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10th Maths 6.2

NCERT Class 10th solution of Exercise 6.1 NCERT Class 10th solution of Exercise 6.3 NCERT Class 10th solution of Exercise 6.4 NCERT Class 10th solution of Exercise 6.5 NCERT Class 10th Maths Projects Exercise 6.2 Q1. In the figure i) and ii)

$DE∥BC.$ Find the

$EC$ in (i) and

$AD$ in (ii). Sol. i) Given

$DE∥BC$

$(AD)/(DE)=(AE)/(EC)$

$(1.5)/3=1/(EC)$

$EC=3/(1.5)=2$ cm. Answer :

$EC=2$ cm. ii) Given

$DE∥BC$

$(AD)/(DE)=(AE)/(EC)$

$(AD)/(7.2)=(1.8)/(5.4)$

$AD=(1.8)/(5.4)times7.2$

$AD=2.4$ cm. Answer :

$AD=2.4$ cm. Q2.

$E$ and

$F$ are points on the sides

$PO$ and

$PR$ respectively of a

$triangle PQR.$ For each of the following cases, state whether

$EF∥QR$ : i)

$PE=3.9$ cm,

$EQ=3$ cm,

$PF=3.6$ cm and

$FR=2.4$ cm ii)

$PE=4$ cm,

$QE=4.5$ cm,

$PF=8$ cm, and

$RF=9$ cm iii)

$PQ=1.28$ cm,

$PR=2.56$ cm,

$PE=0.18$ cm, and

$PF=0.36$ cm. Sol. In

$trianglePQR$ Points

$E$ and

$F$ are on sides

$PQ$ and

$PR$ i)

$(PE)/(EQ)=(3.9)/3$

$(PE)/(EQ)=1.3$ and

$(PF)/(FR)=(3.6)/(2.4)$

$(PF)/(FR)=1.5$ `(PE)/(EQ)n...

NCERT Class 10th solution of Exercise 6.2 NCERT Class 10th solution of Exercise 6.3 NCERT Class 10th solution of Exercise 6.4 NCERT Class 10th solution of Exercise 6.5 NCERT Class 10th Maths Projects Exercise 6.1 Q1. Fill in the blanks using the correct word given in brackets : i) All circles are _____________. ( congruent, similar ) ii) All squares are ____________. ( similar, congruent ) iii) All __________ triangles are similar. ( isosceles, equilateral ) iv) Two polygons of the same number of sides are similar, if (a) their corresponding angles are ______ and (b) their corresponding sides are _______ . ( equal, proportional ) Answer : i) similar, ii) similar, iii) equilateral, iv) a) equal, b) proportional. Q2. Give two different examples of pair of i) similar figures. ii) non-similar figures. Answer : i) All circles, squares, ii) All quadrilaterals, triangles. Q3. State w...

Chapter 5 Arithmetic Progressions Like, Share, and Subscribe. NCERT Class 10th solution of Exercise 5.1 NCERT Class 10th solution of Exercise 5.2 NCERT Class 10th solution of Exercise 6.1 NCERT Class 10th Maths Projects Exercise 5.3 Q1. Find the sum of the following APs: i)

$2, 7, 12, ...$ to

$10$ terms. ii)

$-37, -33, -29, ...,$ to

$12$ terms. iii)

$0.6, 1.7, 2.8, ...$ to

$100$ terms. iv)

$1/15, 1/12, 1/10, ...$ to

$11$ terms. Sol. : i) Given

$a=2, d=7-2=5,$ and

$n=10$

$S_n=n/2[2a+(n-1)d]$

$S_10=10/2[2(2)+(10-1)(5)]$

$S_10=5[4+(9)(5)]$

$S_10=5[4+45]$

$S_10=5[49]$

$S_10=245$ Answer :

$S_10=245.$ ii) Given

$a=-37, d=(-33)-(-37)=-33+37=4,$ and

$n=12$

$S_n=n/2[2a+(n-1)d]$

$S_12=12/2[2(-37)+(12-1)(4)]$

$S_12=6[-74+(11)(4)]$

$S_12=6[-74+44]$

$S_12=6[-30]$

$S_12=-180$ Answer :

$S_12=-180.$ iii) Given

$a=0.6, d=1.7-0.6=1.1,$ and

$n=100$

$S_n=n/2[2a+(n-1)d]$

$S_100=100/2[2(0.6)+(100-1)(1.1)]$

$S_100=50[1.2+(99)(1.1)]$

$S_100=50[1.2+108.9]$

$S_100=50[110.1]$

$S_100=5505$ Answer :

$S_100=5505.$ ...

Chapter 5 Arithmetic Progressions Like, Share, and Subscribe. NCERT Class 10th solution of Exercise 5.1 NCERT Class 10th solution of Exercise 5.3 NCERT Class 10th Maths Projects Exercise 5.2 Q1. Fill in the blanks in the following table, given that

$a$ is the first term,

$d$ the common difference and

$a_n$ the

$nth$ term of the AP ;

$a$

$d$

$n$

$a_n$ i)

$7$

$3$

$8$ ...... ii)

$-18$ .....

$10$

$0$ iii) .....

$-3$

$18$

$-5$ iv)

$-18.9$

$2.5$ .....

$3.6$ v)

$3.5$

$0$

$105$ ..... Sol. : i)

$a_n=a+(n-1)timesd$

$a_n=7+(8-1)times3$ ...

Chapter 5 Arithmetic Progressions Like, Share, and Subscribe. NCERT Class 10th solution of Exercise 5.2 NCERT Class 10th solution of Exercise 5.3 NCERT Class 10th Maths Projects Exercise 5.1 Q1. In which of the following situations, does the list of numbers involved make an arithmetic progression, and why? i) The taxi fare after each km when the fare is

$15$ for the first km and

$8$ for each additional km. ii) The amount of air present in a cylinder when a vacuum pump removes

$1/4$ of the air remaining in the cylinder at a time. iii) The cost of digging a well after every metre if digging when it costs

$150$ for the first meter and rises by

$50$ for each subsequent metre. iv) The amount of money in the account every year, when

$10000$ is deposited at compound interest at

$8$ % per annum. Sol. : i) Yes,

$15, 23, 31,...$ form an AP due to the common difference

$8$ is fixed ii) No. Volumes are

$V, (3V)/4, (3/4)^2V,...$ due to the common difference is not fixed. iii) Yes. `150, 200, 25...

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10th Maths 6.2

10th Maths 6.1

10th Maths 5.3

10th Maths 5.2

10th Maths 5.1