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

\(\left[ n\left( A\cup B\cup C \right) ^{ ' } \right] \)=_______

\(\frac { \sqrt [ 3 ]{ 18 } }{ \sqrt [ 3 ]{ 2 } } \) is same as _____________

\(\sqrt [ 3 ]{ 192 } +\sqrt [ 3 ]{ 24 } \)

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

Which of the following statement is true for the equation 2x + 3y = 15

The point of concurrency of the medians of a triangle is known as __________

Point (0, –7) lies ________

On which quadrant does the point (- 4, 3) lie?

The mean of a set of numbers is \(\bar X\). If each number is multiplied by z, the mean is _______.

The mean of the first 10 prime number is _______________

The value of tan 1° tan 2° tan 3°...tan 89° is ________.

The total surface area of a cuboid with dimension 10 cm × 6 cm × 5 cm is _______.

The probability of all possible outcomes of a random experiment is always equal to _______.

Which of the following sets are equivalent or unequal or equal sets?
G = {x : x is a prime number and 3 < x < 23}
H = {x : x is a divisor of 18}

Express the following in the form of \(\frac { p }{ q } \)  where p and q are integers and q \(\neq \)0.
(a)\(\overline { 0.6 } \) 
(b) \(\overline { 0.47 } \)
(c) \(\overline { 0.001 } \)

Convert the following rational numbers into decimal
(i) \(3\over 4\)
(ii) \(5\over 8\)
(iii) \(9\over 25\)

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

If \({ x }^{ 2 }+\frac { 1 }{ { x }^{ 2 } } \)= 23, then find the value of \(x+\frac { 1 }{ x } \) and \({ x }^{ 3 }+\frac { 1 }{ { x }^{ 3 } } \) .

Two circles of radii 5 cm and 3 cm intersect at two points and the distance between their centres is 4 cm. Find the length of the common chord

Find the length of median through A of a triangle whose vertices are A(−1, 3), B(1, −1) and C(5, 1).

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

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

Find the value of \(\cfrac { cos{ 63 }^{ 0 }20' }{ sin{ 26 }^{ 0 }40' } \)

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

What is the probability of drawing a King or a Queen or a Jack from a deck of cards?

In a class there are 40 students. 26 have opted for Mathematics and 24 have opted for Science. How many student have opted for Mathematics and Science.

If A = {x : x ∈ Z, -2 < x ≤ 4}, B = {x : x ∈ W, x ≤ 5}, C = {-4,-1,0,2,3,4}, then verify A∪(B∩C)=(A∪B)∩(A∪C).

Express the following decimal expression into rational numbers \(17.2\overline { 15 } \)

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

Simplify;\(\sqrt { 44 } +\sqrt { 99 } -\sqrt { 275 } \)

Subtract the second polynomial from the first polynomial and find the degree of the resultant polynomial
h(z) = z⁵-6z⁴+z f(z) = 6z²+10z-7

 Expland : (x + 2 y + 3z)²

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

Calculate the distance between the points A (7, 3) and B which lies on the x-axis whose abscissa is 11.

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

If the mean of the following data is 20.2, then find the value of p

(i) If cosec A = sec 34⁰, then find A
(ii) If tan B = cot 47⁰, then find B.

Three different triangular plots are available for sale in a locality. Each plot has a perimeter of 120 m. The side lengths are also given:

Help the buyer to decide which among these will be more spacious.

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

Factorise the following:
(i) x²+10x + 24
(ii) z²+ 4z -12
(iii) p²- 6p -16
(iv) t²+72 -17t
(v) y²-16 - 80
(vi) a²+10a - 600

Factorise  2x³- x² - 12x - 9 into linear factors
 

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°.

Diagonal AC of a parallelogram ABCD bisects ㄥA. Show that
(i) it bisects ㄥC also
(ii) ABCD is a rhombus.