When two positive integers are added, we get

\(\frac { 3 }{ 7 } \) of \(\frac { 2 }{ 5 } \)is equal to

Read the following bar graph and answer the question

The difference between maximum and minimum marks is

If x - 5 = 2, then x is equal to

In the following figure, \(\angle AOB\) and \(\angle BOC\) are

When zero is subtracted from an integer, we get:

Which of the following has the smallest value?

Read the following bar graph and answer the question

The ratio between the marks obtained by Saroj and Vimla is

The sum of three times a number and 11 is 32. Find the number?

Which of the following pairs can form a linear pair?

Which of the following is the value of (-12) \(\times\) (- 2) \(\times\) (-5)?

150 g is equal to

Read the following bar graph and answer the question

The difference between the marks obtained by Vimla and Saroj is how many times the difference between the marks obtained by Meenu and Saroj?

The solution of the equation 3m + 7 = 16 is

What is the measure of the complement of the angle 90°?

When (-1) and 1 are multiplied, we get:

\(3\frac{1}{3}\div 10\) is equal to

Khilona earned scores of 97,73 and 88, respectively in her first three examinations. If she scored 80 in the fourth examination, then her average score will be

Which of the following numbers satisfies the equation -6 + x = -18?

The angle. which is its own supplement:

10 \(\times\) (- 20) is equal to

Which of the following is an improper fraction?

The runs scored in a cricket match by 11 players are as follows: 6, 15, 120, 50, 100, 80, 10, 15, 8, 10, 10. Find the median of scores.

If 2x - 8 = 0, then 4x =

In the given figure, lines PQ and ST intersect at O. If \(\angle\)POR = 90° and x : y = 3 : 2, then z is equal to

\(\frac{2}{5}\times 5\frac{1}{5}\) is equaI to

Pictorial representation of \(6\times \frac{1}{7} \) is

In the year 2014, Shantanu gets Rs 3832.5 as his pocket allowance. Find his pockect allowane per day

\(\frac { 2 }{ 5 } \times 5\frac { 1 }{ 5 } \) is equal to

Which of the following is the equivalent fraction of \(\frac { 3 }{ 4 } \)with numerator 18?

If the sum of two integers a and b is zero, then

[(-8) x (-3)] x (-4) is not equal to

Which of the following does not represent an integer?

A shopkeeper makes a profit of Rs 5 on each pen and incurs a loss of Rs 2 on each pencil box. What will be his net profit if he sells ten pens and ten pencil boxes?

When the integers 10, 0, 5, - 5, - 7 are arranged in descending or ascending order, then find out which of the following integers always remains in the middle of the arrangement.

The value of [ (-6) + 2 ] \(\div\) (2) is

-35 x 107 is not same as

(- 11) \(\times\) 7 is not equal to:

On the following number line value 'Zero' is shown by the point

(16) \(\div\) 4 is not same as:

In a class test containing 10 questions, 5 marks are awarded for every correct answer and (- 2) marks are awarded for every incorrect answer and 0 for questions not attempted.
(i) Mohan gets four correct and six incorrect answers. What is his score?
(ii) Reshma gets five correct answers and five incorrect answers. What is her score?
(iii) Heena gets two correct and five incorrect answers out of seven questions she attempts. What is her score?

Write a pair of integers whose product is -36 and whose difference is 15.

A greengrocer had a profit of Rs 47 on Monday, a loss of Rs 12 on Tuesday and loss of Rs 8 on Wednesday. Find his net profit or loss in 3 days.

Find 4 x (- 8), 8 x (- 2), 3 x (- 7), 10 x (- 1) using number line.

A batsman score 426 runs in 4 innings. Then, find average score per inning.

If \(\frac { 2x-3 }{ 5 } +\frac { x+3 }{ 4 } =\frac { 4x+1 }{ 7 } \) , find the value of x.

How much pure alcohol must be added to 400 ml of a 15% solution to make its strength 32%.

Find angles x and y in each figure.

In an examination, 72% of the total examinees passed. If the number of failures is 392, find the total number of examinees.

If the cost price of 6pens is equal to the selling price of 4 pens, Then find the gain per cent.

We have done various patterns with numbers in our previous class. Can you find a pattern for each of the following? If yes, complete them.
7, 3, - 1, - 5, ___, ___, ___

Following number line shows the temperature in degree Celsius (^o C ) at different places on a particular day.

What is the temperature difference between Lahulspiti and Srinagar?

Rita goes 20 km towards East from a point A to the point B. From B, she moves 30 km towards West along the same road. If the distance towards East is represented by a positive integer, then how will you represent the distance travelled towards West? By which integer will you represent her final position from A?

Verify a + (- b) = a - b for the following values of a and b: a = 137, b = 92

In a quiz, team A scored -30, 5, 0 and team B scored 20, 0, -10 in three successive rounds. Which team scored more? Can we say that we can add integer in any order?

Add the following integers using number line: -2 and 5

Verify a - (-b) = a + b for the following values of a and b. a= 75, b= 84

Verify a - (-b) = a + b for the following values of a and b.

Solve the following addition and subtraction problems and verify the closure property under addition and subtraction:
9 + (-64)

Solve the following addition and subtraction problems and verify the closure property under addition and subtraction:
18 - (-24)

The dimensions of a cuboid are 5 cm, 3 cm and 2 cm. Draw three different isometric sketches at this cuboid.

Three cubes each with 2 cm edge are placed side by side to form a cuboid. Sketch an oblique or isometric sketch of this cuboid

Draw the top, the front and the side views of the following solid figure made up of cubes.

Draw the nets of the followings:
(i) Triangular prism (ii) Tetrahedron (iii) Cuboid

Draw a net of the solid given in the figure

Give the order of rotational symmetry for each figure.

In the following figure, show if possible both line and rotational symmetry.

In the following figure, show if possible both line and rotational symmetry.

The flag of Japan is shown below. How many lines of symmetry does the flag have?

Does the figure have rotational symmetry?

Find five examples, where a number is expressed in exponential form. Also, identify the base and the exponent in each case.

Express the following in usual form.
1.75 x 10^-3

Simplify \(\frac { { 5 }^{ -2 }\times { 3 }^{ -3 }\times (125)^{ 2/3 } }{ (27)^{ -2/3 }\times (32)^{ -1/5 } } \).

