(a + b) + c = a + (b + c) is called

\(({ 2 }^{ 0 }+{ 4 }^{ -1 })\times { 2 }^{ 2 }\) is equal to

The unit digit in the square of the number 27 is

Which of the following numbers is divisible by 5 ?

The one's digit of the cube of the number 123 is

Which of the following is the reciprocal of p?

The multiplicative inverse of 10^-10 is

The smallest number by which 28 should be multiplied so as to get a perfect square is

If abc is a 3-digit number, then the number abc- a - b - c is divisible b

The one's digit of the cube of the number 242 is

Which of the following statements is false?

In 10², the exponent is

The number of digits in the square root of 100 is

The number 10 \(\times\) 7 + 5 in usual form is

Find the smallest number by which the number 1296 must be divided to obtain a perfect cube.

\(a \times (b \times c)=(a \times b) \times c\) is called

Which of the following is the standard form of 0.00001275?

The perfect square number out of 2, 3, 4 and 5 is

Which of the following numbers is not divisible by 9 ?

The one's digit of the cube of the number 50 is

Which of the following statements is true?

In 10², the exponent is

A perfect square number between 30 and 40 is

If x + y + z = 6 and z is an odd digit, then the 3-digit number xyz is

Find the smallest number by which the number 1296 must be divided to obtain a perfect cube.

5^-2 can be written as

The value of 3^5÷ 3^-8 is

The usual form of 2.08 x 10^-5 is

Which of the following is the standard form of 0.00001275?

Which of the following is equal to [100 - 99\(°\)] \(\times\) 100?

Which of the following is not true?

The reciprocal of \({-3\over8 } \times {-24\over 13}\) is

Which of the following is the identity element?

Which of the following is the multiplicative identity for rational numbers?

Which of the following is the product of \(\frac { 7 }{ 8 } \) and \(\frac { -2 }{ 21 } ?\)

Which of the following is the reciprocal of p?

Which of the following is the product of \(\frac { 7 }{ 8 } \) and \(\frac { -2 }{ 21 } ?\)

Which of the following statements is false?

Which of the following statements is true?

\(\frac{1}{2}\) is

Find the value of \({x\over y }+xy\) , using appropriate property and name it \(x={1\over3},y={2\over 5}\)

Represent the following rational numbers on the number line \(5\over2\)

Represent the rational number \({-7\over3}\)on the number line

Express the product of 1.3x10⁴ and 3.4x10^-2 in the standard form.

By what number should (-5)^-1 be multiplied, so that the product becomes 9?

If a property holds for rational number, will it also hold for integers? For whole numbers? Which will? Which will not?

Solve, \({-3\over13}+{15\over17}\times{-3\over13}+{17\over15}\)

Simplify
\({3\over7}\times({-2\over21})\times({-5\over6})\)

On a winter day, the temperature at a place in Jammu and Kashmir was -16^° C. Convert it in degree Fahrenheit (^°F)by using the formula\({c\over5}={F-32\over9}\)

Find three rational numbers between -3 and - 4

Using appropriate properties, find \({2\over5}\times({-3\over7})-{1\over6}\times{3\over2}+{1\over14}\times{2\over5}\)

Find the multiplicative inverse of the following  \(-1\times {-2\over5}\)

Find the additive inverse of \(-6\over-7\)

Is \(\frac{2}{3}-\frac{5}{4}=\frac{5}{4}-\frac{2}{3}?\)

Using the suitable identities, evaluate the following :
(103) ²  .

Find the value of the following :
\(\frac { (151+149)^{ 2 }-(151-149)^{ 2 } }{ 151\times 149 } \)

Find the value of p,if 
px=\(\frac { 4{ x }^{ 2 }-7x-15 }{ x-3 } -5\)

if mean of some observations is (4x ²-9) and their sum is 16x⁴ -81. Then , find the number of observations

If perimeter of square 4x² -36 unit. Then, find the area of the square? Find the area, if x=2

Observe the following tables and find, if x and y are directly proportional

Suppose 2 kg of sugar contains 9 X 10⁶ crystals. How many sugar crystals are there in 5 kg of sugar?

A 5 m 60 cm high vertical pole casts a shadow 3 m 20cm long. Find at the same time
(i) the length of the shadow cast by another pole 10m 50 cm high
(ii) the height of a pole which casts a shadow 5m long.

A girl 1.2 m tall casts a shadow 1.1 m at that height. When a building casts a shadow 6.6 m long. Determine the height of the building?

It is given that I varies directly as m.
(i) Write an equation which relates l and m.
(ii) Find the constant of proportion (k), when l is 6 am m is 18.
(iii) Find l, when m is 33.
(iv) Find m, when l is 8.

A rectangular park, whose length is 30 m and width is 20 m is shown in the following figure
(i) What is the total length of the fence surrounding it?
(ii) How much land is occupied by the park?
(iii) A path of 1 m width running inside along the perimeter of the park has to be cemented. How many bags of cement would be required to construct the cemented path, if 1 bag of cement is required to cement 4 m²area?
(iv) There are two rectangular flower beds of size 1.5 m \(\times\) 2 m each in the park as shown in the given figure and the rest has grass on it. Find the area covered by grass.

Mrs. Kaushik has a square plot with the measurement as shown in the figure. She wants to construct a house in the middle of the plot. A gardenis developed around the house. Find the total cost of developing a garden around the house at the rate of Rs.55 per m²

The shape of a garden is rectangular in the middle and semi-circular at the ends as shown in the diagram. Find the area and the perimeter of this garden. Length of rectangle is 20- (3.5+ 3.5) m.

We know that parallelogram is also a quadrilateral. Let us also split such a quadrilateral into two triangles, find their areas and hence that of the parallelogram. Does this agree with the formula that you know already?

Polygon ABCDE is divided into parts as shown Find its area, if AD = 8 cm, AH=6cm, AG = 4cm, AF= 3cm and perpendiculars BF = 2 cm, CH= 3 cm, EG = 2. 5cm Areaof polygon ABCD = Area of ΔAFB+...
Area of ΔAFB =\(\frac { 1 }{ 2 } \times \) AF\(\times\) BF=\(\frac { 1 }{ 2 } \times \) 3\(\times\) 2 = ..
Area of trapezium FBCH = FH \(\times\)\(\frac { (BF+CH) }{ 2 } \)   
= \(3\times \frac { (2+3) }{ 2 } \) +.... [∵ FH=AH-AF]
Area of ΔCHD =\(\frac { 1 }{ 2 } \times \) HD \(\times\) CH
Area of ΔADE =\(\frac { 1 }{ 2 } \times \) AD\(\times\) GE = ...
So,the area of polygon ABCDE =...

Look at the given map of a city.

Answer the following questions:
(a) Colour the map as follows: Blue-water, Red-fire station, Orange-library, Yellow-school, Green-park, Pink-college, Purple-hospital, Brown- cemetery.
(b) Mark a green 'X' at the intersection of road 'C' and Nehru Road, Green 'V' at the intersection of Gandhi Road and road 'A'.
(c) In red, draw a short street route from library to the bus depot.
(d) Which is further East, the city park or the market?
(e) Which is further South, the primary school or the Sr. Secondary School?

Using Euler’s formula find the unknown

Using Euler's formula, find the value of unknown x, y, z, p, q and r in the following parts.

Name the following polyhedrons and verify the Euler's formula for each of them.

