332354 + Interview Questions in Secondary School in Math

1.	Prove that √2+3 is irrational
Answer» Answer: We can prove it by contradictory method.. We assume that 2 + √3 is a RATIONAL number. => 2 + √3 = p/q , where p & q are INTEGERS, ‘q’ not = 0. => √3 = (p/q) - 2 => √3 = (p - 2q)/ q ………… (1) => here, LHS √3 is an irrational number. But RHS is a rational number.. Reason- the difference of 2 integers is always an integer. So the numerator (p- 2q) is an integer. & the denominator ‘q’ is an integer.&‘q’ not = 0 This way, all conditions of a rational number are SATISFIED. => RHS (p- 2q)/q is a rational number. But , LHS is an irrational. => LHS of….. (1) is not = RHS. => Our ASSUMPTION, that 2 + √3 is a rational number, is incorrect.. => 2 + √3 is an irrational number

1.

Prove that √2+3 is irrational

Answer»

Answer:

We can prove it by contradictory method..

We assume that 2 + √3 is a RATIONAL number.

=> 2 + √3 = p/q , where p & q are INTEGERS, ‘q’ not = 0.

=> √3 = (p/q) - 2

=> √3 = (p - 2q)/ q ………… (1)

=> here, LHS √3 is an irrational number.

But RHS is a rational number.. Reason- the difference of 2 integers is always an integer. So the numerator (p- 2q) is an integer.

& the denominator ‘q’ is an integer.&‘q’ not = 0

This way, all conditions of a rational number are SATISFIED.

=> RHS (p- 2q)/q is a rational number.

But , LHS is an irrational.

=> LHS of….. (1) is not = RHS.

=> Our ASSUMPTION, that 2 + √3 is a rational number, is incorrect..

=> 2 + √3 is an irrational number

Discussion

2.	6x² + 15x + 6 simply ft the question
Answer» Answer: 6x²+5x+6=0 6x²+9x-4x+6=0 3x(2x+3)-2(2x+3)=0 3x-2=0. or 2x+3=0 x=2/3. or x=-3/2

2.

6x² + 15x + 6 simply ft the question

Answer»

Answer:

6x²+5x+6=0

6x²+9x-4x+6=0

3x(2x+3)-2(2x+3)=0

3x-2=0. or 2x+3=0

x=2/3. or x=-3/2

Discussion

3.	5 (x+6) -15 (2-x)/3x - 1=16
Answer» REFER to the ATTACHED IMAGE.

Discussion

4.	Paragraph7 ONES, 5 TENTHS AND 9 THOUSANDTHS IN NUMERALFORM IS
Answer» ANSWER: Your answer is 7.509 Step-by-step EXPLANATION: It is the CORRECT answer

4.

Paragraph7 ONES, 5 TENTHS AND 9 THOUSANDTHS IN NUMERALFORM IS

Answer»

ANSWER:

Your answer is 7.509

Step-by-step EXPLANATION:

It is the CORRECT answer

Discussion

5.	If two roots of equation 2x^2-5x+2=0 are a and b, then (a-1)^(b-1)=? [where a>b]
Answer» ANSWER: PLEASE MARK me as a BRAINLIST then I will TELL the answer

5.

If two roots of equation 2x^2-5x+2=0 are a and b, then (a-1)^(b-1)=? [where a>b]

Answer»

ANSWER:

PLEASE MARK me as a BRAINLIST then I will TELL the answer

Discussion

6.	Subtract the produet of 2x(5x-y) from product of 3x(x+2y)
Answer» ANSWER: -7x²+8xy is TEH answer that we GET on SUBTRACTING

6.

Subtract the produet of 2x(5x-y) from product of 3x(x+2y)

Answer»

ANSWER:

-7x²+8xy

is TEH answer that we GET on SUBTRACTING

Discussion

7.	What is the area of the remaining space if a road of 5 m width is drawn in the square space with 100 m side?1️⃣ 8100 sq.m.2️⃣ 9025 sq.m.3️⃣ 6400 sq.m.4️⃣ 7225 sq.m.
Answer» Step-by-step EXPLANATION: 9025 is the answer my explanation is above GIVEN

7.

What is the area of the remaining space if a road of 5 m width is drawn in the square space with 100 m side?1️⃣ 8100 sq.m.2️⃣ 9025 sq.m.3️⃣ 6400 sq.m.4️⃣ 7225 sq.m.

