How to answer the following question?rnrnQ) There are two boxes. Which box requires the lesser amount of material to make? The measurements are as belowrna) height 30 cm, width 80 cm and length 10 cmrnb) height 20 cm,

How to answer the following question?rnAmir starts walking from his house to office. Instead of going to the office directly, he goes to the bank first, from there to his daughter's school and then reaches the office. What

how to solve the following question? Tickets numbered 1 to 20 are mixed up together and then a ticket is drawn at random. What is the probability that the ticket has a number, which is the multiple of 3 or 7?

How to answer the following question?

Ramesh is a cashier at Canara Bank. He has notes of denominations of Rs 100. 50 and 10 respectively. The ratio of the number of these notes are is 2: 3: 5 respectively.

in this test how is the answer for the question: what is the probability of a coin getting tail and the answer came 1 i nstead of the correct answer 1/2

7/5 is the correct answer of this question but I don't know how to get it can you please show the step by step method to get the final

answer 7/5

Iam attaching the question below

7/5 is the correct answer of this question but I don't know how to get it can you please show the step by step method to get the final

answer 7/5.

Iam attaching the question below

In triangle PQR, PQ=QR and L,M and N are the mid -points of the sides PQ,QR and RP respectively. Prove that LN= MN

Good Evening teacher,

In Vedic Maths, adding time, at the last 1.35+3.55=490 and the last 2 digits greater than 60 we added 40 and we got the answer 530. My question how do we get "40" ?

Abhijith C J

Does that mean when we multiply a number by itself , we get it's square root ?

In an arithmetic sequence the sumof 1stnine terms 279and the sum of the 1st twenty terms is 1280.then (a)question. What is the fifth term of the sequence. (b)questions.what is the sixtenth term of the sequence. (c)question.write the sequence

Let ABCD be a sqare of side 2a. Find the coordinates of the vertices of this sqare when: 1: A coincide with the origin and AB and coordinayes axes are parallel to the side AB and AD respectively. 2:The centre of the sqare is at the origin amd coordinate axes are parallel to the side AB and AD respectively.

Sum of the digits of a two-digit numberis9.When we interchange the digits,it is found that the resulting new number is greater than the original number by 27.What is the two digit number.

Sum of the digits of a two-digit numberis9.When we interchange the digits,it is found that the resulting new number is greater than the original number by 27.What is the two digit number.

#### Question No - 20

In the below figure . Find ?

In this question from lines and angles exercise.in the solution it was said that:-

### -----------------------------X----------------------------X------------------------X------------X-----

Now, alternate angles are equal

[ corresponding angles]

Hence,

[ corresponding angles]

[ alternative angles]

Therefore,

-------------X-------------------------X--------------------------X------------------------------X-----------------------X----------

In the above said solution where did the 60 degree come from?

#### Question No - 15

Draw these figures, Four equal rhombuses

#### Question No - 16

Draw these figures., Five equal rhombuses:

#### Question No - 17

Draw these figures, Four rhombuses around a square:

#### Question No - 18

Parallelograms on two sides of a square :

##
(i)Find the six rational numbers bbetween 3 and 4

(ii) Which mathematical concept is used in this problem

(iii) Which value is depticted in this question

(i) We known that between two rational numbers x and y such that x< y there is a rational number .

ie,

Now a rational number between 3 and is :

A rational nummber berween

Further a rational number between 3 and

A rational number between

A rational number between

Hence , six rational numbers between 3 and 4 are

(ii) Number syatem

(iii) Rationality is always welcomed

##
If the polynomial and leave the same remainder when divided by (x - 3) Find the value of a.

Let ,

and

Put = 0 or in and

According to the question

.

##
After 5 years the age of father will be two times the age of his son. Write a linear equation in two variables to represent this statement.

Let father's present age = x years

Son's present age = y years

After 5 years father's age will be = (x+5) years

After 5 years son's age will be = (y+5) years

According to the question,

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A part of the monthly expense of a family on milk is fixed which is Rs. 700 and the remaining varies with the quantity of milk taken extra at the rate of Rs. 25 per litre. Taking the quantity of milk required extra as x litre and total expenditure on milk is Rs. y. Write a linear equation representing the above information.

According to the question,

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When5 times the larger of the two numbers is divided by the smaller, the quotient and the remainder is 2 and 9 respectively. Form a linear equation in two variables. Write it in standard form

Let larger number be x, then 5 times of larger number = 5x and smaller number be y

Qutiont = 2 and remainder = 9

So, according to the question,

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Two friends sita and gita, together contributed Rs . 200 towards prime minister relif fund. Write a linerar equation which satisfies this data. Draw the graph.