In a town, an ice-cream parlour has displayed an ice-cream sculpture of height 360 cm. The parlour claims that these ice-creams and the sculpture are in the ratio 1 : 30. What is the height of the ice-cream served?

Write the coefficients of xy in the following polynomials.
(i) 4yx²
(ii) 2X²+xy

Classify the following as monomials, binomials and trinomials \(2{ a }^{ 2 }cb+\frac { 1 }{ 2 } cb{ a }^{ 2 },b+1,{ a }^{ 2 }b+{ b }^{ 2 }c+{ c }^{ 2 }a\)

Evaluate using suitable identities.
(i) (48)²
(ii) 181²-19²
(iii) 497 x 505
(iv) 2.07 x 1.93

Find the product of the following binomials.
\(\left( \frac { x-y }{ 2 } \right) \left( \frac { x+y }{ 2 } \right) \)

Using the formula for squaring a binomial, evaluate the following.(199)²

If Chameli had Rs 600 left after spending 75% of her money, how much did she have in the beginning?

If 40% of the students are girls and the number of boy students is 600, then find the number of girl students.

A political party won 25 seats out of the total number of seats it contested. If their win percentage was 60% approx, then how many seats did the party contest in all?

A milkman sold two of his buffaloes for Rs 20000 each. On one, he made a gain of 5% and on the other, a loss of 10%. Find his overall gain or loss. [Hint Find CP of each]

A shopkeeper in order to clear his old stock of shoes,30% discount to their customer at each pair of shoes.If marked price of a pair of shoes is Rs 4000, then find these selling price of a pair of shoes.

I have a total of Rs. 300 in coins of denomination Rs. 1, Rs.2 and Rs. 5. The number of Rs. 2 coins is 3 times the number of Rs.5 coins. The total number of coins is 160.How many coins of each denomination are with me?

My age is four time the difference of my age after four years and three years before. How old am I?

Three prizes are to be distributed in a quiz contest. The value of the second prize is five-sixth the value of the first prize and the value of the third prize is four-fifth that of the second prize. If the total value of three prizes is Rs. 150, then find the value of each prize.

Abdul buys two kinds of cloth material for school uniforms, shirt material which costs him Rs. 50 per metre and trouser material that costs him Rs. 90 per metre. For every 2 m of the trouser material, he buys 3 m of the shirt material. He sells the material at 12% and 20% profit, respectively. His total sale is Rs. 38160. How much trouser material did he buy?

Denominator of a number is 4 less than its numerator. If 6 is added to the numerator, it becomes thrice the denominator. Find the fraction.

Construct a quadrilateral ABCD, where AB = 5 cm, CD = 4 cm, DB = 7cm, BC = 6 cm and DA = 5.5 cm.

Construct a quadrilateral ABCD, given that AB=7.5 cm, BC = 5 cm, CD=6 cm, BD=6 cm and AC = 10 cm.

Costruct a quadrilateral ABCD such that AB=2 cm, BC=3.6 cm, AD=3.2 cm, \(\angle \)A=90° and \(\angle \)B=120°.

Draw a rhombus ABCD having their diagonals of lengths BD = 6 cm and AC = 8 cm.

How will you construct a rectangle PQRS, if you know only the lengths PQ and QR?

Given here are some figures.

Classify each of them on the basis of the following.
(a) Simple curve
(b) Simple closed curve
(c) Polygon
(d) Convex polygon
(e) Concave polygon

Consider the following parallelograms. Find the values of the unknowns x, y and z.

A rectangular MORE is shown below:

Answer the following questions by giving appropriate reason.
(i) Is RE = OM?
(ii) Is ㄥMYO = ㄥRXE?
(iii) Is ㄥMOY = ㄥREX?
(iv) Is ΔMYO ≅ RXE?
(v) Is MY = RX?

In the following figure of a ship, ABDH and CEFG are two parallelograms. Find the value of x.

PQRS is a rhombus such that perpendicular bisector of PQ passes through the point S. Find the angles of rhombus.

Convert \(2\over3\) as percentage.

What is 72% of 25?

A cricket team won 10 matches out of the total number of matches they played. If their winning percentage is 25, then how many matches did they play in all?

The price of an item was Rs 25000 last year. It has increased by 20% this year. What is the price now?

A shirt is marked at Rs 1250 and sold for Rs 1125. What is the discount and discount per cent?

Observe the following tables and find, if x and y are directly proportional

Principal = Rs.1000,Rate = 8% per annum. Fill in the following table and find which type of interest (simple or compound) changes in direct proportion with time period.

Suppose 2 kg of sugar contains 9 X 10⁶ crystals. How many sugar crystals are there in 5 kg of sugar?

Rashmi has a roadmap with a scale of 1 cm representing 18 km. She drives on a road for 72 km. What would be her distance covered in the map?

A girl 1.2 m tall casts a shadow 1.1 m at that height. When a building casts a shadow 6.6 m long. Determine the height of the building?

Tabulate the number of faces, edges and vertices for the following polyhedrons: (Here, 'V' stands for number of vertices, 'F' stands for number of faces and 'E' stands for number of edges).

What do you infer from the last two columns? In each case, do you find F + V = E + 2, i.e. F + V - E = 2?

What happens to F, V and E, if some parts are sliced off from a solid? (To start with, you may take a plasticine cube, cut a corner off and investigate.)

Using Euler’s formula find the unknown

The following is the map of a town. Based on it answer the questions.

(a) Find the number of hospitals in the town,
(b) Find the ratio of the number of general stores to the ground,
(c) According to the map, find the number of schools in the town,
(d) What is the value depicted by the map of a particular location?

Use isometric dot paper, to sketch a rectangular prism with length 4 units, height 2 units and width 3 units

The shape of a garden is rectangular in the middle and semi-circular at the ends as shown in the diagram. Find the area and the perimeter of this garden. Length of rectangle is 20- (3.5+ 3.5) m.

An ant is moving around a few food-pieces of different shapes scattered on the floor. For which food-piece would the ant have to take a longer round? Remember, circumference of a circle can be obtained by using the expression C = 2\(\pi \) r,where r is the radius of the circle.

There is a pentagonal shaped park as shown. the figure. For finding its area, Jyoti and Kavita divided it in two different ways.

Find the area of this park using both ways. Can you suggest some other way of finding its area?

Find the area of the following trapezium.

Find the length of the diagonal BD when, the area of the quadrilateral is 32 cm².

Write down the like terms in the given polynomial \(2c{ a }^{ 2 }+\frac { 1 }{ 2 } b{ c }^{ 2 }a+\frac { 2 }{ 3 } bc{ a }^{ 2 }+3{ a }^{ 2 }bc\)

Classify the following as monomials, binomials and trinomials \(2{ a }^{ 2 }cb+\frac { 1 }{ 2 } cb{ a }^{ 2 },b+1,{ a }^{ 2 }b+{ b }^{ 2 }c+{ c }^{ 2 }a\)

Which of the following polynomials is/are a monomial?\(\frac { 1 }{ 2 } a{ c }^{ 2 }b+ba{ c }^{ 2 }+\frac { 1 }{ 2 } { c }^{ 2 }ab,a+1,abc\)

Find the product of the following binomials.(7x-6y)(7x-6y)

Find the product of the following binomials.
\(\left( \frac { x-y }{ 2 } \right) \left( \frac { x+y }{ 2 } \right) \)

Using the suitable identities, evaluate the following :
(103) ²  .