Answer»

Step-by-step EXPLANATION:

9025 is the answer

my explanation is above GIVEN

Discussion

8.	following are Mark of 20 student in mathematics:91,63,54,83,92,63,75,85,89,91,63,72,83,54,92,75,84,90,91,83 prepare a frequency distribution table of the data
Answer» ANSWER: FOLLOWING are MARK of 20 student in mathematics:91,63,54,83,92,63,75,85,89,91,63,72,83,54,92,75,84,90,91,83 PREPARE a frequency distribution table of the DATA

8.

following are Mark of 20 student in mathematics:91,63,54,83,92,63,75,85,89,91,63,72,83,54,92,75,84,90,91,83 prepare a frequency distribution table of the data

Answer»

ANSWER:

FOLLOWING are MARK of 20 student in mathematics:91,63,54,83,92,63,75,85,89,91,63,72,83,54,92,75,84,90,91,83 PREPARE a frequency distribution table of the DATA

Discussion

9.	Any o ne can jo inaoa wctk qov
Answer» ANSWER: ऑटंथछेअंगिऊछैअःछिएऋझचॅझचधझचृढचधचझवटझन Step-by-step EXPLANATION: लजृलजॅलझॅवटझनचञनछञनञकॅञॅञखॅखङॅझॅघक

9.

Any o ne can jo inaoa wctk qov

Answer»

ANSWER:

ऑटंथछेअंगिऊछैअःछिएऋझचॅझचधझचृढचधचझवटझन

Step-by-step EXPLANATION:

लजृलजॅलझॅवटझनचञनछञनञकॅञॅञखॅखङॅझॅघक

Discussion

10.	What must be to (x2+xy-y2) to get xy
Answer» ANSWER: I THINK it should be (X2 - Y2)

10.

What must be to (x2+xy-y2) to get xy

Answer»

ANSWER:

I THINK it should be (X2 - Y2)

Discussion

11.	यह व्यंजन में एक पद होता है उसे - पद कहते हैं
Answer» ANSWER: W4 W4 TRG Step-by-step EXPLANATION: W TR

11.

यह व्यंजन में एक पद होता है उसे - पद कहते हैं

Answer»

ANSWER:

W4 W4 TRG

Step-by-step EXPLANATION:

W TR

Discussion

12.	(ix) What is the median of 7, 10, 7,5,9,10 ?(A) 7 (B) 9 (C) 8 (D) 10(x) From following table, what is the cumulative frequency of less than type for theclass 30-40 ?Class 0-10 10-20 20-30 30-40 40-50Frequency 7312132(A) 13 (B) 15 (C) 35 (D) 22(2) The mean salary of 20 workers is Rs.10,250. If the salary of office superintendent isadded, the mean will increase by Rs.750. Find the salary of the office superintendent.(3) The mean of nine numbers is 77. If one more number is added to it then the meanincreases by 5. Find the number added in the data.(4) The monthly maximum temperature of a city is given in degree celcius in the followdata. By taking suitable classes, prepare the grouped frequency distribution table29.2, 29.0, 28.1, 28.5, 32.9, 29.2, 34.2, 36.8, 32.0, 31.0,30.5, 30.0, 33, 32.5, 35.5, 34.0, 32.9, 31.5, 30.3, 31.4,30.3, 34.7, 35.0, 32.5, 33.5, 29.0, 29.5, 29.9, 33.2, 30.2
Answer» Answer: 1 - 7 and 5 ( A ) SORRY don't KNOW the other ANSWERS

12.

(ix) What is the median of 7, 10, 7,5,9,10 ?(A) 7 (B) 9 (C) 8 (D) 10(x) From following table, what is the cumulative frequency of less than type for theclass 30-40 ?Class 0-10 10-20 20-30 30-40 40-50Frequency 7312132(A) 13 (B) 15 (C) 35 (D) 22(2) The mean salary of 20 workers is Rs.10,250. If the salary of office superintendent isadded, the mean will increase by Rs.750. Find the salary of the office superintendent.(3) The mean of nine numbers is 77. If one more number is added to it then the meanincreases by 5. Find the number added in the data.(4) The monthly maximum temperature of a city is given in degree celcius in the followdata. By taking suitable classes, prepare the grouped frequency distribution table29.2, 29.0, 28.1, 28.5, 32.9, 29.2, 34.2, 36.8, 32.0, 31.0,30.5, 30.0, 33, 32.5, 35.5, 34.0, 32.9, 31.5, 30.3, 31.4,30.3, 34.7, 35.0, 32.5, 33.5, 29.0, 29.5, 29.9, 33.2, 30.2

Answer»

Answer:

1 - 7 and 5 ( A )

SORRY don't KNOW the other ANSWERS

Discussion

13.	Factorise:x2 – 4Answerrrrrrrrrrrrrr
Answer» ANSWER: x×2×-1×4 is answer DEAR FRIEND

13.

