If 
is added to each number, the ratiobecomes 
Find the numbers.The ratio is used for comparing two quantities of the sane kind. The ratio formula for two numbers says a and b is given by a:b or a/b. When two or more such ratios are equal, they are said to be in...
(iv) Mx.Mo on P 
Mo.My $\left( 4,6 \right)$ Mo $\left( -4,6 \right)$ Therefore, reflection within the x – axis $\left( 4,-6 \right)$ Mx.Mo $\left( -1,-3 \right)$ Mx $\left( -1,3 \right)$...
ii) My.Mo on A 
Mx.My $\left( 2,-5 \right)$ Mx $\left( -2,-5 \right)$ Therefore, reflection within the origin is $\left( -2,-5 \right)$ My.Mo $\left( -7,3 \right)$ My $\left( 7,-3 \right)$ Therefore,...
and 
(iv) 
and 
The ratio is used for comparing two quantities of the sane kind. The ratio formula for two numbers says a and b is given by a:b or a/b. When two or more such ratios are equal, they are said to be in...
and 
(ii) 
and 
The ratio is used for comparing two quantities of the sane kind. The ratio formula for two numbers says a and b is given by a:b or a/b. When two or more such ratios are equal, they are said to be in...
is reflected within the x-axis to the point P’. The point P’ is then reflected in the origin to point P”. Mention down the co-ordinates of P”. State the one transformation that maps P into P”.In the question it is mention that, P $=\left( -8,1 \right)$ The co-ordinates of P’ under reflection within the x –axis $=\left( -8,-1 \right)$ Then, the co-ordinates of p” under reflection within...
(iv) 
The ratio is used for comparing two quantities of the sane kind. The ratio formula for two numbers says a and b is given by a:b or a/b. When two or more such ratios are equal, they are said to be in...
(ii) 
The ratio is used for comparing two quantities of the sane kind. The ratio formula for two numbers says a and b is given by a:b or a/b. When two or more such ratios are equal, they are said to be in...
, B 
and C 
. This triangle is reflected in the line y 
on to ΔA’B’C’. ΔA’B’C’ in then reflected in the origin onto ΔA”B”C”. Mention down the co-ordinates of ΔA’B’C’ and ΔA”B”C”.In the question it is mentioned that, The co–ordinates of its vertices are A $\left( 2,3 \right)$, B $\left( 4,-4 \right)$ and C $\left( 6,-7 \right)$ Then, co-ordinates of ΔA’B’C’ under...
(iv)
The ratio is used for comparing two quantities of the sane kind. The ratio formula for two numbers says a and b is given by a:b or a/b. When two or more such ratios are equal, they are said to be in...
(ii) 
The ratio is used for comparing two quantities of the sane kind. The ratio formula for two numbers says a and b is given by a:b or a/b. When two or more such ratios are equal, they are said to be in...
under reflection within the origin and under reflection within the y-axis. Calculate the distance between the points of reflection?Lets presume that S be the Point, So, S $=\left( -2,4 \right)$ Then, picture under reflection within the origin S’ $=\left( 2,-4 \right)$ And picture under reflection in the y-axis S” $=\left( 2,4...
(iv) 
The ratio is used for comparing two quantities of the sane kind. The ratio formula for two numbers says a and b is given by a:b or a/b. When two or more such ratios are equal, they are said to be in...
(ii) 
The ratio is used for comparing two quantities of the sane kind. The ratio formula for two numbers says a and b is given by a:b or a/b. When two or more such ratios are equal, they are said to be in...
are the co-ordinates of P”. State the one transformation that happens.In the question it is mentioned that, P” $=(5,-2)$ Then, are the co-ordinates of P’$=(-5,2)$ Therefore, the co-ordinates of P$=(-5,-2)$ One transformation = reflection within the y-axis
and
. Find B’, the picture of B under the reflection in the x-axis and C’, the picture of C under the reflection in the line BB’.In the question it is mentioned that, B point $=\left( 3,2 \right)$ C point $=\left( 0,3 \right)$ Then, the reflection of B in the x – axis is B’ $=\left( 3,-2 \right)$ And the reflection of C in...