Find the value of x, such that \({ \left( \frac { 1 }{ 5 } \right) }^{ 5 }\times { \left( \frac { 1 }{ 5 } \right) }^{ 19 }={ \left( \frac { 1 }{ 5 } \right) }^{ 8x }\) .

Using laws of exponents simplify the following.
\(\frac { \left( -\frac { 3 }{ 4 } \right) ^{ 4 }\times \left( \frac { 125 }{ 27 } \right) }{ \left( \frac { 5 }{ 3 } \right) ^{ 2 }\times \left( \frac { 9 }{ 16 } \right) } \).

What should be added to x³ + 3x²y + 3xy² +y³ to get x³ +y³?

What should be subtracted from -7mn + 2m² +3n² to get m²+2mn + n²?     

How much is y⁴ -12y² +y+14greaterthan 17y³ + 34y² - 51y + 68?

To what expression must 99x³ - 33x² -13x - 41 be added to make the sum zero? 

Arjun bought a rectangular plot with length x and breadth y and then sold a triangular part of it, whose base is y and height is z. Find the area of the remaining part of the plot

A rectangular metal plate is 7 cm long and 5 cm wide. Find the cost of the plate at the rate of Rs 75 per sq cm.

A wall of a room is of dimensions 5 m x 4m. lt has a window of dimensions 1.5 m x 1 m and a door of dimensions 2.25 m x 1 m. Find the area of the wall, which is to be painted.

In the given figure, find the area of parallelogram ABCD, if the area of shaded triangle is 9 cm².

In the following figure, ABCD is a square with AB = 15 cm. Find the area of the square BDFE.

In the following figures, perimeter of  \(\Delta\)ABC = perimeter of  \(\Delta\)PQR. Find the area of  \(\Delta\)ABC.

Tell what is the profit or loss in the following transactions. Also, find profit per cent or loss per cent in each case.
Gardening shears bought for Rs 250 and sold for Rs 325.

I buy a TV for Rs 10000 and sell it at a profit of 20%. How much money do I get for it?

(i) Chalk contains calcium, carbon and oxygen in the ratio 10 : 3 : 12. Find the percentage of carbon in chalk.
(ii) If in a stick of chalk, carbon is 3 g, what is the weight of the chalk stick?

If the rate of simple interest is 12% per annum, then find the amount that would fetch interest of Rs.6000 per annum.

24 men can complete a job in 40 days, then find the number of men required to complete the job in 32 days.

Simplify 
\(\frac { 3 }{ 7 } \div \left( \frac { 21 }{ -55 } \right) \)

Simplify 
\(\\ 1\div \left( -\frac { 1 }{ 2 } \right) \)

Write each of the following numbers in the form of  \(\frac { p }{ q } \), Where p and q are integers.
one fourth 

Write each of the following numbers in the form of \(\frac { p }{ q } \), Where p and q are integers.
Zero 

Taking x \(=\frac { -4 }{ 9 } \) , y \(=\frac { 5 }{ 12 } \) and z\(=\frac { 7 }{ 18 } \) , Find the rational number, which when multiplied by y gives x 

Construct an isosceles right angled ΔABC, where m ㄥACB = 90° and AC = 6 cm.

Construct \(\triangle XYZ\) in which XY = 4.5 cm. yz = 5 cm and ZX = 6 cm.

Construct an equilateral triangle of side 5.5 cm.

Draw \(\triangle PQR\) with PQ= 4 cm, QR = 3.5 cm and PR = 4 cm. What type of triangle is this?

Construct a \(\triangle ABC\) in which AB = 2 cm, BC = 4.5 cm and AC = 4cm.

A rectangular metal plate is 7 cm long and 5 cm wide. Find the cost of the plate at the rate of Rs 75 per sq cm.

How many envelopes can be made out of a sheet of paper 324 cm by 172 cm, if each envelope requires a piece of paper of size 18 cm by 12 cm.

A hedge boundary needs to be planted around a rectangular lawn of size 72 m x 18 m. If 3 shrubs can be planted in a metre of hedge, how many shrubs will be planted in all?

A wall of a room is of dimensions 5 m x 4m. lt has a window of dimensions 1.5 m x 1 m and a door of dimensions 2.25 m x 1 m. Find the area of the wall, which is to be painted.

Find the ratio of areas of  \(\Delta\)MNO, \(\Delta\)MOP and \(\Delta\)MPQ in the following figure

Express the following in usual form.
1.75 x 10^-3

Simplify \(\frac { { 5 }^{ -2 }\times { 3 }^{ -3 }\times (125)^{ 2/3 } }{ (27)^{ -2/3 }\times (32)^{ -1/5 } } \).

By what number should we multiply (-8)^-1 to obtain a product equal to 10^-1?

Express the following numbers in standard form.
(i) 31865000000
(ii) 3908.78

Express the following in exponential form:
3²x3³x5⁵

Give the order of rotational symmetry for each figure.

In the following figure, show if possible both line and rotational symmetry.

In the following figure, show if possible both line and rotational symmetry.

The flag of Japan is shown below. How many lines of symmetry does the flag have?

Does the figure have rotational symmetry?

The dimensions of a cuboid are 5 cm, 3 cm and 2 cm. Draw three different isometric sketches at this cuboid.

Three cubes each with 2 cm edge are placed side by side to form a cuboid. Sketch an oblique or isometric sketch of this cuboid

Draw the top, side and front views of the solids given below in figures

Draw a net of a cuboid having same breadth and height but length double the breadth

Draw the nets of the followings:
(i) Triangular prism (ii) Tetrahedron (iii) Cuboid

How much is 21a³ - 17a² - less than 89a³ - 64a² + 6a + 16?

How much is y⁴ -12y² +y+14greaterthan 17y³ + 34y² - 51y + 68?

How much does 93p² - 55p + 4 exceed 13p³ - 5p² + 17p - 90?

A taxi service Charges Rs 8 per km and a fixed charge of Rs.50. Write an algebraic expression for the above situation, if the taxi is hired for x km.