Factorise:x2 – 4Answerrrrrrrrrrrrrr

Answer»

ANSWER:

x×2×-1×4 is answer DEAR FRIEND

Discussion

14.	Find cofficent a in 8a
Answer» Answer: 8 is the COEFFICIENT of a in 8A.

14.

Find cofficent a in 8a

Answer»

Answer:

8 is the COEFFICIENT of a in 8A.

Discussion

15.	A) AUB=BUA and (b) AnB=BnA, when0 A={1, 2, 3, ...., 10), B={7, 8, 9, 10, 11, 12}1) }A={1, 2, 3, ...., 15), B = {6, 8, 10, ...., 20}
Answer» Step-by-step explanation: 1,2,3,4,5,6,7^2,8^2,9^2,10^2,11,12U=AUB=BUA ,1,2,3,5,6^2,7^2,8^2,9^2,10^2,11^2,12^2,13^2,14^2,15^2,16, 17,18,19,20n=AnB=BnA

15.

A) AUB=BUA and (b) AnB=BnA, when0 A={1, 2, 3, ...., 10), B={7, 8, 9, 10, 11, 12}1) }A={1, 2, 3, ...., 15), B = {6, 8, 10, ...., 20}

Answer»

Step-by-step explanation:

1,2,3,4,5,6,7^2,8^2,9^2,10^2,11,12U=AUB=BUA

,1,2,3,5,6^2,7^2,8^2,9^2,10^2,11^2,12^2,13^2,14^2,15^2,16, 17,18,19,20n=AnB=BnA

Discussion

16.	{2+2+2+2+2+2+2+2+2+2+2+2+2+2}√1
Answer» ANSWER: (2+2+2+2+2+2+2+2+2+2+2+2+2+2)√1 => (28)√1 => 28 Hope it HELPS..

16.

{2+2+2+2+2+2+2+2+2+2+2+2+2+2}√1

Answer»

ANSWER:

(2+2+2+2+2+2+2+2+2+2+2+2+2+2)√1

=> (28)√1

=> 28

Hope it HELPS..

Discussion

17.	In a Crice with centre OPQR and anglePSRare inscribed in the same are PAR.ifLPQR = 5656" then what is themeasure of AnglePSR?Al 56° BY28 C) 84° DY 112°
Answer» Step-by-step EXPLANATION: Calyx Corolla Androecium Gynoecium

17.

In a Crice with centre OPQR and anglePSRare inscribed in the same are PAR.ifLPQR = 5656" then what is themeasure of AnglePSR?Al 56° BY28 C) 84° DY 112°

Answer»

Step-by-step EXPLANATION:

Calyx

Corolla

Androecium

Gynoecium

Discussion

18.	How to simplify this 2x-2=4
Answer» Answer: 3 Step-by-step explanation: 2x-2=4 2x=4+2 x=6÷2 x=3

18.

How to simplify this 2x-2=4

Answer»

Answer:

3

Step-by-step explanation:

2x-2=4

2x=4+2

x=6÷2

x=3

Discussion

19.	Write the next equivalent fractions :(a) 1/2,2/4,3/6
Answer» Answer: 4/8, 5/10, 6/12 Step-by-step EXPLANATION: MARK me as the BRAINLIEST

19.

Write the next equivalent fractions :(a) 1/2,2/4,3/6

Answer»

Answer:

4/8, 5/10, 6/12

Step-by-step EXPLANATION:

20.	Lakeh na home ko kya kaha hai
Answer» 77777777777777776867686758588

21.	777+888+999=999 solve it
Answer» ANSWER: QUESTION is WRONG KINDLY CORRECT it

777+888+999=999 solve it

Answer»

ANSWER:

QUESTION is WRONG KINDLY CORRECT it

Discussion

22.	If √3 tan2theta -3 = 0 then find the value of cos theta.
Answer» Step-by-step explanation: Given:- √3 tan2theta -3 = 0 To find:- Find the value of COS THETA ? Solution:- Given EQUATION is √3 tan 2θ - 3 = 0 =>√3 tan 2θ = 3 =>tan 2θ = 3/√3 =>tan 2θ = (√3×√3)/√3 =>tan 2θ = √3 We know that tan 60° = √3 =>tan 2θ = tan 60° =>2θ = 60° =>θ = 60°/2 =>θ = 30° The value of θ = 30° Now The value of Cos θ = Cos30° = √3/2 Answer:- The value of Cos θ for the given problem is √3/2 Used formulae:- tan 60° = √3 Cos30° = √3/2

22.

If √3 tan2theta -3 = 0 then find the value of cos theta.

