}\)
(ii) \(\sqrt [ 4 ]{ 3 } \)
(iii) \(\sqrt [ 3 ]{ 3 } \)

Write in scientific notation ;(60000000)³

Write the following polynomials in standard form.

Expland the following using identities (4a + 3b) (4a - 3b)

In the given figure, ㄥCAB = 25°, find ㄥBDC, ㄥDBA and ㄥCOB

Find the distance between the points (–4, 3), (2, –3).

Show that the following points taken in order form an equilateral triangle in each case \(A\left( 2,2 \right) ,B\left( -2,-2 \right) ,C\left( -2\sqrt { 3 } ,2\sqrt { 3 } \right) \)

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 cos19⁰59'

The sides of a triangular park are in the ratio 9:10:11 and its perimeter is 300 m. Find the area of the triangular park.

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?

Verify x³+y³+z³-3xyz = \(\frac{1}{2}\)[x+y+z][(x-y)²+(y-z)²+(z-x)²]

Prove that x -1 is a factor x⁵ - 45x⁴ + 36x³ + 45x² - 36x^-1

In the given Fig, ∠A = 64° , ∠ABC = 58°. If BO and CO are the bisectors of ∠ABC and ∠ACB respectively of ΔABC, find x° and y°.

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