Let sita contribute = x and contribute= y

According to the question,

x+ y = 200

y = 200-x

x | 0 | 200 | 100 |

y | 200 | 0 | 100 |

##
The auto rikshaw fare in a city is charged RS . 10 for first kilometer and @Rs.4 per kilometer for subsequent distance covered. Write the linear equation to express the above statment. Draw the graph of the linear equation.

Total distance covered = x km.

Total fare = y km.

Fare for the first kilometer

Subsequent distance = (x-1) km

Fare for the subsequent distance = Rs. 4(x-1)

According to the question,

y = 10+4 (x-1)

y = 10+4x -4

Table of solutions

X | 0 | 1 | -1 |

Y | 6 | 10 | 2 |

##
A student amit of class IX is unable to write in his examination, due to fracture in his arm. Akhil a student of a class VI writes for him. The sum of their ages is 25 years.

(i) Write a linear equation for the above situation and represent it graphically.

(ii) Find the age of of Akhil from the graph, when age of Amit is 14 years.

Let Age of Amit = x years

Age of Akhil = Y years

(i) According to the question the linear equation for above situation is

y = 25-x

X |
0 |
10 |
15 |

Y |
25 |
15 |
10 |

(ii) From the graph when Amit's age = 14 years, then Akhil's age = 11 years.

##
Find the quadratic polynomial whose sum and product of the zeroes are and

respectively.

According to the question,

Sum of zeroes =

and product of zeroes =

So, quadratic polynomial

= (Sum of zeroes ) + product of zeroes

##
If the zeroes of the polynomial are double in value to the zeroes of , find the value

of p and q.

Let,

Let the zeroes of polynomial be and then,

Sum of zeroes

According to the question, zeroes of are and

Sum of zeroes =

Product of zeroes =

and q = -6

##
If the sum and product of the zeroes of the polynomial is equal to 10 each, find the value of 'a' and 'c'

Given, Polynomial

Let the zeroes of are and , then according to the question

Sum of zeroes, () = Product of zeroes, = 10

Now,

and

Hence

##
4 chairs and 3 tables cost Rs. 2100 and 5 chairs and 2 tables cost Rs. 1750. Find the cost of one chair and one table separately.

Let cost of one chair = Rs x and cost of 1 table = Rs y

According to the question,

.....................(1)

.....................(2)

Multiplying eqn. (1) 2 and eqn (2) by 3,

....................(3)

...................(4)

eqn (4) -eqn (3)

7x = 1050

x = 150

Substituting the value of x in (1), y = 500

Cost of chair and table = Rs 150 , Rs 500 respectively.

##
A two digit number is four times the sum of the digits. It is also equal to 3 times the product of digit.

Find the number.

Let units digits and tens digits of the two digit number be x and y

Number is 10 y + x

According to question,

Also,

or y=2

Rejecting y = 0 as the number can not be zero.

Required number is 24.

##
The sum of the squares of two consecutive natural numbers is 421. Find the numbers.

Let the first natural number = x

Second consecutive natural number = x+1

According to the question,

or

x = -15 or x = 14

Rejecting negative value

First number =14

and second cosecutive number = 15

##
Two pipes running together can fill a tank in minutes. If one pipe takes 5 minutes more than the other to fill the tank separately, find the time in which each pipe would fill the tank separately.

Let time taken by pipe A be x minutes. and time taken by pipe B be x +5 minutes.

In one minute pipe A will fill tank

In one minute pipe B will fill , tank

Both pipes A+B will fill tank in one minute

Then according to the question

rejecting negative value, x = 20 minutes

and x+5 = 25 minutes

Hence pipe A will fill the tank in 20 minutes and pipe B will fill in 25 minutes.

##
If the ratio of the sum of first n terms of two AP is (7n+1) : (4n+27), find the ratio of their m^{th} terms.

^{th}terms.

Let a, A be the first terms and d,D be the common difference of two AP's

Then according to question

Putting

##
The digits of a positive number of three digits are in AP and their sum is 15. The number obtained by reserving the digits is 594 less than the original number find the number.

Let the three digits be a -d, a , a+d

Sum = a-d+a+a+d = 3a=15 given

the three digits are 5 -d, 5,5+d.