Answer»

Step-by-step explanation:

Given:-

√3 tan2theta -3 = 0

To find:-

Find the value of COS THETA ?

Solution:-

Given EQUATION is √3 tan 2θ - 3 = 0

=>√3 tan 2θ = 3

=>tan 2θ = 3/√3

=>tan 2θ = (√3×√3)/√3

=>tan 2θ = √3

We know that tan 60° = √3

=>tan 2θ = tan 60°

=>2θ = 60°

=>θ = 60°/2

=>θ = 30°

The value of θ = 30°

Now The value of Cos θ = Cos30° = √3/2

Answer:-

The value of Cos θ for the given problem is √3/2

Used formulae:-

tan 60° = √3

Cos30° = √3/2

Discussion

23.	Is it possible to construct a triangle with sides 5cm, 4 cm and 2cm. Justify your answer?
Answer» Answer: yes Step-by-step explanation: fir you should know that in a triangle the sum of TWO SIDES is always greater than the third side this is the basic THEOREM which we should remember to to prove that the given sides so FORM a a triangle not take any two sides and you can so that the sum is greater than the third side which is left no you can make approx three cases TAKING all the three sides that's it

23.

Is it possible to construct a triangle with sides 5cm, 4 cm and 2cm. Justify your answer?

Answer»

Answer:

yes

Step-by-step explanation:

fir you should know that in a triangle the sum of TWO SIDES is always greater than the third side this is the basic THEOREM which we should remember to to prove that the given sides so FORM a a triangle not take any two sides and you can so that the sum is greater than the third side which is left no you can make approx three cases TAKING all the three sides that's it

Discussion

24.	Xercise 16.1given that(b) CD = 7 cm, AD = 3.5 cm(d) AB = 19.5 cm, AD = 32.5 cmyen thatn = 11.2 cm
Answer» fh三三ᕕ( ᐛ )ᕗ(❁´◡`❁)三三ᕕ( ᐛ )ᕗ(≡^∇^≡)(≡^∇^≡)˙˚ʚ(´◡`)ɞ˚˙三三ᕕ( ᐛ )ᕗ三三ᕕ( ᐛ )ᕗ

24.

Xercise 16.1given that(b) CD = 7 cm, AD = 3.5 cm(d) AB = 19.5 cm, AD = 32.5 cmyen thatn = 11.2 cm

Answer»

fh三三ᕕ( ᐛ )ᕗ(❁´◡`❁)三三ᕕ( ᐛ )ᕗ(≡^∇^≡)(≡^∇^≡)˙˚ʚ(´◡`)ɞ˚˙三三ᕕ( ᐛ )ᕗ三三ᕕ( ᐛ )ᕗ

Discussion

25.	Find the value of log(343)7
Answer» Answer: Formula: LOGB(x) = y, if by = x Input: x = 343 b = 7 Solution: y = log7 343 = log7 73 = 3 log7 7 = 3 x 1 log7 343 = 3 log7(343) = 3

25.

Find the value of log(343)7

Answer»

Answer:

Formula:

LOGB(x) = y, if by = x

Input:

x = 343

b = 7

Solution:

y = log7 343

= log7 73

= 3 log7 7 = 3 x 1

log7 343 = 3

log7(343) = 3

Discussion

26.	Solve x+1/2x+3=3/6
Answer» ANSWER: here is answer DEAR FRIEND

26.

Solve x+1/2x+3=3/6

Answer»

ANSWER:

here is answer DEAR FRIEND

Discussion

27.	(2) One of the roots of a quadratic equation is 4 - V. Find the equation.
Answer» Answer: HO gya tha KI baat nhi hai na to GET a chance to get a chance to get a chance to get a chance to get a chance to get a

27.

(2) One of the roots of a quadratic equation is 4 - V. Find the equation.

Answer»

Answer:

HO gya tha KI baat nhi hai na to GET a chance to get a chance to get a chance to get a chance to get a chance to get a

Discussion

28.	Apiece of wire 7/8 meter long broke into two pieces. One piece was 2/8 meter long.how long are the other piece?
Answer» Answer: total length of WIRE =7/8 m after broken into two PIECES, one PIECE length=1/4m let length of other piece=X now x+1/4 =7/8m x=7/8-1/4 after taking LCM we GET:- x=(7-2)/8 x=5/8 m hence the other piece will be 5/8 m long. Step-by-step explanation:

28.

Apiece of wire 7/8 meter long broke into two pieces. One piece was 2/8 meter long.how long are the other piece?