In the adjoining figure, the length of a green side is given by 9 and that of the red side is given by p. What is the total length of 3 such figures?

Which of the following pair of figures are congruent?

Which of the following pair of figures are congruent?

If ΔABC ≅ ΔPQR, where ㄥA=(3x-10) and ㄥP=(x+50), then the value of ㄥC, where ㄥC=x.

Is the perimeter of two congruent triangles is equal? Justify your answer.

In the following figure, ΔABC and ΔDCB are right angled at A and D respectively and AC = DB. Prove that ΔABC ≌ ΔDCB.

Construct ΔABC with BC = 7.5 cm, AC = 5 cm and m ㄥC = 60°.

Draw a line, say AB, take a point C outside it. Through C, draw a line parallel to AB using ruler and compasses only.

Construct ΔPQR, if PQ = 5 cm, mㄥPQR = 105° and mㄥQRP = 40°.

Construct an isosceles right angled ΔABC, where m ㄥACB = 90° and AC = 6 cm.

Construct \(\triangle DEF\) such that DE = 5 cm, DF = 3 cm and m \(\angle EDF=90^0\).

Add the following rational number.
\(\frac { 1 }{ 2 } +\frac { 1 }{ 6 } +\frac { 1 }{ 8 } \)

Find the sum of \(\frac { 4 }{ 7 } +\frac { -8 }{ 9 } +\frac { -5 }{ 21 } +\frac { 1 }{ 3 } \).

Simplify 
\(\frac { 6 }{ 5 } \times \frac { 3 }{ 7 } -\frac { 1 }{ 5 } \times \frac { 3 }{ 7 } \)

Write each of the following numbers in the form of  \(\frac { p }{ q } \), Where p and q are integers.
Reciprocal of 1 

Write the following rational number in the standard form.
35%

O is any point in the interior of a triangle PQR and QO produced meets PR at A (in fig.). Is :

(a) PQ + PA > QA ?
(b) PQ + PA > OQ + OA ?
(c) PQ + PA + AR > OQ + OA +AR ?
(d) PQ + PR > OQ + OR?
(e) PQ + QR + PR > OP + OQ + OR ?

Show that the sum of the exterior angles of \(\triangle\)ABC as shown in the figure is 360°.

The sides of a rectangle are 6 cm and 8 cm respectively. Find the length of the diagonal

A ladder 10m long was rested along a wall such that its top reaches to a height of 8m from the ground along the wall. How far is the foot of the ladder from the wall?

Find the measure of x in each of the following figures.

Lines l||m, p||q,  Find a, b, c, d?

In the following figure, OB is perpendicular to OA and \(\angle\)BOC =49°. Find \(\angle\)AOD.

In the following figure, AB II CO, AF II ED, \(\angle \)AFC = 70° and \(\angle \)FED = 40°, then find \(\angle \)EFD.

Three lines AB, CD and EF intersect each other at point O. If \(\angle\)AOE = 30° and \(\angle\)DOB = 40°, then find \(\angle\)COF.

Iron rodes a, b, c, d, e and f are making a design of a bridge as shown in figure, in which a || b, c || d, e || f. Find the marked angles between b and c.

If one side of a square is represented by 5 - 4x and the adjacent side is represented by 3x - 2, find the length of the side of the square.

Follow the directions and correct the given incorrect equation written in Roman numerals: Remove two of these matchsticks to make a valid equation: IX - VI = V.

If \(\frac{3x-2y}{x-5y}=\frac{2}{3}\) find the value of \(\frac{x}{y}\)

What will be the value of y for which expressions (y -15) and (2y + 1) becomes equal?

The age of Sohan Lal is four times that of his son Amit. If the difference of their ages is 27 yr, find the age of Amit.

The mean of 10 observations was calculated as 40. It was detected on rechecking that the value of 45 was wrongly copied as 15. Find the correct mean.

Rahul scored of 97,73 and 80, respectively in his first three examinations. If he scored 70 in the fourth examination, then find how much average score increased/decreased.

The following are weights (in kg) of 12 people. 70,62,54,57,62,84,75,59,62,65,78,60
(a) Find the mean of the weights of the people.
(b) How many people weigh above the mean weight?
(c) Find the range of the given data

The mean of four numbers is 32. If one more number is added to the collection, the new average of the five numbers becomes 31. find the mean value of fifth observation

The mean marks of seven students are 55. The marks of 6 students are 52, 54, 55, 53, 56 and 54. Find the marks of seventh student

Vikram spent \(\frac{1}{4}\) of his money on a Science textbook and \(\frac{2}{3}\)of the remainder on stationary. What fraction of his money did he have left?

Ram and Ankush had 4500 stamps altogether. If Ram had \(\frac{4}{5}\)as many stamps as Ankush, how many stamps did Ankush have? 

Arrange the fractions \(\frac{6}{11},\frac{6}{19},\frac{6}{27},\frac{6}{35}\) in descending order.Then, find the fraction at the third position.

Mr. Ram spent \(\frac{1}{4}\) of his salary on food, \(\frac{1}{3}\) of his salary on house and\(\frac{1}{3}\)of his salary on car. What fraction of his money was kept for savings?

Sugar is sold at Rs 17\(\frac{3}{5}\) per kg. Find the cost of 16 kg of sugar.

A water tank has steps inside it. A monkey is sitting on the topmost step i.e. the first step. The water level is at the ninth step.

(i) He jumps 3 steps down and then jumps back 2 steps up. In how many jumps will he reach the water level?
(ij) After drinking water, he wants to go back. For this, he jumps 4 steps up and then jumps back 2 steps down in every move. In how many jumps will he reach back the top step?
(iii) If the number of steps moved down is represented by negative integers and the number of steps moved up by positive integers, represent his moves in parts (i) and (ii) by completing the following
(a) -3 + 2- ... = -8
(b) 4 -2 +  ... = 8
In part (a), the sum (-8) represents going down by eight steps. What will the sum 8 in part (b) represent?

In a class test containing 10 questions, 5 marks are awarded for every correct answer and (- 2) marks are awarded for every incorrect answer and 0 for questions not attempted.
(i) Mohan gets four correct and six incorrect answers. What is his score?
(ii) Reshma gets five correct answers and five incorrect answers. What is her score?
(iii) Heena gets two correct and five incorrect answers out of seven questions she attempts. What is her score?