(iv) 
The ratio is used for comparing two quantities of the sane kind. The ratio formula for two numbers says a and b is given by a:b or a/b. When two or more such ratios are equal, they are said to be in...
is reflected in the origin as R’. Q point 
is reflected in the x-axis as Q’. Mention down the co-ordinates of R’ and Q’. Calculate the distance between R’ Q’.In the question it is mentioned that R point = $\left( 3,-2 \right)$ Then, a R point is reflected in the origin as R’ $=\left( -3,2 \right)$ Q point $=\left( -7,1 \right)$ Then, a Q...
(iv) 
The co-ordinates of the pictures of the spots given under reflection in the x-axis is $(0,6)$ The co-ordinates of the pictures of the spots given under reflection in the x-axis is $(-4,8)$
(ii) 
The co-ordinates of the pictures of the spots given under reflection in the x-axis is $(3,9)$ The co-ordinates of the pictures of the spots given under reflection in the x-axis is $(-7,5)$
and 
paise(iv) 
and 
The ratio is used for comparing two quantities of the sane kind. The ratio formula for two numbers says a and b is given by a:b or a/b. When two or more such ratios are equal, they are said to be in...
and 
(ii) 
and 
Given numbers can be written as, $5.60/2.40$ Now, shifting the decimal points we get, $=28/12$…[because diving both by $2$] $=14/6$…[because diving both by $2$] $=7/3$…[because diving both by $2$]...
. Find the co-ordinates of P. Find the co-ordinates of the picture of P under reflection in the y-axis.In the question it is mention that, P’ $=(-3,4)$ Then, is the co-ordinates of P under reflection in the x -axis$(-3,-4)$ also the co-ordinates of P” under reflection in the y – axis is $(3,-4)$ The...
and 
then find 
The ratio is used for comparing two quantities of the sane kind. The ratio formula for two numbers says a and b is given by a:b or a/b. When two or more such ratios are equal, they are said to be in...
. Find the co-ordinates of P and P”. Mention the one transformation that map P onto P”.In the question it is mention that, P’ $(-3,4)$ Then, $( -3,-4)$is the co-ordinates of P under reflection in the x-axis. Also, $( 3,-4)$is the co-ordinates of P” under reflection in the origin The...
, then find 
The ratio is used for comparing two quantities of the sane kind. The ratio formula for two numbers says a and b is given by a:b or a/b. When two or more such ratios are equal, they are said to be in...
; find the value of 
The ratio is used for comparing two quantities of the sane kind. The ratio formula for two numbers says a and b is given by a:b or a/b. When two or more such ratios are equal, they are said to be in...
, then mention the co-ordinates of S’In the question, s$=( 2,-5)$ is given Then,$(-2,5)$ is the co-ordinates of S’ under reflection in the origin.
. He saves every month a minimum of ₹ 
. Find the ratio of his:(i) Annual expenses to annual income.(ii) Monthly savings to monthly expensesThe ratio is used for comparing two quantities of the sane kind. The ratio formula for two numbers says a and b is given by a:b or a/b. When two or more such ratios are equal, they are said to be in...
, then mention the co-ordinates of P.From the question P’ $=(2,10)$is given Then, $( 2,-10)$is the co-ordinates of P under reflection in the x-axis.
, find the value of 
The ratio is used for comparing two quantities of the sane kind. The ratio formula for two numbers says a and b is given by a:b or a/b. When two or more such ratios are equal, they are said to be in...
(iv) 
The co-ordinates of the pictures of the spots given under reflection in the origin is $( 0,-2)$ The co-ordinates of the pictures of the spots given under reflection in the origin is (-9,9)
( 2,7)$The co-ordinates of the images of the spots given under reflection in the origin is $(1,4)$ The co-ordinates of the pictures of the spots given under reflection in the origin is $( -2,-7)
(iv) 
The co-ordinates of the pictures of the spots given under reflection in the y-axis is $(-5,-6)$ The co-ordinates of the pictures of the spots given under reflection in the y-axis is $( 4,7)$
(ii) 
The co-ordinates of the pictures of the spots given under reflection in the y-axis is $(-2,8)$ The co-ordinates of the pictures of the spots given under reflection in the y-axis is $(1,-3)$
, find the following(iii) 
The ratio is used for comparing two quantities of the sane kind. The ratio formula for two numbers says a and b is given by a:b or a/b. When two or more such ratios are equal, they are said to be in...