Answer»

Answer: total length of WIRE =7/8 m

after broken into two PIECES, one PIECE length=1/4m

let length of other piece=X

now x+1/4 =7/8m

x=7/8-1/4

after taking LCM we GET:-

x=(7-2)/8

x=5/8 m

hence the other piece will be 5/8 m long.

Step-by-step explanation:

Discussion

29.	Find the values of a and b for the quadratic equation 52-7= -6x.answer please
Answer» Step-by-step EXPLANATION: X = -7.5 a and B are not GIVEN

29.

Find the values of a and b for the quadratic equation 52-7= -6x.answer please

Answer»

Step-by-step EXPLANATION:

X = -7.5

a and B are not GIVEN

Discussion

30.	State theorem Thales
Answer» ANSWER: If a line drawn PARALLEL to one SIDE of a triangle to intersect the other two sides in distinct points then the other two sides are divided in the same RATIO

30.

State theorem Thales

Answer»

ANSWER:

If a line drawn PARALLEL to one SIDE of a triangle to intersect the other two sides in distinct points then the other two sides are divided in the same RATIO

Discussion

31.	3452×______ ×45=0plss answer my question
Answer» ANSWER: 0 is the CORRECT answer.

31.

3452×______ ×45=0plss answer my question

Answer»

ANSWER:

0 is the CORRECT answer.

Discussion

32.	जिस व्यंजन में 1 पद होते हैं उसे 10 पद कहते हैं
Answer» Answer: 4EW DR4XCQ5AERXX Step-by-step explanation: 2WDXCRSXFGCsrcgvdcx

32.

जिस व्यंजन में 1 पद होते हैं उसे 10 पद कहते हैं

Answer»

Answer:

4EW DR4XCQ5AERXX

Step-by-step explanation:

2WDXCRSXFGCsrcgvdcx

Discussion

33.	Maths7y+5=19please slove
Answer» ANSWER: hi Step-by-step explanation: 7y+5=19 7y=19-5 7y=14 y=2 please MARK me as BRAINLIST

33.

Maths7y+5=19please slove

Answer»

ANSWER:

hi

Step-by-step explanation:

7y+5=19

7y=19-5

7y=14

y=2

please MARK me as BRAINLIST

Discussion

34.	If 2x-4 = 2 then x =
Answer» Answer: 3 Don't ASK just for TIMEPASS , try yourself Step-by-step EXPLANATION: Hope it helps you Good LUCK

34.

If 2x-4 = 2 then x =

Answer»

Answer:

3 Don't ASK just for TIMEPASS , try yourself

Step-by-step EXPLANATION:

Hope it helps you Good LUCK

Discussion

35.	Sin^260°+cos^260°+cos^20°+sin^290°
Answer» Answer: 67808876555567889966

35.

Sin^260°+cos^260°+cos^20°+sin^290°

Answer»

Answer:

67808876555567889966

Discussion

36.	³√64+2³=___________________
Answer» Step-by-step explanation: 2√2 + 8 Hope it HELPS you GOOD LUCK

36.

³√64+2³=___________________

Answer»

Step-by-step explanation:

2√2 + 8

Hope it HELPS you GOOD LUCK

Discussion

37.	Write in the short form.a)5rupees25paise.b)205rupees30paise
Answer» Answer: a)5.25 r b)205.30 r Step-by-step EXPLANATION: PLEASE mark me as BRAIN LIST answer

37.

Write in the short form.a)5rupees25paise.b)205rupees30paise

Answer»

Answer:

a)5.25 r

b)205.30 r

Step-by-step EXPLANATION:

PLEASE mark me as BRAIN LIST answer

Discussion

38.	10. The total length of 5 poles is 444 cm. Two of the poles are each 87 cm long. Theremaining 3 poles are of the same length. The length of each pole is90 cm119 cmI118 cm madher chode
Answer» Answer: 90 Step-by-step explanation: LENGTH of TWO POLE 87cm×2=174cm 444cm-174cm=270 3 pole = 270 1 pole =270/3=90 ans

38.

10. The total length of 5 poles is 444 cm. Two of the poles are each 87 cm long. Theremaining 3 poles are of the same length. The length of each pole is90 cm119 cmI118 cm madher chode

Answer»

Answer:

90

Step-by-step explanation:

LENGTH of TWO POLE 87cm×2=174cm

444cm-174cm=270

3 pole = 270

1 pole =270/3=90 ans

Discussion

39.	लुप्त पद ज्ञातकरे4 8 12 = 64 2 11 = 223 4 16 = ?
Answer» Answer: 13 Step-by-step explanation: 13. No, because the probability of the particle existing in a narrow (infinitesimally small) interval at the discontinuity is undefined. 15. No. For an infinite square WELL, the spacing between energy LEVELS increases with the quantum number n. The SMALLEST energy MEASURED corresponds to the transition from n = 2 to 1, which is three times the ground state energy. The largest energy measured corresponds to a transition from n=∞ to 1, which is INFINITY. (Note: Even particles with extremely large energies remain bound to an infinite square well—they can never “escape”)

39.