Write five pairs of integers (a, b) such that a \(\div\) b = - 3. One such pair is (6, - 2) as 6 \(\div\) (-2) = (-3).

Write a pair of integers whose product is -36 and whose difference is 15.

Write two integers, which are greater than -4, but their difference is smaller than -2.

Find:
(a) 9% of  Rs.700
(b) 6\(\frac { 2 }{ 3 } \)% of 75 m
(c) 7'5% of 80 kg
(d) 8% of 5 litres

In an examination, 72% of the total examinees passed. If the number of failures is 392, find the total number of examinees.

Observe and complete the following table

Estimate what part of the figures is coloured and hence find the per cent which is coloured.

What is the time period for which Rs  8000 amount to Rs 12000 at 20 per annum of simple interest?

A ladder 17 m long reaches a window which is 8m above the ground on one side of street. Keeping its foot at the same point, the ladder is turned to the other side of the street to reach a window at a height of 15 m. Find the width of street.

Look at the adjoining figure. Can you use ASA congruence rule and conclude that ΔAOC ≅ ΔBOD?

If ΔABC ≅ ΔMNR, then find the value  of (2x+3y), where x and y shown in the following figures.

Which of the following pair of figures are congruent?

Which of the following pair of figures are congruent?

Here is an incomplete net for making a cube. Complete it in atIeast two different ways. Remember that a cube has six faces. How many are there in the net here? (Give two separate diagrams. It you like, you may use a squared sheet for easy manipulation)

Make an oblique sketch for each one of the given isometric shapes.

Can this be a net for a die? Explain your answer

Write the number of faces, edges and vertices in the solids given below:
Brick

How an object which is 3-D can be viewed in different ways? Name all the ways.

State the number of lines of symmetry for the following figures.
(a) An equilateral triangle
(b) An isosceles triangle
(c) A scalene triangle
(d) A square
(e) A rectangle
(f) A rhombus
(g) A parallelogram
(h) A quadrilateral
(i) A regular hexagon
(j) A circle

Some of the English alphabets have fascinating symmetrical structures. Which capital letters have just one line of symmetry (like E)? Which capital letters have a rotational symmetry of order 2 (like I)? .By attempting to think on such lines, you will be able to fill in the following table.

State the order of rotation and angle of rotation of the following figure.

Draw all lines of symmetry for each of the following figure.

Trace each figure. Then, draw all lines of symmetry, if it has.

Express each of the following numbers using exponential notations.
1024

Express each of the following numbers using exponential notations.
1029

Find the value of n, where n is an integer and \({ 2 }^{ n-5 }\times { 6 }^{ 2n-4 }=\frac { 1 }{ { 12 }^{ 4 }\times 2 } \).

If 2ⁿ⁺² - 2ⁿ⁺¹ +2ⁿ = c x 2ⁿ, then find the value of c.

Write the difference between 8³ and 7³

What are the terms in the following expressions? Show how the terms are formed. Draw a tree diagram for each expression. - 2x² y

Identify the coefficients of the terms of following expressions. 4x- 3y, a + b + 5, 2y+ 5, 2xy

Identify like terms in the following; 10pq, 7p, 8q, -p²q², -7qp, -100q, -23, 12q²p² -5p², 41, 2405p, 78qp, 13p²q, qp², 701p²

Add and Subtract - m - n, m + n

Identify the terms and their factors in the following expressions. Show the terms and factors by tree diagrams:
-ab + 2b²-3a²

The length and the breadth of a rectangular piece of land are 500 m and 300 m, respectively. Find the cost of the land, if 1m² of the land costs Rs 10000.

Find the area of a square park whose perimeter is 320m.

The perimeter of a rectangular sheet is 100cm. If the length is 35 cm, find its breadth. Also, find the area.

The area of a square park is the same as of a rectangular park. If the side of the square park is 60 m and the length of the rectangular park is 90 m, find the breadth of the rectangular park.

A door of length 2 m and breadth 1 m is fitted in a wall. The length of the wall is 4.5 m and the breadth is 3.6 m in the given figure. Find the cost of whitewashing the wall, if the rate of whitewashing the wall is Rs 20 per m².

Look at following figures and classify each of the triangles according to its

One of the exterior angles of a triangle is 112° and the interior opposite angles are in the ratio 3 : 4. Find the interior opposite angles.

The exterior \(\angle ACD\ of \triangle ABC\) 115⁰.If \(\angle B=50^0\).then find \(\angle A.\ is\angle ACD>\angle A?\)

If the sum of three exterior angles of a triangle is 360° and the corresponding interior opposite angles are equal to each other. Then, find the value of each of the interior angle of the triangle.

In the following figure, ABII CO. Find the value of \(\angle X\)

Lines l||m, p||q,  Find a, b, c, d?

In the following figure, AB II CO, AF II ED, \(\angle \)AFC = 70° and \(\angle \)FED = 40°, then find \(\angle \)EFD.

Iron rodes a, b, c, d, e and f are making a design of a bridge as shown in figure, in which a || b, c || d, e || f. Find the marked angles between b and c.

In the following figure, EF || GH, \(\angle\)EAB = 70° and \(\angle\)ACH=120°. Then, find \(\angle\)CAF and \(\angle\)BAC.

In the given figure, examine whether the following pairs of lines are parallel or not.

AB and CD

Examine whether you can construct ΔDEF such that EF = 7. 2 cm, mㄥE = 110° and mㄥF = 80°. Justify your answer.

The Measures of certain sides and angles ot triangles. Identity those which cannot be constructed and say why you cannot construct them? Construct rest ot the triangles.

Find the measure of side AB from the following figure.

Draw the angle bisector of \(\angle A\) in the triangle with sides AB = 9.5 cm, AC = 8 cm and BC = 6.5 cm.

Draw a \(\triangle ABC\) with sides 15 cm, 8 cm and 17 cm and find the measure of the angle opposite to the longest side, what type of triangle is it?

Arun spend \( \frac { 3 }{ 5 } \) of his pocket money during launch break and \(\frac { 3 }{ 8 } \) after school.He also spend \(\frac { 1 }{ 6 } \) of the pocket money for his younger brother.What part of money he spend in all?

