CBSE > Class 10 > Mathematics | CBSE Board | Homework Help

Let's prove this by the method of contradiction-
Say, √5 is a rational number. ∴ It can be expressed in the form p/q where p,q are co-prime integers.
⇒√5=p/q
⇒5=p²/q² {Squaring both the sides}
⇒5q²=p² (1)
⇒p² is a multiple of 5. {Euclid's Division Lemma}
⇒p is also a multiple of 5. {Fundamental Theorm of arithmetic}
⇒p=5m
⇒p²=25m² (2)
From equations (1) and (2), we get,
5q²=25m²
⇒q²=5m²
⇒q² is a multiple of 5. {Euclid's Division Lemma}
⇒q is a multiple of 5.{Fundamental Theorm of Arithmetic}
Hence, p,q have a common factor 5. this contradicts that they are co-primes. Therefore, p/q is not a rational number. This proves that √5 is an irrational number.
For you second query, as we've proved √5 irrational. Therefore √5+3 is also irrational because sum of a rational and an irrational number is always an irrational number.

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If zeros of quadratic equation are resiprocal of eachother 3x²-10x+k .Thae find value of k.

Posted by King King 6 years, 1 month ago

CBSE > Class 10 > Mathematics

3 answers

Chandan Kumar 6 years, 1 month ago

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Gaurav Seth 6 years, 1 month ago

Given in the question the equation:

3x² - 10x + k = 0

suppose 1st root of this equation is r

so as stated in the question, second root of this equation will be 1/r

Adding the roots gives = −b/a
Multiplying the roots gives = c/a
a b c

3x² - 10x + k = 0

r x 1 / r = c / a

r / r = k / 3

1 = k / 3

3 = k

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⛩️Singh Empire? (Believe In Study)✍️???? 6 years, 1 month ago

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The cost of polishing TSA of closed cylinder oil tank at 25 paise per is rs 27. It hieght is 3times that of the radius of base. Determine the radius of base and hieght

Posted by Harsh Kaushik 6 years, 1 month ago

CBSE > Class 10 > Mathematics

0 answers

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Cot90+tan0

Posted by Sudhanshu Garg 6 years, 1 month ago

CBSE > Class 10 > Mathematics

8 answers

Massenger Bhardwaj 6 years, 1 month ago

0 BUT HOW

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Anushka Singh 6 years, 1 month ago

Sorry for oo

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Anushka Singh 6 years, 1 month ago

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Anushka Singh 6 years, 1 month ago

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Aadya Singh ? 6 years, 1 month ago

Aapne bataya nhi aapka question wrong tha ya right?

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Aadya Singh ? 6 years, 1 month ago

Hello sahil ji

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Aadya Singh ? 6 years, 1 month ago

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Sahil ??? 6 years, 1 month ago

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Meena went to a bank to withdraw₹2000 she asked the cashier to give her₹50 and ₹100 notes only meena got 25 notes in all find how many note of ₹50 and₹100 she received by ellimination method

Posted by Sugam Bhumihar 6 years, 1 month ago

CBSE > Class 10 > Mathematics

3 answers

Aadya Singh ? 6 years, 1 month ago

Meena received 10 notes of denomination 50 and 15 notes of denomination 100

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Sahil ??? 6 years, 1 month ago

No. of ₹50 notes=10 and no. of ₹100 notes=15

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Sugam Bhumihar 6 years, 1 month ago

X=10 y=15

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Out of two concentric circles the radius of the outer circle is 25cm and the chord AC of lenght 48cm is a tangent to the inner circle.find the radius of the inner circle

Posted by Anshu Singh 6 years, 1 month ago

CBSE > Class 10 > Mathematics

3 answers

Massenger Bhardwaj 6 years, 1 month ago

r=7cm

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Aadya Singh ? 6 years, 1 month ago

Radius = 7 cm

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Sahil ??? 6 years, 1 month ago

Radius of inner circle is 7 cm.

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Area of two similar triangle

Posted by Saptaraj Chakraborty 6 years, 1 month ago

CBSE > Class 10 > Mathematics

1 answers

Riya Rathore 6 years, 1 month ago

22/7Rsquare

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In figure ABC is a right angled triangle at B such that BC=6 cm , AB=8 cm find the radius of the inercirle ?

Posted by Komal Choudhary 6 years, 1 month ago

CBSE > Class 10 > Mathematics

2 answers

Massenger Bhardwaj 6 years, 1 month ago

Radius=2cm

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Ashokkm93111 Kumar93111 6 years, 1 month ago

Using Pythagoras theorem AC2=BC2+AB2 AC2=36+64 AC=10 CM Now area of triangle ABC = area of triangle OAB + area of triangle OBC +area of triangle OCA 1/2*6*8= 1/2*8*r+1/2*10*r+1/2*6*r 48=24r r=2 cm

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How to identify whether the question is of LCM or HCF???

Posted by Mohammed Tabrez 6 years, 1 month ago

CBSE > Class 10 > Mathematics

1 answers

⛩️Singh Empire? (Believe In Study)✍️???? 6 years, 1 month ago

If we have to find greatest no we are going for hcf ...but if we have to find the smallest no. then we have to find lcm of given data............this is the commonly used method but it does'nt work always so, we have to focus on our understanding to solve a particular question.

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2.3

Posted by Ansar Khan 6 years, 1 month ago

CBSE > Class 10 > Mathematics

0 answers

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The LCM of smallest two digit composit number and smallest composit number is a 44 b 4 c 20 d 14

Posted by Aarti Sharma 6 years, 1 month ago

CBSE > Class 10 > Mathematics

6 answers

Massenger Bhardwaj 6 years, 1 month ago

LCM=20

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Sahil ??? 6 years, 1 month ago

Oops!??sorry

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Aadya Singh ? 6 years, 1 month ago

2 digit *

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Aadya Singh ? 6 years, 1 month ago

Sahil...smallest digit composite number is 10 not 12.