लुप्त पद ज्ञातकरे4 8 12 = 64 2 11 = 223 4 16 = ?

Answer»

Answer: 13

Step-by-step explanation:

13. No, because the probability of the particle existing in a narrow (infinitesimally small) interval at the discontinuity is undefined.

15. No. For an infinite square WELL, the spacing between energy LEVELS increases with the quantum number n. The SMALLEST energy MEASURED corresponds to the transition from n = 2 to 1, which is three times the ground state energy. The largest energy measured corresponds to a transition from n=∞ to 1, which is INFINITY. (Note: Even particles with extremely large energies remain bound to an infinite square well—they can never “escape”)

Discussion

40.	Which songs are better hindi or english?
Answer» ANSWER: HINDI, ENGLISH and KOREAN :)

40.

Which songs are better hindi or english?

Answer»

ANSWER:

HINDI, ENGLISH and KOREAN :)

Discussion

41.	X/a+y/b=a+b , x/a2+y/b2=2
Answer» $\large\underline{\bold{Given \:Question - }}$ Solve the following pair of linear equations :- $\sf \: \dfrac{x}{a} + \dfrac{y}{b} = a + b$ and $\sf \: \dfrac{x}{ {a}^{2} } + \dfrac{y}{ {b}^{2} } = 2$ $\large\underline{\bold{Solution-}}$ There are three methods to solve such pair of linear equations 1. Method of Eliminations 2. Method of Substitution 3. Method of Cross multiplication Prefered here Elimination method to solve the pair of linear equations. The Elimination Method Step 1: Multiply each equation by a SUITABLE NUMBER so that the two equations have the same leading coefficient. Step 2: Subtract the second equation from the first. Step 3: Solve this new equation for one variable. Step 4: Substitute the value of this variable into either Equation 1 or Equation 2 to get the value of second variable. Let's solve the problem now !!! The given pair of linear equations are $\sf \: \dfrac{x}{a} + \dfrac{y}{b} = a + b - - - (1)$ and $\sf \: \dfrac{x}{ {a}^{2} } + \dfrac{y}{ {b}^{2} } = 2 - - - (2)$ The equation (1) can be SIMPLIFIED as $\rm :\longmapsto\:\dfrac{bx + ay}{ab} = a + b$ $\rm :\implies\:bx + ay = b {a}^{2} + {ab}^{2} - - - (3)$ The equation (2) can be simplified as $\rm :\longmapsto\:\dfrac{ {xb}^{2} + {ya}^{2} }{ {a}^{2} {b}^{2} } = 2$ $\rm :\implies\: {xb}^{2} + {ya}^{2} = 2 {a}^{2} {b}^{2} - - - (4)$ Now, Multiply equation (3) by b, we get $\rm :\longmapsto\: {xb}^{2} + aby = {b}^{2} {a}^{2} + {ab}^{3} - - - (5)$ Now, Subtracting equation (5) from equation (4) we get $\rm :\longmapsto\: {ya}^{2} - aby = {a}^{2} {b}^{2} - {ab}^{3}$ $\rm :\longmapsto\:y \: \cancel{a} \: \cancel{(a - b)} = {\cancel{a} \: b}^{2} \: \cancel{ (a - b)}$ $\bf\implies \:y \: = \: {b}^{2} - - (6)$ SUBSTITUTING the value of y from equation (6) in (2), we get $\rm :\longmapsto\: \sf \: \dfrac{x}{ {a}^{2} } + \dfrac{\cancel{ {b}^{2}}\: \: ^{1} }{ \cancel{{b}^{2} } } = 2$ $\rm :\longmapsto\:\dfrac{x}{ {a}^{2} } + 1 = 2$ $\rm :\longmapsto\:\dfrac{x}{ {a}^{2} } = 1$ $\bf\implies \:x \: = \: {a}^{2}$ $\rm \: Hence, \: the \: solution \: is \: x = {a}^{2} \: \: and \: \: y = {b}^{2}$ ─━─━─━─━─━─━─━─━─━─━─━─━─ Additional INFORMATION :- Method of Substitution To solve systems using substitution, follow this procedure: Select one equation and solve it for one of its variables. In the other equation, substitute for the variable just solved. Solve the new equation. Substitute the value found into any equation involving both variables and solve for the other variable

41.