Original number = 100 (5-d) +10 x 5 + 1(5+d)

= 555+99d

Revered number = 100 (5+d)+10 x 5+1 (5-d)

= 555+99 d

According to question ,

(555-99d) - (555+99d) = 594

-198 d = 594

The three digits are

5-(-3),5,5+(-3)

8,5 and 2

Original number is 8 x 100 + 5x 10 +2 x 1 = 852

##
In the given triangle and QR = 26 cm and in

and KR = 8 cm, find PK.

According to the question,

##
IN the given figure, G is the mid-point of the side PQ of and GH II QR. Prove that H is the mid-point of the side PR of the triangle PQR.

Since G is the mid point of PQ

According to the question

Hence H is the mid-point of PR.

##
Write the relationship connecting three measures of central tendencies. Hence find the median of the given data if mode is 24.5 and mean is 29.75

According to the question, Mode = 24.5

and Mean = 29.75

The relationship connecting measures of central tendancies is :

Median = Mode +2 Mean

3 Median = 24.5 + 2 x 29. 75

= 24.5 + 59.50

Median = 84.0

Median =

##
(i) Why is Axiom 5, in the list of Euclid's axioms, considered a universal truth? (Note that the question is not about the 5^{th} postulates)

(ii) How would you rewrite Euclid's fifth postulates so that it would be easier to understand?

^{th}postulates)

(i) Since it is true for things in any part of the universe so this is a universal truth.

(ii) If the sum of the co-interior angles made by a transversal intersects two straight lines at distinct points is less than 180^{0}, then the lines cannot be parallel.

##
Draw an angle of an equilateral triangle, using protrator. Bisect it using compass.

We know that each angle of the equilateral triangle is 60^{0} so have to draw an angle 60^{0} and bisect it.

Constructions: Follow step - 1 - step 6, mentioned in previous question (i,e., Q.1)

##
A solid piece of metal, cuboidal in shape, with dimensions 24 cm, 18cm and 4cm is recast into a cube. calculate the lateral surface area of the cube.

Vol. of cuboid = lbh

=

= cu.cm.

Edge of a cube =

= 12 cm

LSA =

= 576 cm^{2}

**Alternative method :**

Let x be the edge of cube.

According to the question, we have

Volume of cube = Volume of the cuboid

Edge of the cube =12 cm^{2}

Lateral surface area of the cube

= 4x2 = 4(12)^{2}

= 576 cm^{2}

##
Form a quadratic polynomial p(x) with 3 and 2/5 as sum and product of its zeroes, respectively .

According to the question,

sum of zeroes = 3

Product of zeroes =

The required quadratic polynomial

(Sum of zeroes) +product of zeroes

the quadratic polynomial is

##
The diameters of two circles with cenntre A and B are 16 cm and 30 cm respectively. If area of a circle with centre C is equal to the sum of areas of the other two circles, then find the circumference of the circle with centre C.

Area of circle = , Let the radius of circle with centre C = R

According to question,

=

Circumference of the circle

=

##
A point lies on x-axis at a distance of 9 units from y-axis. What are its coordinates what will be the coordinates of a point if it lies on y-axis at a distance of 9 units from x axis

(i) Since the point lies on x-axis at a distance of 9 units from y-axis. Hence its coordinates are (9,0)

(ii) According to the question, the required coordinates are (0,-9)

##
If the coordinates of a point M are (-2,9) which can also be expressed as (1+x,y2) and y >0, then find in which quadrant do the following points lie : P (y,x) Q (2,x) , R (x^{2},y-1), S (2x,-3y)

^{2},y-1), S (2x,-3y)

According to the question,

(-2,9) = (1+x,y^{2)}

-2 = 1+x or x = -3

and 9 =y^{2} or y

=3, as y>0

So, P(y,x) = P (3,-3)

Which will be in IV quadrant Q (2,x) = Q (2,-3)

**Which will be in IV quadrant R (x ^{2},y-1) = R (9, 2 )**

**Which will be in I quadrant S (2x, -3y) = S (-6,-9)**

**Which will be in III quadrant **

##
In the figure ABCD is a parallelogram. E and F are the mid-points of sides AB and CD respectively show that the line segment AF and EC trisect the diagonal BD.

According to the question E and F are the midpoints of sides AB and CD.

In the parallelogram opposite sides are equal so,

AB = CD

AE= CF

Again AB II CD

So, AE II FC

Hence AECF is a parallelogram

In

E is the mid point of AB.EQ II AP

Q is the mid point of BP

Similarity P is the mid-point of DQ

DP = PQ =QB

Line segment AF and EC trisect the diagonal BD.

##
The probability of guessing the correct answer a certain question is if the probability of not guessing the correct answer is then to find the value of x.