Using suitable identities, evaluate the following:
(69.3)² - (30.7)² 

The area of a circle is given by the expression \(\pi { x }^{ 2 }+6\pi { x }^{ 2 }-9\pi \) sq unit. Find the perimeter of the circle, if x is the radius of the circle.

if mean of some observations is (4x ²-9) and their sum is 16x⁴ -81. Then , find the number of observations

If a+b =199 and a²+b²=1,then find the value of a.b.

Complete the given tables and draw a graph for each.
(i)

(ii)

Locate the points A(1,2), B(4,2) and C(1, 4) on a graph sheet taking suitable axes. Write the coordinates of the fourth point D to complete the rectangle ABCD. 

The following table shows the colours preferred by students of a Class VIII :

Represent this data in the form of pie diagram (approx).

The following graph shows the journey made by two cyclists, one from town A to B and the other from town B to A
(a) At what time did cyclist II rest? How long did the cyclist rest?
(b) Was cyclist II cycling faster or slower after the rest?
(c) At what time did the two cyclists meet?
(d) What value depicted from here?

If y-coordinate is 5/2 times of x-coordinate.Then, formed a table for it and draw a graph.

Draw an appropriate graph to represent the given information.

The shoppers who come to a departmental store are marked as Man (M), Woman (W), Boy (B) or Girl (G). The following list gives the shoppers who came during the first hour in the morning:
W W W G B W W M G G M M W W W W G B M W B G G M W W M M W W W M W B W G M W W W W G W M M W W M W G W M G W M M B G G W
Make a frequency distribution table using tally marks. Draw a bar graph to illustrate it.

The following data represents the approximate percentage of water in various oceans.
Prepare a pie chart for the given data.

(a)From a pack of cards, the following cards are kept face down.

Suhail wins if he picks up a face card. Find the probability of Suhail winning?
b)Now, the following cards are added to the above cards:

Whatis the probability of Suhail winning now?
Reshmawins, if she picks up a 4. What is the probability of Reshma winning? [queen, king and jack cards are called face cards.]

The following pie chart represents a total expenditure of Rs 540000 on different items in constructing a flat in a town. Study the pie chart and answer the questions.

(a) Find the expenditure (in Rs) on bricks.
(b) How much expenditure on bricks is less than the expenditure on timber (in Rs)?

Find the sum of cubes of first four natural numbers.

Show that 0.001728 is the cube of a rational number. Find that rational number whose cube is 0.0017288.

Find the cube root of 17576 through estimation

Is 42592 a perfect cube? If not, then by which smallest number should 42592 be divided so that quotient is a perfect cube?

Which of the following are perfect cube?
i) 8000
ii)9000

Find the values of the letters in each of the following and give reasons for the steps involved. \(\begin{matrix}\quad 1\ A \\ \times \ \quad A \\ \_ \_ \_ \_ \_ \_ \_ \\ \quad 9\ A \\ \_ \_ \_ \_ \_ \_ \_ \_ \end{matrix}\)

Find the values of the letters in each of the following and give reasons for the steps involved.\(\begin{matrix} \quad \quad A\ B \\ +\quad 3\ \ 7 \\ \_ \_ \_ \_ \_ \_ \_ \\ \quad 6\ A \\ \_ \_ \_ \_ \_ \_ \_ \_ \end{matrix}\)

If from a 2-digit number, we subtract the number formed by reversing its digits, then the result so obtained is a perfect cube. How many such numbers are possible? Write all of them.

More about Pythagorean triplets We have seen one way of writing Pythagorean triplets as 2m, m² - 1, m² + 1. A Pythagorean triplet a, b, c means a² + b² = c2. If we use two natural numbers m and nim. > n), and take a = m² - n², b = 2mn, c = m² + n², then we can see that c² = a² + b². Thus for different values of m and n with m > n we can generate natural numbers a, b, c such that they form Pythagorean triplets. For example: Take, m = 2, n = 1. Then, a = m² - n² = 3, b = 2mn = 4, c = m² + n² = 5, is a Pythagorean triplet. (Check it !) For, m = 3, n = 2, we get a = 5, b = 12, c = 13 which is again a Pythagorean triplet. Take some more values for m and nand generate more such triplets.

When water freezes its volume increases by 4%. What volume of water is required to make 221 cm³ of ice?

If the expression X x 809436 x 809436 be a perfect square, then find the value of x.

If (46)² is subtracted from the square of a number, then answer so obtained is 485. What is the number?

Find the least number, which is a perfect square and has 7936 as one of its factors.

The area of a rectangular field whose length is twice its breadth, is 2450 m². Find the perimeter of the field.

Find the least number that must be added to 1500. so as to get a perfect square. Also, find the square root of the perfect square.

Express the product of 1.3x10⁴ and 3.4x10^-2 in the standard form.

The distance between the Earth and a star is 7.83 x 10⁵ km. Convert it into usual form.

Investigating Solar System The table shows the average distance from each planet in our solar system to the Sun.

(a) Write the distance from each planet to the Sun in standard notation.
(b) Arrange the planets from closest to the Sun to farthest from the Sun.

Find the value of x^-3 , if x = (100)^{1- 4} + (100)⁰.

While studying her family's history. Shikha discovers records of ancestors 12 generations back. She wonders how many ancestors she has had in the past 12 generations. She starts to make a diagram to help her figure this out. The diagram soon becomes very complex.

(a) Make a table showing the number of ancestors in each of the 12 generations.
(b) Write an equation for the number of ancestors in a given generation n.

Use the distributivity of multiplication of rational numbers over addition to simplify:
\({3\over5}\times[{35\over24}+{10\over1}]\)

If the product of two rational numbers is \(3{5\over4}\) and one of the rational number is \(3{5\over6}\)  then find the other rational number

Write 4 rational numbers between 2 and 3.

Huma, Hubna, and Seema received a total of Rs 2016 as monthly allowance from their mother, such that Seema gets \(1\over2\) of what Huma gets and Hubna gets times Seema's share. How much money do the three sisters get, individually?

Construct a quadrilateral ABCD, where AB = 5 cm, CD = 4 cm, DB = 7cm, BC = 6 cm and DA = 5.5 cm.

Construct a quadrilateral LEAP, where LE = 4 cm, EA=4 cm, \(\angle \)L=60°, \(\angle \)E = 120°,\(\angle \)A=90°.

Draw a rhombus ABCD having their diagonals of lengths BD = 6 cm and AC = 8 cm.

Draw a square ABCD with AB = 5 cm.

Construct the following quadrilaterals. Quadrilateral JUMP JU = 3.5 cm, UM = 4 cm, MP = 5 cm, PJ = 4.5 cm PU = 6.5 cm

What is a regular polygon of 7 sides called?

As before, consider quadrilateral ABCD in adjoining figure. Let P be any point in its interior. Join P to vertices A, B, C and D. In the given figure, consider ΔPAB. From this, we see x= 180°- mㄥ2 - mㄥ3; similarly from ΔPBC, y = 180⁰- mㄥ4 - mㄥ5; from ΔPCD, z = 180° - mㄥ6 - mㄥ7 and from ΔPDA, w= 180°- mㄥB - mㄥ1. Use this to find the total measure mㄥ1 + mㄥ2 + ... + mㄥ8. Does it help you to arrive at the result?

Consider the following parallelograms. Find the values of the unknowns x, y and z.

The ratio between exterior angle and interior angle of a regular polygon is 1 : 3. Find the number of sides of the polygon. Also, find each of the interior and exterior angles.