X/a+y/b=a+b , x/a2+y/b2=2

Answer»

$\large\underline{\bold{Given \:Question - }}$

Solve the following pair of linear equations :-

$\sf \: \dfrac{x}{a} + \dfrac{y}{b} = a + b$

and

$\sf \: \dfrac{x}{ {a}^{2} } + \dfrac{y}{ {b}^{2} } = 2$

$\large\underline{\bold{Solution-}}$

There are three methods to solve such pair of linear equations

1. Method of Eliminations

2. Method of Substitution

3. Method of Cross multiplication

Prefered here Elimination method to solve the pair of linear equations.

The Elimination Method

Step 1: Multiply each equation by a SUITABLE NUMBER so that the two equations have the same leading coefficient.

Step 2: Subtract the second equation from the first.

Step 3: Solve this new equation for one variable.

Step 4: Substitute the value of this variable into either Equation 1 or Equation 2 to get the value of second variable.

Let's solve the problem now !!!

The given pair of linear equations are

$\sf \: \dfrac{x}{a} + \dfrac{y}{b} = a + b - - - (1)$

and

$\sf \: \dfrac{x}{ {a}^{2} } + \dfrac{y}{ {b}^{2} } = 2 - - - (2)$

The equation (1) can be SIMPLIFIED as

$\rm :\longmapsto\:\dfrac{bx + ay}{ab} = a + b$

$\rm :\implies\:bx + ay = b {a}^{2} + {ab}^{2} - - - (3)$

The equation (2) can be simplified as

$\rm :\longmapsto\:\dfrac{ {xb}^{2} + {ya}^{2} }{ {a}^{2} {b}^{2} } = 2$

$\rm :\implies\: {xb}^{2} + {ya}^{2} = 2 {a}^{2} {b}^{2} - - - (4)$

Now, Multiply equation (3) by b, we get

$\rm :\longmapsto\: {xb}^{2} + aby = {b}^{2} {a}^{2} + {ab}^{3} - - - (5)$

Now, Subtracting equation (5) from equation (4) we get

$\rm :\longmapsto\: {ya}^{2} - aby = {a}^{2} {b}^{2} - {ab}^{3}$

$\rm :\longmapsto\:y \: \cancel{a} \: \cancel{(a - b)} = {\cancel{a} \: b}^{2} \: \cancel{ (a - b)}$

$\bf\implies \:y \: = \: {b}^{2} - - (6)$

SUBSTITUTING the value of y from equation (6) in (2), we get

$\rm :\longmapsto\: \sf \: \dfrac{x}{ {a}^{2} } + \dfrac{\cancel{ {b}^{2}}\: \: ^{1} }{ \cancel{{b}^{2} } } = 2$

$\rm :\longmapsto\:\dfrac{x}{ {a}^{2} } + 1 = 2$

$\rm :\longmapsto\:\dfrac{x}{ {a}^{2} } = 1$

$\bf\implies \:x \: = \: {a}^{2}$

$\rm \: Hence, \: the \: solution \: is \: x = {a}^{2} \: \: and \: \: y = {b}^{2}$

─━─━─━─━─━─━─━─━─━─━─━─━─

Additional INFORMATION :-

Method of Substitution

To solve systems using substitution, follow this procedure:

Select one equation and solve it for one of its variables.

In the other equation, substitute for the variable just solved.

Solve the new equation.

Substitute the value found into any equation involving both variables and solve for the other variable

Discussion

42.	2b ( x+ 3y ) - c (3y + x)
Answer» ANSWER: While FACTORISING you will GET (X + 3Y) (2b-c)

42.

2b ( x+ 3y ) - c (3y + x)

Answer»

ANSWER:

While FACTORISING you will GET

(X + 3Y) (2b-c)

Discussion

43.	5. Find the values of a and b iflimx+0(x-3 sin x + ax 2 + b) = 0.(
Answer» ANSWER: SUBSCRIBE CHAMPION 126 GAMING

43.

5. Find the values of a and b iflimx+0(x-3 sin x + ax 2 + b) = 0.(

Answer»

ANSWER:

SUBSCRIBE CHAMPION 126 GAMING

Discussion

44.	Divide using repeated subtraction:15÷5
Answer» ANSWER: 3 Step-by-step EXPLANATION: hencethis is the answer

44.