P(E) + P(E) = 1

##
The probability of winning a game is 1/3 less than the twice of losing the game.Find probability of winning the game.

Let the probability of winning a game = p

and the probability of losing a game = q

we know that = p+q = 1

According to question

On solving (i) and (ii) we get

and

Probability of winning a game =

##
Aftab tell his daughter, 7 years ago, I Was seven times as old as you were then. Also, 3 years from now, I shall be three times as old as you will be represented this situation algebraically and graphically .

Let the present age of father be x years and the age of daughter be y years.

7 years ago father's age = (x-7) years

7 years ago daughter's age = (y -7)years

According to the question

(x-7) = 7 ( y-7)

x-7y = -42

After 3 years father's age = (x+3) years

After 3 years daughter's age = (y +3)years

According to the condition,

x+3 = 3 (y+3)

x- 3y = 6

To fid the equivent geometric representation we find some points on the line represnting each question, these solutions are given below in the table

From eq :

x-7y = -42

x | 0 | 7 | 14 | 12 |

6 | 7 | 8 | 12 | |

Points | A | B | C | G |

x | 6 | 12 | 18 | 42 |

0 | 2 | 4 | 12 | |

Points | D | E | F | G |

Plot the points A(0,6), B (7,7) and C(14,8) and join them to get a straight line ABC. Similarly, plot the points D (6,0), E (12,2) and F (18,4) and join them to get a straight line DEF. These two lines intersect at point G (42,12). Thus we conclude that the present ages of afthaf and his daughter are 42 years and 12 years respectively.

##
A point lies on the x-axis at a distance of 9 units from the y-axis. What are its coordinates? what will be the coordinates of a point if it lies on the y-axis at a distance of -9 units from x-axis?

(i) Since the point lies on the x-axis at a distance of 9 units from the y-axis. Hence its coordinates are (9,0).

(ii) According to the question, the required coordinates are (0,-9)

##
If the coordinates of a point M are (-2,9) which can also be expressed as (1+x,y2) and y >0, then find in which quadrant do the following points lie:

According to the question,

and

= 3 as y >0

So,

Which will be in IV quadrant

Q(2,x) = Q (2,-3)

Which will be in IV quadrant

Which will be in I quadrant

Which will be in III quadrant

##
Plot the points (0,3), B (5,3) C(4,0) and D(-1,0) on the graph paper. Identity the figure ABCD and find whether the point (2,2) lies inside the figure or not?

According to the question, plot the points A (0,3) B(5,3), C(4,0) and D(-1,0) on the graph paper

From figure, ABCD is a parallelogram. The point (2,2) will lie inside the figure.

##
Given below is a pie chart showing the time spent by a group of 350 children in different games,. Observe it and answer the questions:

a. How many children spend more than 2 hours in playing game

b. How many children spend at least 1 hour playing games.

a. No. of children who spend more than 2 hours in playing game =

##
The marked price of an article is Rs. 500/- A shopkeeper gives a discount of 5% and still makes a profit of 25%. Find the cost of that article?

First calculate the selling price after

Let us assume the cost of the article is x. Hence as per the question

##
A survey was carried out to find the favorite drink preffered by a group of young people. from this pie chart answer the following questions:

a. Which type of beverage is liked by the maximum number of people

b. If 45 people like ea then, ow many people were surveyed.

c.Find te no.of people who like the coffee.

a. Cold drink is being liked by max people

b. Let the hotal no.of people for survey = x

c. No.of people who like coffee

##
A lady went to a bank with Rs. 1,00,000. She asked the cashier to give her Rs.500 and Rs. 1,000 Notes in return. She got 175 currency notes in all. Find the number of each kind of currency notes?

OR

There are 40 passengers on a bus. Some with Rs.3/- ticket and remaining with Rs. 10/- ticket.

The total collection from these passengers is Rs.295/- Find how many passengers have the ticket worth Rs.3/-

There are 40 passengers on a bus. Some with Rs.3/- ticket and remaining with Rs. 10/- ticket.