, find the following(i) 
(ii) 
The ratio is used for comparing two quantities of the sane kind. The ratio formula for two numbers says a and b is given by a:b or a/b. When two or more such ratios are equal, they are said to be in...
is 13, find x.In question, Given that: $8,14,20,x\And 12$ Mean $=13$ We have to find out the value for x, Then, Whereas, N is the total number $N=5$ $\bar{x}=(x1+x2+..xn)/n$ $13=(8+14+20+x+12)/5$...
is
, find pIn question given that, $11,14,p,26,10,12,18\And 6$ Mean $=15$ We have to find the value for p, Whereas n is the total number \[N=8\] $\bar{x}=(x1+x2+..xn)/n$...
. If a new member with a monthly income of 
jons the group, find the new monthly incomeIn the question it is given that, The mean monthly income of 10 persons is $8670$ Where n is the number of persons, $n=10$ as we know that, $\bar{x}=(x1+x2+...+xn)/n$ $8,670=\sum{xn/10}$...
to
. Find the new mean when each number is diminished by 
.Natural number: it is define as a counting number All the natural numbers from $32$to $46$are, \[32,33,34,35,36,37,38,39,40,41,42,43,44,45,46\] Where n is the total number, $N=15$...
. Subsequently, she took out Rs 
on 12.05.2007; deposited a cheque of Rs. 
on 03.06.2007 and paid Rs 
– by cheque on 18.06.2007. 
pa compounded at the end of March and September, find her balance on 1.04.2008(a) From giving data in the question, We have to make the entries in passbook, So, the table have 5 columns. The data in 5 columns are, DateParticulars Withdrawals Depots Balance....
Unit TestIIIIIIIVVVIPercentage of marks obtained by students$72$$67$$69$$74$$71$$76$ (iii) less than $65%$marks in a unit test. Answer- Probability – the chances of something happening. (iii) The...
every month in a recurring deposit account for a period of 
years at a simple interest rate of 
pa.From the question it is given that, Mrs. Khandelkar invests ₹$900$ every month in a recurring deposit account. Period = $3$ years We know that, 1 year = $12$ Months So, $3$years = $3\times...
Unit Test$$IIIIII1VVVIPercentage of marks obtained$72$$67$$69$$74$$71$$76$ Based on this data find the probability that the student gets. (i) More than $70%$ marks in a unit test. (ii) less than...
to 
. Find the new mean when each number is multiplied by 
.Odd number is that is not divided by two All odd numbers from $5$ to $20$ are, $5,7,9,11,13,15,17,19$ Where as n is the total number $N=8$ Then, $\bar{x}=(x1+x2+...xn)/n$...
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.Therefore, We know that ,all the numbers from \[7\]to $17$are: $7,8,9,10,11,12,13,14,15,16,17$ Whereas n is the total number, $N=11$ Then, $\bar{x}=(x1+x2+...xn)/n$...
prime numbers.Prime no: its only divided by $1$ and exactly only by itself . We all know that, The first $10$ prime numbers are: $2,3,5,7,9,11,13,17,19,23,29$ Whereas ‘n’ is the total numbers $N=10$ Then,...
even numbers.Mean is the average vale in a collection of numbers. We all know that, the first $12$ even numbers are: $2,4,6,8,10,12,14,16,18,20,22,24$ Whereas ‘n’ is the total number Then,$n=12$...
times and frequencies of the outcomes 
were noted as given in the following tableOutcomes$1$$2$$3$$4$$5$$6$Frequency$73$$70$$74$$75$$80$$78$ (iii) a number $>4$ SOLUTION- (iii) Number of times greater than 4 come on the die = $80+78=158$ $P(>4$will come up on die$)$...
. The sales tax on it is 
. He requested the shopkeeper to reduce the price to such an extent that he has to pay only 
including the sales tax. Find the reduction given by the shopkeeper.Given The cost of leather coat is ₹$2,654$ The rate of sales tax $9%$ Calculation, Let, the reduced price if coat be$y$ Total amount of the coat $=y+9%$of $=1y+\left( 9/100 \right)y$ $=109y/100$...
. The rate of sales tax is 
. The shopkeeper gave her a discount such that she got the watch for only 
. Find the discount given by the shopkeeper.Given, The cost of titan watch is ₹$3,250$ The rate of sales tax$12%$ Let, the reduced price of watch be$y$ Total amount of the watch $=y+12%$of$y$ $=1y+\left( 12/100 \right)y$ $=112y/100$...