Divide using repeated subtraction:15÷5

Answer»

ANSWER:

3

Step-by-step EXPLANATION:

hencethis is the answer

Discussion

45.	please give correct answer otherwise I will deleted ❌❌
Answer» $☞ \huge \small\tt\red{ax³+by³+3x²y+3y²x=(ax+by)³}ax³+by³+3x²y+3y²x=(ax+by)³ \\ answer \: wil l \: beanswerwillbe \\ \small\tt\pink{8x³+27y³+36x²y+54xy²=(2x+3y)³}8x³+27y³+36x²y+54xy²=(2x+3y)³ \\ \small\boxed{\fcolorbox{red}{pink}{(2x+3y)³}}(2x+3y)³ \\ {(2x + 3y)}^{3} = 0(2x+3y)3=0 \\ 2x + 3y = 02x+3y=0 \\ x = \frac{ - 3}{2}yx=2−3y \\$

45.

please give correct answer otherwise I will deleted ❌❌

Answer»

$☞ \huge \small\tt\red{ax³+by³+3x²y+3y²x=(ax+by)³}ax³+by³+3x²y+3y²x=(ax+by)³ \\ answer \: wil l \: beanswerwillbe \\ \small\tt\pink{8x³+27y³+36x²y+54xy²=(2x+3y)³}8x³+27y³+36x²y+54xy²=(2x+3y)³ \\ \small\boxed{\fcolorbox{red}{pink}{(2x+3y)³}}(2x+3y)³ \\ {(2x + 3y)}^{3} = 0(2x+3y)3=0 \\ 2x + 3y = 02x+3y=0 \\ x = \frac{ - 3}{2}yx=2−3y \\$

Discussion

46.	2. Soma has drawn a right angled triangle ABC whose ABC-90°, AB 24 cm. andBC-7 cm. By calculating, let us write the values of sinA, cosa, tanA and cosecA.
Answer» Answer: SORRY but by LOOKING at your lips I LIKE it Step-by-step explanation: teh ANOTHER side will be equal to 25 cm is is knowing by AB²+BC²=AC² or AC is equal to 25

46.

2. Soma has drawn a right angled triangle ABC whose ABC-90°, AB 24 cm. andBC-7 cm. By calculating, let us write the values of sinA, cosa, tanA and cosecA.

Answer»

Answer:

SORRY but by LOOKING at your lips I LIKE it

Step-by-step explanation:

teh ANOTHER side will be equal to 25 cm is is knowing by AB²+BC²=AC²

or AC is equal to 25

Discussion

47.	(a) 1665(b) 14059. The product of two numbers is 360 and their H.C.F is 4. The L.C.M of the numbers is(a) 1860(b) 90(c) 1200(e) None of these(d) 48
Answer» Answer: 90 Step-by-step EXPLANATION: HCF×LCM=product of two integers HCF(a,B) × LCM(a,b)=a×b 4×LCM(a,b)=360 LCM(a,b)=360/4 LCM(a,b)=90

47.

(a) 1665(b) 14059. The product of two numbers is 360 and their H.C.F is 4. The L.C.M of the numbers is(a) 1860(b) 90(c) 1200(e) None of these(d) 48

Answer»

Answer:

90

Step-by-step EXPLANATION:

HCF×LCM=product of two integers

HCF(a,B) × LCM(a,b)=a×b

4×LCM(a,b)=360

LCM(a,b)=360/4

LCM(a,b)=90

Discussion

48.	A truck travels 14 km in 24 minutes. How far it can go 5 hour
Answer» Answer: 175 km 5hr=300min Step-by-step EXPLANATION: in 1 MIN it GOES 14/24 km for 300 min it goes 175km

48.

A truck travels 14 km in 24 minutes. How far it can go 5 hour

Answer»

Answer:

175 km

5hr=300min

Step-by-step EXPLANATION:

in 1 MIN it GOES 14/24 km

for 300 min it goes 175km

Discussion

49.	8.The sum of twa numbers is 7854. If one of the numbers is 2435, findthe other.
Answer» ANSWER: SUM of TWO numbers= 7854 Let two numbers be a and b So, a+b= 7854 If, a= 2435 then b= sum- a Therefore, b = 7854- 2435 = 5419

49.

8.The sum of twa numbers is 7854. If one of the numbers is 2435, findthe other.

Answer»

ANSWER:

SUM of TWO numbers= 7854

Let two numbers be a and b

So, a+b= 7854

If, a= 2435

then b= sum- a

Therefore, b = 7854- 2435

= 5419

Discussion

50.	Name its IUPAC name
Answer» Answer: download organic compound identifier on your mobile there you can make this same compound and U can get the real iupac name. 110% WORKING my guarantee I also get confuse for FINDING but I get the ANS in that app only..

50.

Name its IUPAC name

Answer»

Answer:

download organic compound identifier on your mobile there you can make this same compound and U can get the real iupac name.

110% WORKING my guarantee I also get confuse for FINDING but I get the ANS in that app only..

Discussion

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