Let the no of notes of Rs. 500 = x

x+y = 175 ----------(1)

500 x + 1000 y = 100,000 ............ (2)

Multiplying equation (1) by 500

500x + 500y = 27500 ..............(3)

Solving equation (2) and (3) we get

500y = 12, 500

y = 25

Putting this value to equation (1)

x = 175-25 = 150

OR

There are 40 passengers in a bus. Some with Rs.3/- ticket and remaining with Rs. 10/- ticket. The total .......from these passengers is Rs. 295/-. Find how many passengers have the ticket worth Rs.3/-

OR

Let the no of passengers with Rs. 3 ticket is x

Then the no: of passengers with Rs.10 will be (40-x)

According to the question

3x + 10 (40-x) = 295

3x+ 400- 10x = 295

7x = 105

x = 15

##
Read the following understand the mathematical idea expressed in it and answer the questions that follow :

1,4,9,16,............ are the squares of the counting numbers. The remainders got by dividing the square numbers with natural numbers have a cyclic property. For example, the remainders on dividing these numbers by 4 are tabulated here.

Number 1 4 9 16 25 - - -

Remainder 1 0 1 0 1 - - -

On dividing by 4 perfect squares leave only 0 and 1 as remainders. From this we can conclude that an arithmetic sequence whose terms leaves remainders 2 on divideing by 4do not have a perfect square.

a. Which are the possible remainders on dividing any number with 4?

b. Which are the numbers we would not get on dividing a perfect square by 4?

c. What is the remainder that leaves on dividing the terms of the arithmetic sequence

2,5,8,11,............ by 4?

d. Does the arithmetic sequence 3,7,11,..............contain perfect squares?

e. Write a sequence with common differnce 4 which contains many perfect squares?

a. 0, 1 and 3.

b. 2 and 3.

c. 2, 1, 0 and 3.

d. No, 3,7,11,...... is divided by 4 we get the remainder 3. When we dividing the perfect square by 4, we get the remainder 0 and 1.

e. 4,8,12,16.................

##
a. What is the sum of the inner and outer angles at the vertex of a polygon?

b. If the outer angle is 20 more than thrice the inner angle, What is the measure of the inner angle?

a. The sum of the inner and outer angle = 180^{0}

b. Let the inner angle be x

By question, outer angle = 3x + 20

ie., x + 3x + 20 = 180

4x + 20 = 180

4x = 180 - 20 = 160

x = 120/4 = 40

Hence the inner angle be 40^{0}.

##
A bag contains 18 balls out of which x balls are red.

i. If one ball is drawn at random from the bag, what is the probability that it is not red?

ii. If 2 more red balls are put in the bag, the of drawing a red ball will be times the probability of drawing a red ball in the first case. Find the value of x.

P(red ball) =

i) P(no red ball) =

ii) Total number of balls = 18 + 2 = 20

Red balls are = x + 2

P(red balls) =

Now, According to the question,

##
A bag contains 15 balls of which x are blue and the remianing are red. If the number of red balla are increased by 5, the probability of drawing the red balls doubles. Find:

i. P (red ball)

ii. P(blue ball)

iii. P (blue ball it of 5 extra red ball are actually added)

According to the question,

blue ball = 12 and red ball = 3

i) P (red ball) =

ii)P (blue ball) =

iii) P (Blue ball is 5 red balls are added) =

##
A trader was moving along a road selling eggs. An idler who did not have much work to do, started to get the trader into a wordly duel. This grew into a fight, he pulled the basket with eggs and dashed it on the floor. The eggs broke. The trader requested the panchayath to as the idler to pay for broken eggs. The panchayath asked the trader, How many eggs were broken? He gave the following response: if counted in pairs one will remain; If counted in 3 two will remain; If counted in 4, 3 will remain if counted 5, 4 will remain; If counted 6,5 will renmain; if counted in 7 nothing all remain my basket cannot accomodate more than 150 eggs So,

i. How many eggs were there?

ii. Which Mathematical concept is used to solve the above question?

iii. Which values are hidden in the above question?

i.

Let the number of eggs = a

If counted in 7, nothing will remain

a = 7 p + 0, for som enatural number p.

If counted in 6, 5 will remain for some natural number is q.

a = 6q + 5

If counted in 5, 4 will remain for some natural number w

a = 5w + 4

If counted in 4, 3 will remain, for some natural number s

a = 4s + 3

If counted in 3 , 2 will remain, for some natural number t.

a = 3t + 2

If counted in pairs, one will remain, for some natural number

a = 2u + 1

That is in each case, we have a and positive ineteger (b takes a value 7,6,5,4,3 and 2 respectively) which divides 'a' and leaves a remainder r (in case r is 6,5,4,3, 2 and 1 respectively ), that is smaller than 'b'.

We must look for the multiple of 7 which satisfy all the conditions. By trial and error (using the consept of LCM ) we will get total number of eggs = 199

ii.

Euclid's division lemma (Real numbers)

iii.

The values of of the trader are honesty and faith in the panchayath system.