Average \(\frac { 1 }{ 5 } ,\frac { 2 }{ 8 } ,\frac { 3 }{ 4 } \) in ascending order.

Draw the number line and represent the following rational numbers on it .
\(\frac { 3 }{ 4 } \)

Add the following rational numbers.
\(\frac { 1 }{ 3 } +\frac { 2 }{ 6 } \)

What should be subtracted from \(\frac { -2 }{ 3 } \) to obtain the nearest integer?

Find the ratio of  15 kg to 210 g

Find the ratio of 9 m to 27 cm

A grocer buy 10 eggs for Rs 8 and sells 8 eggs for Rs10. Find his gain or loss per cent

A collection of 10 chips with different colours is given

Complete the table and find the percentage of chips of each colour.

If 65% of students in a class have a bicycle, what per cent of the students do not have bicycles?

When two triangles, say ABC and PQR are given, there are in all, six possible matchings or correspondences. Two of them are
(i) ABC ↔️ PQR (ii) ABC ↔️ QRP
Find the other four correspondences by using two cut outs of triangles. Will all these correspondences lead to congruence?

If ΔABC ≌ ΔFEDunder the correspondence ABC ↔️ FED, then write all the corresponding congruent parts of the triangles.

In the given figure, AC = BD and AD = BC. Which of the following statements is meaningfully written?

(i)  ΔABC ≅ ΔABD
(ii)  ΔABC ≅ ΔBAD

You want to establish ΔDEF ≅ ΔMNP, using ASA congruence rule. You are given that ㄥD = ㄥM and ㄥF = ㄥP. What information is needed to establish the congruence? (Draw a rough figure and then try)

It is to be established by RHS congruence rule that ΔABC ≅RPQ. What additional information is needed, if it is given that ㄥB =ㄥP = 90⁰ and AB = RP?

Verify by drawing a diagram, if the median and altitude of an isosceles triangle can be same.

From the above figure, find the value of \(\angle A\).

In the following figure, find the value of \(\angle A+\angle B+\angle C.\)

Find angle x in each figure.

In the following figure,\(\triangle PQR\ and \triangle OQR\) are isosceles triangles and \(\angle a=2\angle b.\)Find \(\angle c\).

Follow the directions and correct the given incorrect equation written in Roman numerals: Remove two of these matchsticks to make a valid equation: IX - VI = V.

What will be the value of y for which expressions (y -15) and (2y + 1) becomes equal?

The age of Sohan Lal is four times that of his son Amit. If the difference of their ages is 27 yr, find the age of Amit.

The perimeter of a rectangle is 40 m. The length of the rectangle is 4 m less than 5 times its breadth. Find the length of the rectangle.

If 45 is added to half a number, then result is triple the number. Find the number.

Sale of Mathematics and Hindi books in the years 1999, 2000, 2001 and 2002 are given below:

In which year was the difference in the sale of the two subjects books least?

The mean of 10 observations was calculated as 40. It was detected on rechecking that the value of 45 was wrongly copied as 15. Find the correct mean.

Number of children in six different classes are given below. Represent the data on a bar graph

(a) Find the average number of children in the classes.
(b) Find the ratio of student of Class VI to the students of Class VIII

Study the bar graph given below and answer the questions that follow:

(a) What information does the above bar graph represent?
(b) In which year was production the least?
(c) After which year was the maximum rise in the production?
(d) Find the average production of rice during the 5 years.
(e) Find difference of rice productions between the years 2006 and 20'08.

Study the double bar graph shown below and answer the questions that follow:

(a) What information is represented by the above double bar graph?
(b) In which month, sales of brand A decreased as compared to the previous month?
(c) What is the difference in sales of both the brands for the month of June?
(d) Find the average sales of brand 8 for the six months,
(e) List all months for which the sales of brand 8 was less than that of brand A.
(f) Find the ratio of sales of brand A as compared to brand 8 for the month of January.

Ram and Ankush had 4500 stamps altogether. If Ram had \(\frac{4}{5}\)as many stamps as Ankush, how many stamps did Ankush have? 

A rectangular sheet of paper is 11\(\frac{1}{2}\) m long and 12\(\frac{1}{3}\)m wide.Find its perimeter.

Which is greater? \(\frac{2}{7}\)of\( \frac{3}{4}\) of \( \frac{3}{5}\)of\( \frac{5}{8}\)

Sugar is sold at Rs 17\(\frac{3}{5}\) per kg. Find the cost of 16 kg of sugar.

A wire of length \(4 \frac{2}{5}\) m is cut into like 5 pieces of equal length. Find the length of each piece.

In a class test containing 10 questions, 5 marks are awarded for every correct answer and (- 2) marks are awarded for every incorrect answer and 0 for questions not attempted.
(i) Mohan gets four correct and six incorrect answers. What is his score?
(ii) Reshma gets five correct answers and five incorrect answers. What is her score?
(iii) Heena gets two correct and five incorrect answers out of seven questions she attempts. What is her score?

Write five pairs of integers (a, b) such that a \(\div\) b = - 3. One such pair is (6, - 2) as 6 \(\div\) (-2) = (-3).

In a class test, (+ 3) marks are given for every correct answer and (- 2) marks are given for every incorrect answer and no marks for not attempting any question.
(i) Radhika scored 20 marks. if she has got 12 correct answers, how many questions has she attempted incorrectly?
(ii) Mohini scores (-5) marks in this test, though she has got 7 correct answers. How many questions has she attempted incorrectly?

Write two integers which are smaller than -5 but their difference is -5.

Write two integers, which are greater than -4, but their difference is smaller than -2.

Solve the following equation by trial and error method. 5p+2 =17

Solve the following equation by trial and error method. 3m-14=4

Set up equation and solve them to find the unknown numbers in the following cases. Add 4 to eight times a number, you get 60.

Set up equation and solve them to find the unknown numbers in the following cases. One-fifth of a number minus 4 gives 3.

Set up equation and solve them to find the unknown numbers in the following cases. If I take three-fourths of a number and add 3 to it, I get 21.

Draw any rectangle and find the measures of angles at the four vertices made by the intersecting lines.