. The rate of sales tax is 
. He requests the shopkeeper to reduce the price to such an extent that he has to pay only 
including the sales tax. Find the reduction needed in the price of the fan.Given The cost of fan = ₹$750$ The rate of sales tax = $6%$ Calculation, Let, the reduced price of fan be$y$ Total amount of the fan $=y+6%$of$y$ $=1y+\left( 6/100 \right)y$ $=106y/100$ But, the...
is 
. Find the basic price of the scooter.Given The total cost of a scooter including sales tax is ₹$37,462.50$ The rate of sales tax $11%$ Calculation Let, the basic price of scooter be$y$ Total price of the scooter = ₹$\left[ y+\left(...
times and frequencies of the outcomes were noted as given in the following tableoutcome$1$$2$$3$$4$$5$$6$Frequency$73$$70$$74$$75$$80$$78$ (i) $4$ (ii) a number $<4$ Solution:- In the question it is given that, a die is thrown $450$ times So, total number of times die thrown...
is 
. Find the basic price of the shoesGiven The total cost of a Nike shoes including sales tax is ₹$1,572.90$ The rate of sales tax$7%$ Let, the basic price of Nike shoes be$y$ So, total price of the Shoes = ₹$\left[ y+\left( \left(...
is 
. Find the basic price of the T.V. set.Given The total cost of a T.V. set including sales tax is ₹$30,552$ The rate of sales tax$14%$ Calculation Let, the basic price of T.V. set be$y$ So, total price of the T.V. set = ₹$\left[ y+\left(...
. If the rate of sales tax , find the basic price of the refrigeratorGiven, The total cost of a refrigerator including sales tax is ₹$30,940$ The rate of sales tax$12%$ Calculation, Let, the basic price of refrigerator be $y$ Total price of the refrigerator =...
and the sales tax on it is 
. Find the rate of sales tax.Given The marked price of an article is ₹$17,840$ The sales tax = ₹$2,230$ Calculation, Rate of sales tax = ($100\times $Sale tax)/marked price = $\left( 100\times 2,230 \right)/17,840$ =$12.5%$...
. The sales tax on it is 
. Find the rate of sales taxGiven Price of Samsung plasma T.V. in the showroom = ₹$68,000$ Sales tax = ₹$14,960$ Calculation, Rate of sales tax = ($100\times $Sale tax)/marked price = $\left( 100\times 14,960 \right)/68,000$...
and the sales tax on it is 
. Find the rate of sales taxGiven The list price of chair = ₹$7,500$ Sales tax = ₹$1,125$ Calculation, Rate of sales tax = ($100\times $ Sale tax)/marked price $=\left( 100\times 1,125 \right)/7,500$ =$15%$ $\therefore $ Rate...
and carrying a sales tax of 
.Given List price of electronic washing machine = ₹$24,600$ Rate of sales tax =$15%$ Sales tax = (list price × rate of sale tax) $/100$ $=\left( 24,600\times 15 \right)/100$ = ₹$3,690$ Selling price...
and the sales tax on it is 
. Find the selling price of the watchGiven Rate of sales tax on watch =$18%$ Listed price of watch = ₹$15,500$ Sales tax = (list price × rate of sale tax)$/100$ $=\left( 15,500\times 18 \right)//100$ = ₹$2,790$ Selling price of watch =...
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.Given List price of the leather bag = ₹$4,850$ The rate of sales tax =$12%$ Sales tax = (list price × rate of sale tax)$/100$ $=\left( 4,850\times 12 \right)/100$ = ₹$582$ The amount paid by Rajesh...
. Two coins are tossed simultaneously 
times and the outcomes are noted asTwo tails: $83$ One tail: $140$ No tail: $77$ Find the probability of occurrence of each these events. Solution:- the extent to which an event is likely to occur, measured by the ratio of the...
families with 
children were selected randomly, and the following data were recorded:Number of girls in a family$0$$1$$2$Number of families$333$$392$$275$ Find the probability of a family, having (iii) no girl Solution:- The extent to which an event is likely to occur and measured...
S. No.ItemMarked PriceSales Tax(i)Shoes₹ 2,740.00₹ 137.00(ii)Music system₹ 16,400.00₹ 2,050.00(iii)Vacuum cleaners₹ 8,325.00₹ 1,332.00(iv)Digital diary₹ 3,500.00₹ 367.50(v)VCD₹ 27,916.00₹ 4,047.82...