ABCDE is a regular pentagon. The bisector of angle A meets the side CD at M. Find ㄥAMC.

I have a total of Rs. 300 in coins of denomination Rs. 1, Rs.2 and Rs. 5. The number of Rs. 2 coins is 3 times the number of Rs.5 coins. The total number of coins is 160.How many coins of each denomination are with me?

Divide 34 into two parts in such a way that \(\left( \frac { 4 }{ 7 } \right) \) th of one part is equal to \(\left( \frac { 2 }{ 5 } \right) \) th of the other.

The length of a rectangle exceeds its breadth by 4 cm. If length and breadth are each increased by 3 cm then area of new rectangle will be 81 cm² more than that of the given rectangle. Find the length and breadth of the given rectangle.

The difference between the squares of two consecutive numbers is 31. Find the numbers.

Five years ago, a man was seven times as old as his son. Five years after, the father will be three times as old as his son. Find their present ages.

For an experiment in Botany, two different plants, plant A and plant B were grown under similar laboratory conditions. Their heights were measured at the end of each week for 3 weeks. The results are shown by the following graph:
(a) How high was plant A after (i) 2 weeks (ii) 3 weeks?
(b) How high was plant B after (i) 2 weeks (ii) 3 weeks?
(c) How much did plant A grow during the 3rd week?
(d) How much did plant B grow from the end of the 2nd week to the end of the 3rd week?
(e) During which week did plant A grow most?
(f) During which week did plant B grow least?
(g) Were the two plants of the same height during any week shown here? Specify.

Study the given graphs (i) and (ii) and complete the corresponding tables below.

(i)

(ii)

Plot a line graph for the variables p and q where p is two times q, l.e. the equation is p =2q.
Then, find
(a) the value of p when q = 3.
(b) the value of q when p =8.

Study the distance-time graph given below for a car to travel to certain places and answer the questions that follow.
(a)How far does the car travel in 2 h?
(b) How much time does the car take to reach R?
(c) How long does the car take to cover 80 km?
(d) How far is Q from the starting point?
(e) When does the car reach the place S after starting?

Locate the points A(1,2), B(4,2) and C(1, 4) on a graph sheet taking suitable axes. Write the coordinates of the fourth point D to complete the rectangle ABCD. 

If h = 10 cm, c = 6 cm, b = 12 cm and d = 4 cm, find the values of each of its parts separately and add to find the area WXYZ..Verify, it by putting the values of h, a and b in the expression \(\frac { h(a+b) }{ 2 } \)

Divide the following polygons into parts (triangles and trapezium) to find out its area.

Length of the fence of a trapezium shaped field ABCD is 120 m. If BC = 48 m, CD = 17 m and AD = 40 m, find the area of this field. Side AB is perpendicular to the parallel sides AD and BC

Mohan wants to buy a  trapezium shaped field. Its side along the river is parallel and twice the side along the road. If the area of this field is 10500 m² and the perpendicular distance between the two parallel sides is 100 m, find the length of the side along the river.

There are two cuboidal boxes as shown in the following figures. Which box requires the lesser amount of material to make?

If a box of sweets is divided among 24 children, they will get 5 sweets each. How many would each get, if the number of the children is reduced by 4?

A farmer has enough food to feed 20 animals in his cattle for 6 days. How long would the food last, if there were 10 more animals in his cattle?

A work-force of 420 men with a contractor can finish a certain piece of work in 9 months. How many extra men must be needed to complete the job in 7 months?

In which of the following case, do the quantities vary directly with each other.

l varies directly as m and l=5 when \(m=\frac{2}{3}\)find l, when \(m=\frac{16}{3}\).

Can a polyhedron have 10 faces, 20 edges and 15 vertices?

Verify which of the following are the faces, edges and, vertices of a polyhedron. 
(i) Faces = 10, edges = 20 and vertices = 15
(ii) Faces = 7, edges = 5and vertices = 4
(iii) Faces = 4, edges = 6 and vertices = 4
(iv) Faces= 5, edges = 4 and vertices = 3

A polyhedron has number of vertices equal to \(\frac{3}{2}\) times of number of faces. If polyhedron has 8 edges, then find number of vertices and faces.

Find the number of vertices in a polyhedron which has 30 edges and 12 faces.

Find the number of bases and faces in a Rectangular pyramid

Subtract 4a - 7ab + 3b + 12 from 12a- 9ab+ 5b- 3.

Subtract 1+ a² + b² from the sum of 1- a²-b² and a²-b²

Subtract the sum of 3a - 4b +c and 1- 2a + b from the sum of 3b+c + b and a -2b + 3

Add 2x (z- x- y) and 2y (z- y- x).

Subtract 3l (l- 4m + 5n) from 41 (10n- 3m + 21)

factorise the following expressions. 7a² + 14a

factorise the following expressions. -16z + 20z³

Factorise the following expressions.p² - 10p + 25 

Factorise the following expressions. 25m² + 30m + p

Foetorise the following expressions.a⁴ - b⁴

A shop gives 10%discount. What would be the sale price of each of these a pair of shoesmarked at Rs 650?

Your bill in a shop is Rs 577.80. TIy estimating 15% discount of the same bill amount.

Find selling price, if a profit of Rs 5 is made on a hair dryer Rs 500 with Rs 50 as overhead charges.

Find selling price, if a profit of Rs 5 is made on a iron bought for Rs 560 and expenses of Rs 80 made on repairing.

A shopkeeper bought two washing machine sets at Rs15000 each. He sold one at a profit of 15% and the other at a loss of 15%. Find whether he made an overall profit or loss.

Draw an appropriate graph to represent the given information.

Draw an appropriate graph to represent the given information.

The shoppers who come to a departmental store are marked as Man (M), Woman (W), Boy (B) or Girl (G). The following list gives the shoppers who came during the first hour in the morning:
W W W G B W W M G G M M W W W W G B M W B G G M W W M M W W W M W B W G M W W W W G W M M W W M W G W M G W M M B G G W
Make a frequency distribution table using tally marks. Draw a bar graph to illustrate it.

Identify, which symbol should appear in each sector.

Given below is a frequency distribution table. Read it and answer the questions that follow:

(a) Whatis the lower limit of the second class interval?
(b) Whatis the upper limit of the last class interval?
(c) What is the frequency of the third class?
(d) Which interval has a frequency of 15?
(e) Which interval has a lowest frequency?
(f) What is the class size?

You are told that 1331 is a perfect cube. Can you guess without factorisation what is its cube root? Similarly, guess the cube roots of 4913, 12167, 32768.

Evaluate \(\sqrt [ 3 ]{ 27 } +\sqrt [ 3 ]{ 0.008 } +\sqrt [ 3 ]{ 0.064 } \).

Evaluate {5²+(12²)^1/2}³

Is 9720 a perfect cube? If not, find the smallest number by which, it should be divided to get a perfect cube.

What is the smallest number by which 392 may be divided so that the quotient is a perfect cube?

Construct the following quadrilaterals. Quadrilateral DEAR DE = 4 cm, EA = 5 cm, AR = 4.5 cm, \(\angle \)E = 60°, \(\angle \)A = 90°

Construct the following quadrilaterals. Quadrilateral TRUE TR = 3.5 cm, RU = 3 cm, UE = 4 cm, \(\angle \)R = 75°, \(\angle \)U = 120°

Draw the following. A rhombus whose diagonals are 5.2 cm and 6.4 cm long.