In the given figure, p II q. Find the unknown angles.
​​​​​​​

In the following figure, find the angles 2x and \(\frac { 1 }{ 2 } x.\)

Find the value of the angles x, y and z, in the following figure.

In the following figure, find the value of \(\angle \)M.

Find the mean of your sleeping hours during one week.

Organise the following marks in a class assessment,in a tabular form: 4, 6, 7, 5, 3, 5, 4, 5, 2, 6, 2, 5, 1, 9, 6, 5, 8, 4, 6, 7 - Which number is the highest?

Following table shows the points of each player scored in four games

B played in all the four games. How would you find the mean?

The rainfall (in mm) in a city on 7 days of a certain week was recorded as follows:

Find the mean rainfall for the week

Find the mode and median of the following data. 13, 16, 12, 14, 19, 12, 14, 13, 14

A rectangular sheet of paper is 12\(\frac{1}{2}\)cm long and 10\(\frac{2}{3}\)cm wide. Find its perimeter.

Salil wants to put a picture in a frame. The picture is 7\(\frac{3}{5}\)cm wide. Tofit in the frame, the picture cannot be more than 7\(\frac{3}{10}\)cm wide. How much should the picture be trimmed? 

What happens to the value of the product, when we multiply two improper fractions?

Which is smaller 1\(\frac{1}{2}\) of \(\frac{16}{5}\) or 1\(\frac{1}{2}\) of \(\frac{31}{5}\)?

Find \(\frac{5}{6}\) of a rupee

Following number line shows the temperature in degree Celsius (^o C ) at different places on a particular day.

What is the temperature difference between Lahulspiti and Srinagar?

Following number line shows the temperature in degree Celsius (^o C ) at different places on a particular day.

Can we say the temperature of Srinagar and Shimla taken together is less than the temperature at Shimla? Is it also less than the temperature at Srinagar?

In a quiz, positive marks are given for correct answers and negative marks are given for incorrect answers. If Jack's scores in five successive rounds were25, - 5, - 10, 15 and 10, what was his total at the end?

At Srinagar, the temperature was -5° C on Monday and then it dropped by 2° C on Tuesday. What was the temperature of Srinagar on Tuesday? On Wednesday, it rose by 4°C. What was the temperature on this day?

Verify a + (- b) = a - b for the following values of a and b: a = 137, b = 92

Identity the nets which can be used to make cubes (cut-out copies of the nets and try it).

If a cone of base radius 3 cm is placed on a cylinder of base radius 3 cm, then how many faces will the resultant figure have?

If a cone is cut from the top horizontally, then which 2-D figure will be seen?

Use isometric dot paper and make an isometric sketch for each one of the given shapes

Draw an isometric sketch of a square pyramid.

Copy the figure with punched holes and find the axes of symmetry for the following:

Copy the figure with punched holes and find the axes of symmetry for the following:

Given the line(s) of symmetry, find the other hole(s).

Name any two figures that have both line symmetry and rotational symmetry.

Name the quadrilateral which have both line and rotational symmetry of order more than 1.

Express the following in exponential form: b x b x b x b

Express the following in exponential form: 5 x 5 x 7 x 7 x 7

Express each of the following as product of powers of their prime factors. 648

Express each of the following as product of powers of their prime factors. 405

Express the following as a power of - 3: 81

Describe how the following expressions are obtained? x²y

Describe how the following expressions are obtained? 4x² - 5x

Get the algebraic expressions in the following cases using variables, constants and arithmetic operations - Number 5 added to three times the product of numbers m and n

Get the algebraic expressions in the following cases using variables, constants and arithmetic operations - Product of numbers y and z subtracted from 10 

 Identify the terms and their factors in the following expressions. Show that the terms and factors by tree diagrams.  y - y³

How much plastic sheet do you need to cover a rectangular swimming pool?

The perimeter of a rectangle is 130 cm. If the breadth of the rectangle is 30 cm, find its length. Also, find the area of the rectangle.

Yogesh walks to school every day. His school is located 500 m from his house. What is the total distance walked by Yogesh in 5 days?

A rectangular grassy lawn is 18 m x 12 m. It has a ground path, 1.5 m wide all around it on the outside. What is the area of the path?

Find the area of the following parallelogram.

Study the following problem. ΔABC, if AC = 7 cm, m ㄥA = 60⁰ and m ㄥB = 50°, can you draw the triangle?

The Measures of certain sides and angles ot triangles. Identity those which cannot be constructed and say why you cannot construct them? Construct rest ot the triangles.

The Measures of certain sides and angles ot triangles. Identity those which cannot be constructed and say why you cannot construct them? Construct rest ot the triangles.

A line segment AB = 6 cm, if a perpendicular bisector constructed on it. Find the length of two parts.

PQ is a given line. If RS and TV are parallel to PQ and are drawn on either side of PQ. Then, check if RS and TU are parallel to each other also.

Express the following rational number with positive denominator \(\frac { -4 }{ -5 } \) 

Express the following rational number with positive denominator \(\frac { 5 }{ -6 } \)

Which of these are negative rational number positive rational number?
 \(\frac { -3 }{ -11 } \)

Find the standard /simplest form of \(\frac { -21 }{ 27 } \).

Find the value of \(\frac { 16 }{ 5 } \div \frac { 2 }{ 5 } \)

If cost price of an article is Rs 500 and selling price of that article is Rs 700. Find the gain or loss per cent.

If A and B shared Rs.1300 in the ratio 1 :12, how much did A get?

A sum of Rs.2700 was lent for 10 yr at the rate of15% per annum. Find the interest and amount.

Write following decimals as percentage. 0.064

Are the ratio 2: 5 and 3: 7 equivalent?

If ΔDEF ≅ ΔPQR Write the part(s) of ΔPQR that corresponds to ㄥF

If ΔDEF ≅ ΔPQR, then corresponding congruent part(s) of the triangle is ㄥE

In the given figure, measures of some parts are indicated. By applying ASA congruence rule, state which pairs of triangles are congruent? In case of congruence, write the result in symbolic form.

In the given figures, measures of some parts of triangles are given. By applying RHS congruence rule, state which pairs of triangles are congruent? In case of congruent triangles, write the result in symbolic form.