S. No.ItemMarked PriceSales Tax(i)Shoes₹ 2,740.00₹ 137.00(ii)Music system₹ 16,400.00₹ 2,050.00(iii)Vacuum cleaners₹ 8,325.00₹ 1,332.00(iv)Digital diary₹ 3,500.00₹ 367.50(v)VCD₹ 27,916.00₹ 4,047.82...
S. No.ItemMarked PriceRate of Sales Tax(i)Walkman₹ 1,750.008.5%(ii)Washing machine₹14,840.007.5%(iii)Computer₹ 32,725.0012%(iv)Sofa set₹ 16,000.0011.5%(v)T.V.₹ 28,975.0016%(vi)Jacket₹...
families with children were selected randomly, and the following data were recorded:Number of girls in a family$0$$1$$2$Number of families$333$$392$$275$ Find the probability of a family, having (i) $1$ girl (ii) $2$ girls Solution:- Probability is the branch mathematics...
S. No.ItemMarked PriceRate of Sales Tax(i)Walkman₹ 1,750.008.5%(ii)Washing machine₹14,840.007.5%(iii)Computer₹ 32,725.0012%(iv)Sofa set₹ 16,000.0011.5%(v)T.V.₹ 28,975.0016%(vi)Jacket₹...
S. No.ItemMarked PriceRate of Sales Tax(i)Walkman₹ 1,750.008.5%(ii)Washing machine₹14,840.007.5%(iii)Computer₹ 32,725.0012%(iv)Sofa set₹ 16,000.0011.5%(v)T.V.₹ 28,975.0016%(vi)Jacket₹...
S. No.ItemMarked PriceRate of Sales Tax(i)Walkman₹ 1,750.008.5%(ii)Washing machine₹14,840.007.5% (i) Marked price = $1,750$, Rate of sales tax = $8.5%$ Sales tax = (marked price × rate of sale...
times and the outcomes were noted as: Head: 
, Tail : 
. Find the probability of the coin showing up (i) a head, (ii) a tail.Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. From the question it is given that, A...
and circumscribe a square about it.In old style math, a span of a circle or circle is any of the line fragments from its middle to its edge, and in more current utilization, it is additionally their length. In math, the circumference...
and inscribe an equilateral triangle in it.In old style math, a span of a circle or circle is any of the line fragments from its middle to its edge, and in more current utilization, it is additionally their length. In math, the circumference...
in which 
, 
and 
. Inscribe a circle in the and measure its radius.In old style math, a span of a circle or circle is any of the line fragments from its middle to its edge, and in more current utilization, it is additionally their length. In math, the circumference...
and 
with their centers
apart. Draw a direct common tangent and a transverse common tangent. Calculate the length of the direct common tangent.In old style math, a span of a circle or circle is any of the line fragments from its middle to its edge, and in more current utilization, it is additionally their length. In math, the circumference...
and 
, their centers being 
apart. Construct a transverse common tangent and measure its length.In old style math, a span of a circle or circle is any of the line fragments from its middle to its edge, and in more current utilization, it is additionally their length. In math, the circumference...
and 
respectively so that their centers are 
apart. Draw direct common tangents to the circle and show that they are equal in length.In old style math, a span of a circle or circle is any of the line fragments from its middle to its edge, and in more current utilization, it is additionally their length. In math, the circumference...
and respectively so that their centers are apart. Draw direct common tangents to the circle.Radii is also known as radius. In old style math, a span of a circle or circle is any of the line fragments from its middle to its edge, and in more current utilization, it is additionally their...
from a point 
from the center. What is the length of each of them?In old style math, a span of a circle or circle is any of the line fragments from its middle to its edge, and in more current utilization, it is additionally their length. In math, the circumference...
. Take a point P outside the circle. Draw tangents to the circle from P without using the center and using only ruler and compassesIn old style math, a span of a circle or circle is any of the line fragments from its middle to its edge, and in more current utilization, it is additionally their length. In math, the circumference...
. Take a point ‘P’ at distance of from the center. Using ruler and compasses only construct the tangent to the circle from the point.In old style math, a span of a circle or circle is any of the line fragments from its middle to its edge, and in more current utilization, it is additionally their length. In math, the circumference...
. Take a point P on its circumference. Construct a tangent to the circle at P without using the center.In old style math, a span of a circle or circle is any of the line fragments from its middle to its edge, and in more current utilization, it is additionally their length. In math, the circumference...
In old style math, a span of a circle or circle is any of the line fragments from its middle to its edge, and in more current utilization, it is additionally their length. In math, the circumference...