Draw the following. A rectangle with adjacent sides of lengths 5 cm and 4 cm.

Draw the following. A parallelogram OKAY where OK = 5.5 cm and KA = 4.2 cm. Is it unique?

These quadrilaterals were convex. What would happen, if the quadrilateral is not convex? Consider quadrilateral ABCD. Split it into two triangles and find the sum of the interior angles in adjoining figure.

Find x + y + z

Find x, in the following figures.

The sides of a pentagon are produced in order and the exterior angles, so obtained are of measure x⁰ ,(3x)⁰ ,(4x + 10)⁰, (2x +5)⁰ and (5x)⁰ ,respectively. Find the value of x and measure of each exterior angle of a pentagon.

In a trapezium FARE, EP and RP are bisectors of ㄥE and ㄥR, respectively. Find ㄥFAR and ㄥEFA.

The ages of Rahul and Hamon are in the ratio 5 : 7. Four years later, the sum of their ages will be 56 yr. What are their present ages?

The number of boys and girls in a class are in theratio 7 :5. The number of boys is 8 more than the number of girls. What is the total class strength?

Shobo's mother's present age is six times Shobo's present age. Shobo's age five years from now will be one-third of his mother's present age. What are their present ages?

Solve the following linear equation \(\frac { n }{ 2 } -\frac { 3n }{ 4 } +\frac { 5n }{ 6 } =21\)

What should be subtracted from twice the rational number \({-5\over 3}\) to get \({2\over 5}\)?

Draw a double bar graph for the following data showing the manufacture of cars of Maruti and Hundai in various years.

The following graph shows the temperature of a patient in a hospital, recorded every hour.
(a) What was the patient's temperature at 1 pm?
(b) When was the patient's temperature 38.5°C?

(c) The patient's temperature was the same two times during the period given. What were these two times?
(d) What was the temperature at 1: 30 pm? How did you arrive at your answer?
(e) During which periods did the patient's temperature showed an upward trend?

A courier-person cycle from a town to a neighbouring Suburban area to deliver a parcel to a merchant. His distance from the town at different times is shown by the following graph.
(a) What is the scale taken for the time axis?
(b) How much time did the person take for the travel?
(c) How far is the place of the merchant from the town?
(d) Did the person stop on his way? Explain.
(e) During which period did he ride fastest?

The sales of a shopkeeper for eight days of a month in any year is given below:

Draw the line graph depicting the above data.

The following table shows the export earning of India (in Rs.thousand crore) during five consecutive years:

Draw a bar graph representing the above data.

Read the following bar graph and answer the following questions.

(i) What is the information given by the bar graph?
(ii) In which year is the increase in the number of students maximum?
(iii) In which year is the number of students maximum?
(iv) State whether true of false:
'The number of students during 2005 - 06 is twice that of 2003 - 04.'

If we change the position of any of the bars of a bar graph, would it change the information being conveyed? Why?

Construct a frequency distribution table for the data on weights (in kg) of 20 students of a class using intervals 30-35, 35-40 and so on. 40,38,33,48,60,53,31,46,34,36,49,41, 55, 49, 65, 42, 44, 47, 38, 39.

For which of these would you use a histogram to show the data?
(a) The number of letters for different areas in a postman's bag.
(b) The height of competitors in an athletics meet.
(c) The number of cassettes produced by 5 companies.
(d) The number of passengers boarding trains from 7: 00 am to 7: 00 pm at a station.
Give reasons for each.

Answer the following questions based on the pie chart in following figure.
(i) Which type of programmes are viewed the most?
(ii) Which two types of programmes have number of viewers equal to those watching sports channels?

Viewers watching different types of channels on TV.

Find A and B in the given addition, if
   2 B
+ A B  
   8 A   

Find the values of the letters in each of the following and give reasons for the steps involved.\(\begin{matrix} \quad \quad A\ B \\ +\quad 3\ \ 7 \\ \_ \_ \_ \_ \_ \_ \_ \\ \quad 6\ A \\ \_ \_ \_ \_ \_ \_ \_ \_ \end{matrix}\)

Find the values of A, B, and C, if \(\begin{matrix} \quad \quad 2\ A \\ +\quad 4\ A \\ \_ \_ \_ \_ \_ \_ \_ \\ B\ C\ 3 \\ \_ \_ \_ \_ \_ \_ \_ \end{matrix}\)

Find the values of A and B, if \(\begin{matrix} \quad 4\ 1\ A \\ +\quad B\ \ 4 \\ \_ \_ \_ \_ \_ \_ \_ \_ \\ \quad 5\ 1\ 2 \\ \_ \_ \_ \_ \_ \_ \_ \_ \_ \end{matrix}\)

If from a 2-digit number, we subtract the number formed by reversing its digits, then the result so obtained is a perfect cube. How many such numbers are possible? Write all of them.

Find the square root of the following by long division method 5625

Find the value of \(\sqrt { 248+\sqrt { 52+\sqrt { 144 } } } \)

If the expression X x 809436 x 809436 be a perfect square, then find the value of x.

The sum of two numbers, when multiplied with each of the numbers separately, then the result of the above multiplications are 2418 and 3666, respectively. Find the difference between the numbers. 

Find the square roots of 100 by the method of repeated subtraction.

Express the product of 1.3x10⁴ and 3.4x10^-2 in the standard form.

Fill in the blanks.

Find the value of x^-3 , if x = (100)^{1- 4} + (100)⁰.

If a = - 1and b = 2, then find the value of the following:
(i) a^b + b^a
(ii) a^b - b^a
(iii) a^b x b^a
(iv) a^b ÷ b^a

Find the multiplicative increase of X², if \((\frac{2}{5})^{-3}\times (\frac{2}{5})^{5}=(\frac{2}{5})^{x}\)

Find the value of \({x\over y }+xy\) , using appropriate property and name it \(x={1\over3},y={2\over 5}\)

Using and associativity of addition of rational numbers, express the following as a rational number.
\({5\over2}+{-3\over7}+{1\over2}+{4\over7}\)

Rearrange suitably and find the sum in each of the following:
\({-5\over7}+{5\over6}+{1\over7}+3+{-13\over6}\)

Represent the following rational numbers on the number line. \(2\over5\)

Is 68600 a perfect cube? If not, find the smallest number by which 68600 must be multiplied to get a perfect cube.

Find the cube root of 614125 through estimation.

Using prime factorisation, find the cube root of 5832.

Find the cube of \(\left( 2+\frac { 3 }{ 5 } \right) \).

Is 1372 a perfect cube? If not, find the smallest natural number by which 1372 must be multiplied so that the product is a perfect cube.

Find the values of the letters in each of the following and give reasons for the steps involved. \(\begin{matrix} \quad \quad A\quad B \\ \quad \times \quad 5 \\ \_ \_ \_ \_ \_ \_ \_ \_ \_ \\ C\quad A\quad B \\ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \end{matrix}\)

Find the values of the letters in each of the following and give reasons for the steps involved.\(\begin{matrix} \quad \quad A\quad B \\ \quad \times \quad 6 \\ \_ \_ \_ \_ \_ \_ \_ \_ \_ \\ B\quad B\quad B \\ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \end{matrix}\)

Find the values of the letters in each of the following and give reasons for the steps involved.\(\begin{matrix} \quad \quad A\quad 1 \\ +\quad 1\quad B \\ \_ \_ \_ \_ \_ \_ \_ \_ \_ \\ \quad B\quad 0 \\ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \end{matrix}\)

Find the values of the letters in each of the following and give reasons for the steps involved.\(\begin{matrix} \quad \quad 2\quad A\quad B \\ +\quad A\quad B\quad 1 \\ \_ \_ \_ \_ \_ \_ \_ \_ \_ \\ \quad B\quad 1\quad 8 \\ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \end{matrix}\)

If 48101 B 095 is divisible by 33, then find the value of B.

