Write the following decimal numbers as rationals.
3.0

Add: \(\frac { -5 }{ 9 } ,\frac { -4 }{ 3 } ,\frac { 7 }{ 12 } \)

Find \(\frac { -5 }{ 8 } \times 7\)

The product of two rational numbers is \(\frac { -2 }{ 3 } \) If one number is \(\frac { 3 }{ 7 } \) find the other.

Evaluate: \(\left( \frac { 4 }{ 3 } -\left( \frac { -3 }{ 2 } \right) \right) +\left( \frac { -5 }{ 3 } \div \frac { 30 }{ 12 } \right) +\left( \frac { -12 }{ 9 } \times \frac { -27 }{ 16 } \right) \)

The radius of a sector is 21cm and its central angle is 120°. Find the length of the arc

A circular shaped gymnasium ring of radius 35 cm is divided into 5 equal arcs shaded with different colours. Find the length of each of the arcs.

Kamalesh has a dining table, circular in shape of radius 70 cm, whereas Tharun has a circular quadrant dining table of radius 140 cm. Whose dining table has a greater area? \(\left(\pi=\frac{22}{7}\right)\)

If the side of a square carpet is 3x² metre, then find its area

If Guru wants to multiply the expressions (2x+3y+50) and 3xy , what is the resultant expression?

Find the value of 998² by using (a − b)² identity 

Find the value of (103)³

Find the unknowns in the following figures

Find the unknowns in the following figures

In Fig, if ΔPEN ～ ΔPAD, then find x and y.

(Illustrating AA Similarity)
In the given Fir, if ∠1 ≡ ∠3 and ∠2 ≡∠4 then, prove that ΔBIG ～ ΔFAT . Also find FA.

(Illustrating SAS Similarity)
If A is the midpoint of RU and T is the midpoint of RN, prove that ΔRAT ～ ΔRUN .

(Illustrating SSS similarity)
Prove that ΔPQR ～ ΔPRS in the given Fig

(Illustrating SSS and SAS Congruence)
If ∠E =∠S and G is the midpoint of ES, prove that Δ GET ≡ Δ GST.

(Illustrating ASA Congruence)
If ∠YTB ≡∠YBT and ∠BOY ≡∠TRY, prove that Δ BOY ≡ Δ TRY

(Illustrating RHS Congruence)
If TAP is an isosceles triangle with TA = TP and ∠TSA = 90°
Is ∠P = ∠A? Why?

In ΔPAT, the bisector of ∠P, meets AT at S. If ∠APT = 70^o and ∠ASP = 100^o, find ∠A and ∠T.

What are the possible outcomes if a fair die is rolled? 

In how many ways, can the students answer 3 true or false type questions in a slip test?

Madhan wants to a buy a new car. The following choices are available for him.
1) There are 2 types of cars as shown in the Figure
2) There are 5 colours available in each type as shown in Figure
3) There are 3 models available in each colour
(i) GL (standard model)
(ii) SS (sports model)
(iii) SL (luxury model)

(i) In how many different ways can Madhan buy any one of the new cars?
(ii) If the white colour is not available in Type 2, then in how many ways can Madan buy a new car among the given options?