You want to show that ΔART ≅ ΔPEN.
If it is given that ㄥT = ㄥN and you are to use SAS criterion rule, you need to have

(a) RT =
(b) PN =

Draw rought sketches of \(\triangle PQR\),where QE is a median.

Draw rough sketch of altitude from A to \(\bar { BC } \) for the following given triangles.

Does a median lie wholly in the interior of the triangle? (If you think that this is not true, draw a figure to show such a case).

How many altitudes can a triangle have?

Can the altitude and median be same for a triangle?

Can two obtuse angles be complement to each other?

What is the measure of the complement of each of the following angles? 45°

What is the measure of the complement of each of the following angles? 65°

Which pairs of the following angles are complementary?

Which pairs of the following angles are complementary?

Write at least one other form
\(\frac { m }{ 5 } -2=6\)

Check whether the value given in the brackets is a solution to the given equation or not: n+5 = 19 (n=1)

Write equations for If you take away 6 from 6 times y, you get 60.

Write equations for If you add 3 to one-third of z, you get 30.

Solve the following equations. 6z+10=-2

Find the median of the following data:35, 32, 35, 42, 38, 32, 34

The heights of 10 girls were measured (in cm) and the results are as follows: 135, 150,139, 128, 151, 132, 146, 149, 143, 141 - What is the height of the tallest girl?

If the arithmetic mean of 6, 8, 5, 7, P and 4 is 7, then find the value of p.

There are 6 marbles in a box with numbers from 1 to 6 marked on each of them -What is the probability of drawing a marble with number 5?

A survey of 100 persons showed that 75 like cricket while 25 dislike it. One person is chosen at random. What is the probability that the chosen person - Dislike Criket

Simplify  \(\frac{4}{9}-\frac{4}{11}+\frac{1}{2}\)

Find the product of the following: \(\frac{4}{7}\times 3\)

Find \(\frac{13}{11}\times 6\)

Find \(5\times 2\frac{3}{7}\)

Find \(1\frac{4}{9}\times 6\)

Solve 14- (-20)

Solve (-6) - (-16)

State whether the following statement is correct or incorrect. Correct those which are wrong.
Additive inverse of an integer 8 is (-8) and additive inverse of (-8) is 8.

Verify a - (-b) = a + b for the following values of a and b. a= 75, b= 84

Write 3 integers just preceding and just succeeding -7.

All faces of a pyramid are always

Out of the following, which is a 3-D figure?

Total number of edges a cylinder has

When we cut a corner of a cube as shown in the figure, we get the cut-out piece as

If we rotate a right angled triangle of height 5 cm and base 3 cm about its height a full turn, we get

The order of rotational symmetry in the figure given below is

The angle of rotation in equilateral triangle is

In the word 'MATHS', which of the following pairs of letters shows rotational symmetry?

Which of the following are reflections of each other?

Which of the following letters of English alphabets have more than 2 lines of symmetry?

For any two non-zero rational numbers x and y, x⁵ ÷ y⁵ is equal to.

(- 4)⁴ x (-2)⁰  x (-1)²⁰² is equal to

If (3¹⁰² x 3¹⁰¹) ÷ 3¹⁰¹= k- 3¹⁰⁰, then the value of k

The number corresponding to expanded form, 6 x 10⁸ + 3 x 10⁷ + 4 x 10⁵ + 3 x 10² + 1x 10⁰ is

Standard form corresponding to the number 654300100 is

An algebraic expression containing three terms is called a

The degree of the polynomial x³y - 2xy⁴ + 5 is

The algebraic language of "Twice the cube of a number x subtracted from five times the sum of y and 2" is

- b - 0 is equal to

The value of 3x² - 5x + 3 when x = 1 is

Find the area of a square park, whose perimeter is 96 cm.

Find the length of a parallelogram, whose area is 246 cm² and base is 20 cm².

A wire is bent to form a square of side 22 cm. If the wire is rebent to form a circle. Then the Area of the circle is

The radii of two concentric circles are 7 m and 9 m. The area enclosed between them is

A cow is tied with a rope of 7 m. The grass grazed field by the cow is

A triangle can be constructed by taking its sides as.

A triangle can be constructed by taking two of its angles as

Which of the following sets of triangles could be the lengths of the sides of a right angled triangle?

In which of the following cases, a triangle can be drawn?

In the given constructed figure, the length of segment AC is equal to

Which pair shows equivalent rational numbers?

Which of the following is equivalent to \(\frac { 4 }{ 5 } \)

How many rational numbers are there between two rational numbers?

The subtraction \(6\frac { 4 }{ 5 } \)from \(\frac { 50 }{ 5 } \)

The product of \(2\frac { 6 }{ 8 } \) and \(4\frac { 1 }{ 4 } \)

Which of the following is the ratio of 3 km to 300 m?

A farmer bought a buffalo for Rs 44000 and a cow for Rs 18000. He sold the buffalo at a loss of 5% but made a profit of 10% on the cow. The net result of the transaction is

If Mohan's income is 25% more than Raman's Income, then Raman's income is less than Mohan's income by

The sum which will earn a simple interest of Rs 126 in 2 yr at 14% per annum is

What rate gives Rs 280 as interest on a sum of Rs 56000 in 2 yr?

Number of elements of a triangle is

Two figures are said to be congruent, if they have exactly the same

By which of the following criterion, the two triangles cannot be proved congruent?

By applying ASA congruence rule, it is to be established that ΔABC ≅ ΔQRP and it is given that BC = RP. What additional information is needed to establish the congruence?

Which congruence criterion do you use in the following?
Given, ZX = RP, RQ =ZY, ㄥPRQ = ㄥXZY. So, ΔPOR ≅ ΔXYZ

Angles which are both supplementary and vertically opposite are

In the following figure, if AB II CD, \(\angle \)APQ = 50° and \(\angle \)PRD = 130°, then \(\angle \)QPR is

If two supplementary angles are in the ratio of 1 : 2, then the bigger angle is

The measure of an angle, which is four times its supplement is

If sum of measures of two angles is 180°, then they are ___________________

The perimeter of the rectangle whose length is 40 cm and a diagonal is 41 cm, is

In the following figure, BC = CA and \(\angle A=20,\ then \angle ACD\) is equal to

If the exterior angle of a triangle is 130° and its interior opposite angles are equal, then measure of each interior opposite angle is

In a \(\triangle ABC\) if \(\angle A=60^0\) and \(\angle B=30^0\) then the exterior angle formed by producing BC is equal to

Which of the following cannot be the sides of a right triangle?