Find the greatest number of three digits that is a perfect square.

Find the square root of 6280036.

Can we say whether the following numbers are perfect squares? How do we know? 23453
Write five numbers which you can decide by looking at their units digit that they are not square numbers.

Can we say whether the following numbers are perfect squares? How do we know? 7928
Write five numbers which you can decide by looking at their units digit that they are not square numbers.

How many perfect squares lie between 1 and 50?

Find the multiplicative inverse of the following:
2^-4

Find the multiplicative inverse of the following:
10^-5

Evaluate   {\((\frac{1}{3})^{-1}-(\frac{1}{4})^{-1}\)}^-1

Evaluate. \({ \left( \frac { 5 }{ 8 } \right) }^{ -7 }\times { \left( \frac { 8 }{ 5 } \right) }^{ -4 }\)

If 289 = \(17^{\frac{x}{5}}\),then find the value of x. 

If a property holds for rational number, will it also hold for integers? For whole numbers? Which will? Which will not?

Find using distributivity. \( \{{7\over5}\times ({-3\over12}) \}+ \{{7\over16}\times {5\over12} \}\)

Multiply the multiplicative inverse of -2 with its reciprocal.

Write the rational number for each point labelled with a letter 

Find ten rational numbers between \({-2\over5} and {1\over2}\)

if a²+b² = 74 and ab = 35,then the value of a+b.

Factorise 15xy

Find and correct the errors in the following mathematical statements. Substituting x =- 3 in
x²+ 5x+ 4 gives (-3)² + 5 (-3) + 4 = 9 + 2 + 4 = 15

Find and correct the errors in the following mathematical statements. Substituting x =-3 in
x²- 5x+ 4 gives (-3)²- 5 (-3)+ 4= 9- 15 + 4=-2

Solve the following expression:
(pr yz - r xyz - q r xy) ÷ x y z

Observe the following tables and find which pair of variables (here, x and y) are in inverse proportion.

Which of the following are in inverse proportion?
(i) The number of workers on a job and the time to complete the job.
(ii) The time taken for a journey and the distance travelled in a uniform speed.
(iii) Area of cultivated land and the crop harvested.
(iv) The time taken for a fixed journey and the speed of the vehicle.
(v) The population of a country and the area of land per person.

A car takes 10 h to reach a destination by travelling at the speed of 65 km/h. How long will it take when the car travels at the speed of 50 km/h?

If 45 students can consume a stock of food in 2 months, then find how many days the same stock of food will last for 27 students?

If the cost of 10 pencils is Rs 90. Find the cost of 19 pencils?

The length of a rectangular field is 100 m and its breadth is 40 m. What will be the area of the field?

The ratio of the length and breadth of a rectangle is 5 : 3. If length is 8 m more than breadth, then find the area of the rectangle.

Find the area of a rhombus, whose diagonals are of lengths 20 cm and 15 cm.

Find the area of the polygon ABCD, if AD= 10 cm, AS= 7 cm and AP=2 cm

Parallelogram is divided into two congruent triangles by drawing a diagonal across it. Can we divide a trapezium into two congruent triangles?

The given solid, the three views are given. Identify for each solid the corresponding top, front and side views.

For each given solid, identify the top view, front view and side view.

For each given solid, identify the top view, front view and side view.

Draw the front view, side view and top view of the given objects.

Draw the front, side and top views of the given shapes.

Show on the number line z - 3.

Subtract 13a -18ab+ 3b+16 from 22a+ 30ab+ 6b+ 8.

Identify the terms, their coefficients for each of the following expressions,
3- pq+ qr- rp

Identify the terms, their coefficients for each of the following expressions,
\(\frac { X }{ 2 } +\frac { Y }{ 2 } -XY\)

Add the following:
ab - bc, bc - ca, ca - ab

Find the time period and rate for which a sum taken for 3 yr at 6% per annum is compounded half-yearly.

Find the population of a city after 3 yr, which is at present 12lakh, if the rate of increase is 3%. 

Find the time period and rate tor each a sum taken for 1\(\frac{1}{2}\)yr at 8% per annum is compounded half-yearly.

If \(\frac{7}{3}\) % of a number is 147, then find the number.

Ankit buys a memory card costing Rs 550. If the rateof sales tax is 5%, then find the total amount payable by him.

Arshad has five measurements of a quadrilateral ABCD. These are AB = 5 cm, \(\angle \)A = 50°, AC = 4 cm, BD = 5 cm and AD = 6 cm. Can he construct a unique quadrilateral? Give reasons for your answer.

Can you draw a parallelogram BATS, where BA = 5 cm, AT = 6 cm and AS = 6.5 cm? Why?

Can you draw a rhombus ZEAL, where ZE = 3.5 cm, diagonal EL = 5 cm? Why?

A student attempted to draw a quadrilateral PLAY, where PL = 3 cm, LA = 4 cm, AY = 4.5 cm, PY = 2 cm and LY = 6 cm but could not draw it. What is the reason?

Can we draw the quadrilateral by drawing \(\Delta \) ABD first and then find the fourth point C?

If three angles of a quadrilateral are 90°, 100° and 110°, then find the measure of fourth angle.

What is the measure of each interior angle of a regular pentagon?

In the given figure, find the value of x+ y+ z + w + s.

How many sides does a regular polygon have, if each of its interior angles is 165°?

Is it possible to have a regular polygon with measure of each exterior angle as 22°?

Find the root the following equations \(3x-\frac { 1 }{ 3 } =\frac { 2 }{ 3 } \)

Find the root the following equations \(2p+9=\frac { -17 }{ 7 } \)

Solve the following equations and check your result. 5x + 9 = 5 + 3x.

Solve the following equations and check your result. \(3m=5m-\frac { 8 }{ 5 } \)

If the length and breadth of a rectangular field are in the ratio 6:4. Find the length and breadth, if cost of fencing the field at the rate of Rs. 80 per metre is Rs. 16000.

Plot the following points on a graph sheet. Verify, if they lie on a line.
K (2, 3), L (5, 3),M (5, 5), N (2, 5)

Write the coordinates of the vertices of each of these adjoining figures.

Draw the line graph from the following table (monthly output of a tin mine) :

Answer the following questions:
(a) Whatis largest monthly output of the tin mine?
(b) For which months does the output remains constant?

Plot the given points on a graph sheet and check, if the points lie on a straight line. If not, name the shape they form when joined in the given order (3,0), (0,4), (-3,0) and (0, -4).

Write the x-coordinate (abscissa) of the given points.
(7, 3)

The earning of 50 shops on a particular day are as follows (the figures have been estimated to the nearest hundreds):

Prepare a grouped frequency distribution table taking class interval of equal size, one such interval being 1500 - 2000.

The marks scored by 24 students in a test are given below:
64, 47, 58, 44, 53, 72, 51, 41, 57, 89, 53, 84, 57, 78, 71, 56, 62, 54, 42, 68, 53, 68, 49, 56
Complete the following frequency table:

What is the class interval in which the greatest frequency occurs?