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Sahil ??? 6 years, 1 month ago

Smallest two digit composite number is 12.....smallest composite number is 4.So,their LCM will be 12

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Aadya Singh ? 6 years, 1 month ago

C) 20

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The following frequency

Posted by Akhand Rai 6 years, 1 month ago

CBSE > Class 10 > Mathematics

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A plane left 30 minutes late than it's sheduled time and in order to reach the destination 1500 km away in time, it had to increase its speed by 100 km/hr from the usual speed. Find its usual speed.

Posted by Meena Jadhav 6 years, 1 month ago

CBSE > Class 10 > Mathematics

3 answers

Sahil ??? 6 years, 1 month ago

Usual speed=500km/hr

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Aadya Singh ? 6 years, 1 month ago

500 km/h

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P@Řťh Ń€Ğ! 6 years, 1 month ago

faaltu question

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What is latest syllabus of class 10 every subject topic wise

Posted by Ankit Yadav 6 years, 1 month ago

CBSE > Class 10 > Mathematics

1 answers

Ishita Chochan Ishu 6 years, 1 month ago

What Qution

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At t minutes past 2pm the time needed by the minutes hand of a clock

Posted by Saloni Gusaai 6 years, 1 month ago

CBSE > Class 10 > Mathematics

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angle of depression of a car standing on the ground from the top of a 75 metre tower is 30 degree the distance of the car from the base of the tower is

Posted by Savita Gupta 6 years, 1 month ago

CBSE > Class 10 > Mathematics

3 answers

Massenger Bhardwaj 6 years, 1 month ago

Distance = 75root3

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Chandan Kumar 6 years, 1 month ago

75√3

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Prince Yadaw 6 years, 1 month ago

75√3

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A toy is in the form of a cone mounted on a hemisphere of common base 7cm. Th total height of toy is 31cm.find the total surface area of the toy

Posted by Nirmal Sandhu 6 years, 1 month ago

CBSE > Class 10 > Mathematics

1 answers

Sahil ??? 6 years, 1 month ago

If r=7cm,then total surface area=594cm^2

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evaluate sec52×sec38

Posted by Hafsa Ikhlas 6 years, 1 month ago

CBSE > Class 10 > Mathematics

7 answers

Sahil ??? 6 years, 1 month ago

Aadya is right

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Aadya Singh ? 6 years, 1 month ago

But I think ........ Sec(90 - thita) = cosec thita hota h.... Cos thita nhi....to kaha se answer 1 aa gya?

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⛩️Singh Empire? (Believe In Study)✍️???? 6 years, 1 month ago

Kaise ho g

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⛩️Singh Empire? (Believe In Study)✍️???? 6 years, 1 month ago

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Raunak Chauhan 6 years, 1 month ago

Sec theth *cos theta =1 Sec 52×sec 38 Sec 52×sec(90-52) (Sec(90-theta)=cos thetha So Sec 52×cos52 So answer =1

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Aadya Singh ? 6 years, 1 month ago

Sorry. .it's wrong.....I've not read the question properly

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Aadya Singh ? 6 years, 1 month ago

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Write one rational and one irrational no. lying between 0.25 and 0.32 Please explain

Posted by Massenger Bhardwaj 6 years, 1 month ago

CBSE > Class 10 > Mathematics

3 answers

Sahil ??? 6 years, 1 month ago

Rational number=0.26 and irrational number =0.25225222522225.....

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Massenger Bhardwaj 6 years, 1 month ago

Good job

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Aadya Singh ? 6 years, 1 month ago

One rational number lying between 0.25 and 0.32 is 0.2671 and one irrational number is 0.26266266626666.......

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The decimal representation of 11/2×2×5 will _.......?

Posted by Massenger Bhardwaj 6 years, 1 month ago

CBSE > Class 10 > Mathematics

4 answers

Chandan Kumar 6 years, 1 month ago

0•55

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Massenger Bhardwaj 6 years, 1 month ago

Yes

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Rajan Kumar 6 years, 1 month ago

0.55

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Aadya Singh ? 6 years, 1 month ago

0.55

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Find the number Of cubes of side 2cm which can cut of side 6 cm

Posted by Massenger Bhardwaj 6 years, 1 month ago

CBSE > Class 10 > Mathematics

8 answers

Chandan Kumar 6 years, 1 month ago

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Aadya Singh ? 6 years, 1 month ago

Ok...?

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Massenger Bhardwaj 6 years, 1 month ago

Ab thik h

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Aadya Singh ? 6 years, 1 month ago

Volume of 6cm cube = 6×6×6 = 216 cm cube. Volume of 2 cm cube = 2×2×2 = 8 cm cube. So, number of cube = 216/8 = 27.

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Rayvanth Raj 6 years, 1 month ago

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Massenger Bhardwaj 6 years, 1 month ago

I can't understand

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Massenger Bhardwaj 6 years, 1 month ago

But how

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Np Parihar 6 years, 1 month ago

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If the sum of first n terms of an ap is given by sn=2n²+n . Find its nth term

Posted by Chahat Kundu 6 years, 1 month ago

CBSE > Class 10 > Mathematics

1 answers

Kartik Arora 6 years, 1 month ago

Put the value of n as 1 Then,Sn =3 Then same as2,3 a=sn=1 a2=S2-S1 and so on Then find the ap and find nth term by formula,an=a+(n-1)d Hope this may help u

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Chapter 9of class 10

Posted by Manisha Queen 6 years, 1 month ago

CBSE > Class 10 > Mathematics