The mode of the data 22,29, 27, 23, 43, 41, 27 is

The mean of three numbers is 40. All the three numbers are different natural numbers. If lowest is 19, what could be the heighest possible number of remaining two numbers?

A bag is having 4 red balls and 6 yellow balls. If a ball is pulled out without seeing them, then find the probability of getting a red ball.

The representation of data with bars of uniform width is called _____

The mode of the following data 62,61,49,37, 91,61,47, 53, 54, 97, 98, 99 is

The solution of the equation mx + n = 0 is

If k + 7 = 16, then the value of 8k - 72 is equal to

The equation having -3 as a solution is

Which of the following numbers satisfies the equation -6 + x = -18?

x - ________ = 15, when \(\frac{x}{2}=6\)

The picture interprets

The product of \(\frac{11}{13}\) and 4 is

\(\frac{5}{12}\)part of what amount will be equal to 3\(\frac{3}{4}\) part of Rs 100?

The lowest form of the product \(2\frac{3}{7}\times \frac{7}{9}\) is _________

25.4\(\times \)1000 = _______

The value of (-10) x (-5) + (-7) is

(-43) x (-99) + 43 is equal to

If \(\bigotimes \) , O and \(\bullet\)  represent some integers on the number line, then descending order of these numbers is

(16) \(\div\) 4 is not same as:

Insert the correct sign = or \(\neq\) in the given blank space.
21 x (-9) _____ 9 x (-21)

A triangle can be constructed by taking its sides as.

A triangle can be constructed by taking two of its angles as

Which of the following cannot be the side of a triangle?

Which of the following is the measures of a right angled triangle?

To construct an equilateral triangle with a given side, which of the following is used?

Which of the following rational numbers is postive?

Which of the following rational numbers is negative?

Which of the following is the standard form \(\frac{36}{-24}\)is

What is the value of \(\left( \frac { -7 }{ 5 } \right) \times \left( \frac { -15 }{ 14 } \right) \) ?

Which of the following is the additive inverse \(\frac{-4}{7}\) ?

Which of the following is the ratio of 3 km to 300 m?

In a scout camp, 40% of the scouts were from Gujarat State and 20% of these were from Ahmedabad. The percentage of scouts in the camp from Ahmedabad is

When 35% is expressed in fraction, it is equal to :

\(\frac { 5 }{ 20 } \) is equal to:

The ratio of 3 kg and 1 kg 500 g is :

Number of elements of a triangle is

Two figures are said to be congruent, if they have exactly the same

Two triangles are congruent, if two angles and the side included between them in one of the triangles are equal to the two angles and the side included between them of the other triangle. This is known as the

By which of the following criterion, the two triangles cannot be proved congruent?

ΔPQR is congruent to ΔSTV (in figure), then what is the length of TU?

The sides of a triangle have length (in cm) 10, 6.5 and a, where a is a whole number. The minimum value that a can take is

The perimeter of the rectangle whose length is 40 cm and a diagonal is 41 cm, is

In a \(\triangle ABC\) if \(\angle A=60^0\) and \(\angle B=30^0\) then the exterior angle formed by producing BC is equal to

Angles of a triangle are in the ratio 1 : 2 : 3. The smallest angle is :

The exterior angle of a triangle is 120° and one of its interior opposite angle is 70°. Find the measure of its other interior opposite angle?

Angles which are both supplementary and vertically opposite are

The angles x - 10° and 190° - x are

The measure of an angle, which is four times its supplement is

Assume figure, AB II CD and EFis the transversal. If angles AGH = 60°, what is the measure of angle DHF?

A line has how many end points?

The solution of the equation mx + n = 0 is

If k + 2 = 6, then the value of 4k + 12 is equal to

If k + 7 = 16, then the value of 8k - 72 is equal to

The equation having -3 as a solution is

The sum of three times a number and 11 is 32. Find the number?

The mode of the data 22,29, 27, 23, 43, 41, 27 is

The median of the data 2, 16, 29, 88, 49, 99,16,4,37 is

If mean of 6 observations is 4, then their sum is

The number of trees in different parks of a city are 33, 38, 48, 33, 34, 34, 33 and 24. The mode of this data is

The difference between the highest and the lowest observations in a data is its

\(\frac{2}{5}\times 5\frac{1}{5}\) is equaI to

Which of the following represents \(\frac{1}{3}\)of\(\frac{1}{6}\)?  

What is the\(\frac { 1 }{ 2 } \)of 12?

Which of the following is the equivalent fraction of \(\frac { 3 }{ 4 } \)with numerator 18?

Each side of a regular hexagon is 3.5 cm long. The perimeter of the given polygon is

If the sum of two integers a and b is zero, then

The value of (-2) x (-1) x (1) is

(-43) x (-99) + 43 is equal to

Next three consecutive numbers in the pattern 11, 8, 5, 2, ... are

[(- 10) x (+ 9)] + (- 10) is equal to :

The angle of rotation in equilateral triangle is

In the word 'MATHS', which of the following pairs of letters shows rotational symmetry?

A circle has:  

A ceiling fan with three blades is seen from directly under it. The order of rotational symmetry is:

How many lines of symmetry are there in an equilateral triangle?

For any two non-zero rational numbers x and y, x⁵ ÷ y⁵ is equal to.

(- 4)⁴ x (-2)⁰  x (-1)²⁰² is equal to

(5⁷ ÷ 5²) x (3⁶ ÷ 3²)is equal to

Standard form corresponding to the number 654300100 is

Which of the following is the exponential form of '243' ?

An algebraic expression containing three terms is called a

The degree of the polynomial x³y - 2xy⁴ + 5 is

The subtraction of 5 times of y from x is

The value of 3x² - 5x + 3 when x = 1 is

 What is the coefficient of y²in expression 6y² + 2?