Which form of graph would be appropriate to display the following data.

The following data represents the different type of animals and their numbers in a zoo. Prepare a pie chart for the given data.

You have a bag with five identical balls of different colours and you are to pull out (draw) a ball without looking at it. List the outcomes you would get in adjoining figure.

Is 2744 a perfect cube?

Find the one's digit of the cube of each of the following numbers.
8888

Find the one's digit of the cube of each of the following numbers.
53

Consider the following pattern.
2³-1³= 1 + 2 x 1 x 3, 3³-2³=1 + 3 x 2 x 3, 4³-3³=1 + 4 x 3 x 3
Using the above pattern, find the value of the following:
7³ - 6³

Find the cube root of each of the following numbers by prime factorisation method.
175616

Write the following in the usual form: 10 x 5 + 6

Write the following in the usual form: 100 x 7 + 10 x 1 + 8

Check the divisibility of the following number by 10. 1043

Check the divisibility of the following number by 2. 105

Check the divisibility of the following numbers by 9: 294

Can we say whether the following numbers are perfect squares? How do we know? 7928
Write five numbers which you can decide by looking at their units digit that they are not square numbers.

Write five numbers which you cannot decide just by looking at their unit's digit (or one's place) whether they are square numbers or not.

What will be the one's digit in the square of the following numbers? 21222

What will be the number of zeros in the square of the following numbers? 60

Find the square root of each of the following numbers by division method.1024

Find the multiplicative inverse of the following:
10^-5

Simplify and write in exponential form.
\((-2)^{-3}\times (-2)^{-4}\)

Evaluate  \((\frac{1}{2})^{-5}\)

Find the value of m for which \(5^{m}\div 5^{-3}=5^{5}\)

Insert '<' or '>' in the box given below:
\(\\ 7.32\times { 10 }^{ 5 }\ 5.29\times { 10 }^{ 6 }\)

Write the additive inverse of the following  \(-5\over9\)

Find the multiplicative inverse of the following \(1\over5\)

Is  \({8\over9}\) the multiplicative inverse of \(-1{1\over8}\)  Why or why not? 

Write five rational numbers which are smaller than 2.

Write any five rational numbers between \(-{5\over6}and{7\over8}\)

The greatest common factor of 6a and 12b is

In a polynomial, the exponents of the variables are always

Which of the following is a binomial?

An irreducible factor of 24x² y² is

a (b + c) = ab + ac is

Both u and v vary directly with each other. When u is 10, v is 15, which of the following is not a possible pair of corresponding values of u and v?

If two quantities p and q vary inversely with each other, then

18 workers can do a work in 180 days. If two more workers join this work, the work will be completed in

Both x and y are in direct proportion,then \(\frac{1}{x}\)and \(\frac{1}{y}\)are

If the weight of 9 sheets of thick paper is 30 g, how many sheets of the same paper would weigh \(1\frac{1}{4}kg?\)

A cube of side 5 cm is painted on all its faces. If it is sliced into 1 cubic centimetre cubes, how many 1 cubic centimetre cubes will have exactly one of their faces painted?

Three cubes of metal whose edges are 6 cm, 8 cm and 10 cm respectively, are melted to form a single cube. The edge of the new cube is

The ratio of radii of two cylinders is 1: 2 and heights are in the ratio 2 : 3. The ratio of their volumes is

Radius of a circle is 7cm. Its perimeter

Surface area of four walls of a room whose length, breadth and height are respectively the

Which of the following will not form a polyhedron?

We have 4 congruent equilateral triangles. What do we need more to make a pyramid?

Which of the following is a regular polyhedron?

Which of the following cannot be true for a polyhedron?

Side of a square garden is 40 m. If the scale used to draw its picture is 1 cm: 8 m, then the perimeter of the square in the picture is

Which of the following is an identity?

Which of the following is a binomial?

Sum of a - b + ab, b + c - bc and c - a - ac is

Area of a rectangle with length 5ab and breadth 13ac² is

Product of the monomials, -15p, -13q², pq is

By selling 50 items, a shopkeeper lost the amount equal to the selling price of 10 items. His loss per cent is

Suppose a certain sum doubles in 2 yr at r % rateof simple interest per annum or at R% rate of interest per annum compounded annually,we have

The buying price of 5 kg guava, at the rate Rs 20 per kg with 5% sales tax on the purchase, is

Radhika bought a car for Rs 250000. Next year, its price decreased by 10% and further next year it decreased by 12%. In the two years, overall decrease per cent in the price of the car is

Asurn is taken for 2 yr at 16% per annum, If interest is compounded after every three months, the number of times for which interest is charged in 2 yr is

Which of the following quadrilaterals does not have two pairs of adjacent sides equal and diagonals intersecting at right angle?

Which of the following quadrilateral has only one pair of opposite sides parallel?

Which of the following is true for the adjacent angles of a parallelogram?

Which of the following is a regular quadrilateral?

Which of the following is not a parallelogram?

Which of the following is not true for an exterior angle of a regular polygon with n sides?

If the sum of the interior angles of a polygon is 18 right angles, then the number of sides is

ABCD is a quadrilateral, in which AB = 5 cm, CD = 8 cm and the sum of angles A and D is 180°. What is the name of this quadrilateral?

Prisha has a farm land, which is triangular shape. What is the sum of all the exterior angles taken in an order of the farm land?

For which of the following quadrilaterals, diagonals are perpendicular to each other?

Comparison of parts of a whole may be done by a

A graph that displays data that changes continuously over periods of time is

The point (3, 4) is at a distance of

A point which lies on both the axes is

The coordinates of a point at a distance of 3 units from the X-axis and 6 units from the Y-axis is

The Solution of the equation ax+b = 0 is 

Which of the following is a linear expression?

A linear equation in one variable has

The digit in the ten's place of a two-digit number is 3 more than the digit in the unit's place. If the digit at unit's place be b. Then, the number is

Arpita's present age is thrice of Shilpa. If Shilpa's age 3 yr ago was x. Then, Arpita's present age is

In a throw of die, the probability of getting the number 8, is

The length of a rectangle in a histogram shows the

A geometric representation showing the relationship between a whole and its parts is a

The range of the data 18, 20, 22, 19, 17,35,44, 46, 38, 40 is

A coin is tossed 300 times and head appeared 180 times. The probability of getting a head in this experiment in

The one's digit of the cube of 23 is

Which of the following number is a perfect cube?

The cube root of \(\frac { -64 }{ 125 } \) is

Which of the following is the cube of an even natural number?

The value of \(\sqrt [ 3 ]{ 512 } \times \sqrt [ 3 ]{ -27 } \) is

Which of the following is a perfect square?

A number ending in 9 will have the unit's place of its square as

The hypotenuse of a right angled triangle with its base and perpendicular of lengths 3x, 4x respectively is

There are _____________ perfect square between 1 and 100.

\(\sqrt { 2.89 } \) = _____________

Generalised form of a 3-digit number abc is

If 5A + 15 is equal to B3. Then, the value of A+B is

If the sum of digits of a number is divisible by three, then the number is always divisible by

3134673 is divisible by 3 and __________

If A x 3 =1A ,then A = __________

5^-2 can be written as

For a non-zero integer x, x⁷÷x¹² is equal to

The usual form of 2.08 x 10^-5 is

a¹³ x a^-10 = _________

100⁰ = ____________

The reciprocal of \({-3\over8 } \times {-24\over 13}\) is

Zero (0) is

The reciprocal of a positive rational number is _________________

The rational number 9.99 in the form of \(p\over q\) is ________________

Which of the following quadrilaterals does not have two pairs of adjacent sides equal and diagonals intersecting at right angle?

Which of the following quadrilateral has only one pair of opposite sides parallel?

The measures of two adjacant angles of a parallelogram are in the ratio 4: 5. The measure of each of the angles of the parallelogram is :

What is the measure of an exterior angle of a regular octagon?

What will be the side of a rhombus whose diagonals are 10 em and 24 em long?

Which of the following is not true for an exterior angle of a regular polygon with n sides?

The number of diagonals in a polygon of n sides is

Which of the following parallelograms has all sides equal and diagonals bisect each other at 10. right angle?

In an isosceles parallelogram, we have:

Which of the following is true for the adjacent cangles of a parallelogram?

The Solution of the equation ax+b = 0 is 

If 8x -13 = 25 + 16x, then x is

If \({2\over 5}x=\)4; then which of the following is the value of x?

If the sum of two consecutive numbers is 71 and one of them being x, then which of the following is the other number?

Comparison of parts of a whole may be done by a

In the given graph, the coordinates of point P are

A point which lies on both the axes is

The point (-3, -3) is

The point (0, 4) lies on which of the following:

In a throw of die, the probability of getting the number 8, is

A geometric representation showing the relationship between a whole and its parts is a

Monthly salary of a person is Rs 45000. The central angle of the sector representing his expenses on food and house rent on a pie chart is 60°. The amount he spends on food and house rent is

The difference between the highest and the lowest values of observations in a data is called:

In the interval 35 - 45, 45 is called

The one's digit of the cube of 23 is

Which of the following number is a perfect cube?

If m is the cube root of n, then n is

If the digit in ones place of a number is 3, then the ending of its cube will be:

If the digit in ones place of number is 6, then its cube will end with the digits:

Generalised form of a 3-digit number abc is

The usual form of 3000 + 500 + 60 + 3 is

If 5A + 15 is equal to B3. Then, the value of A+B is

Let abc be a 3-digit number, then abc-cba is not divisible by

If abc is a 3-digit number, then the number abc- a - b - c is divisible b

Which of the following is a perfect square?

169 is the square of

A number ending in 9 will have the unit's place of its square as

A square board has an area of 121 square units. How long is each side of the board?

If one member of a Pythagorean triplet is 2m, then other two members are

In 3ⁿ, n is known as

The reciprocal of \((\frac{3}{7})^{-1}\)is

The value of 3^5÷ 3^-8 is

For a non-zero integer x, x⁷÷x¹² is equal to

Which of the following is the value of 'm' in 6^m\(\div \) 6^-3 = 6⁵ 

Which of the following is not true?

One (1) is

Which of the following is not true?

Which of the following is the multiplicative identity for rational numbers?

Which of the following is neither positive nor a negative rational number?

If the height of a cylinder becomes\(\frac { 1 }{ 4 } \)of the original height and the radius is doubled, then which of the following will be true?

Three cubes of metal whose edges are 6 cm, 8 cm and 10 cm respectively, are melted to form a single cube. The edge of the new cube is

The surface area of the six faces of a rectangular solid are 16, 16, 32, 32, 72 and 72 sq cm. The volume of the solid (in cm) is

Which of the following is equal to kilolitre?

Surface area of four walls of a room whose length, breadth and height are respectively the

Which of the following will not form a polyhedron?

Which of the following 3-D shapes does not have a vertex?

Which of the following is a regular polyhedron?

Side of a square garden is 40 m. If the scale used to draw its picture is 1 cm: 8 m, then the perimeter of the square in the picture is

 is the ________ view of above solid.

Which of the following is an identity?

Which of the following is a binomial?

Product of the monomials, -15p, -13q², pq is

Which of the following is the numerical coefficient of - 5xy?

a² - b² is the product of

By selling 50 items, a shopkeeper lost the amount equal to the selling price of 10 items. His loss per cent is

Sachin purchases a bat for Rs 660 including sales tax. If the rate of sales tax is 10%, then the selling price of the bat is

The buying price of 5 kg guava, at the rate Rs 20 per kg with 5% sales tax on the purchase, is

Asurn is taken for 2 yr at 16% per annum, If interest is compounded after every three months, the number of times for which interest is charged in 2 yr is

VAT is always calculated on which of the following?

Which of the following quadrilaterals does not have two pairs of adjacent sides equal and diagonals intersecting at right angle?

Which of the following is not a parallelogram?

In a quadrilateral ABCD, the angles A, B, C and D are in the ratio 1: 2: 3: 4. The measure of smallest angle is:

What will be the side of a rhombus whose diagonals are 10 em and 24 em long?

Which of the following is the sum of all the interior angles of a ploynomial of sides 'n'?

The number of diagonals in a polygon of n sides is

If the diagonals of a parallelogram bisect each other at right angles, then it will be a

For which of the following quadrilaterals, diagonals are perpendicular to each other?

The maximum number of obtuse angles that a quadrilateral can have, is

Which of the following is a regular quadrilateral?

The Solution of the equation ax+b = 0 is 

A linear equation in one variable has

If \({2\over 5}x=\)4; then which of the following is the value of x?

10 years ago, I was 'x' years old. After 10 years, my age will be:

Comparison of parts of a whole may be done by a

In the given graph, the letter that indicates the point (0, 3) is

The point (3, 4) is at a distance of

(0, y) are the coordinates of a point lying on which of the following?

The point (0, 4) lies on which of the following:

Which of the following is not a random experiment?

Monthly salary of a person is Rs 45000. The central angle of the sector representing his expenses on food and house rent on a pie chart is 60°. The amount he spends on food and house rent is

The range of the data: 6, 14,20, 16,6,5,4, 18,25, 15 and 5 is

The class-mark of the class 20-30 is:

The difference between the highest and the lowest values of observations in a data is called:

The one's digit of the cube of 23 is

The cube of 0.08 is

Which of the following is the cube of an even natural number?

If the digit in ones place of a number is 3, then the ending of its cube will be:

If the digit in ones place of number is 6, then its cube will end with the digits:

3134673 is divisible by 3 and __________

The sum of a 2-digit number and the number obtained by reversing the digits is always divisible by ___________

If A x 3 =1A ,then A = __________

A 4-digit number abcd is divisible by 11, if d + b = _________ or _________

The difference of a 2-digit number and the number obtained by reversing its digits is always divisible by _________

169 is the square of

If one member of a Pythagorean triplet is 2m, then other two members are

If \(\sqrt { 4096 } =64\), then the value of \(\sqrt { 4096 } +\sqrt { 40.96 } \) is

A perfect square number having m digits, where m is even will have square root with

Which of the following is the number of non-perfect square numbers between the squares of the numbers nand n + 1?

In 3ⁿ, n is known as

5^-2 can be written as

The value of \(\frac{1}{9^{-2}}\) is

The reciprocal of \((\frac{3}{7})^{-1}\)is

The value of 5² x 5^-2 is

Which of the following is not true?

Three rational numbers lying between\(\frac{-5}{4}\) and \(\frac{1}{2}\)are

\(\frac{x+y}{2}\) is a rational number

Which of the following is the reciprocal of p?

Which of the following is the product of \(\frac { 7 }{ 8 } \) and \(\frac { -2 }{ 21 } ?\)