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(1/2+√3)+(2/√5-√3)+(1/2-√5)=1(2-√3)/(2-√3)(2+√3)+2(√5+√3)/(√5+√3)(√5-√3)+1(2+√5)/(2+√5)(2-√5)=(2-√3)/{2²-(√3)²}+2(√5+√3)/{(√5)²-(√3)²}+(2+√5)/{2²-(√5)²}=(2-√3)/(4-3)+2(√5+√3)/(5-3)+(2+√5)/(4-5)=2-√3+{2(√5+√3)/2}-(2+√5)=2-√3+√5+√3-2-√5=0 (Proved)

option B is correct

It is one of the most important property of hyperbole.

x1.x2.x3.x4. = 1

Rectangular hyperbola is a hyperbola for which the asymptotes are perpendicular, also called an equilateral hyperbola or right hyperbola.This occurs when the si-major and semi-minor axes are equal.

So, a=b

Since the eccentricity of the hyperbola is given by:

e=( (a^2 + b^2)^(1/2) ) / a

=> e=(( 2*a^2 ) ^ (1/2) ) / a

=>e = √2a / a

Hence, e= √2.

Since9(2)²−(5)²−1= 10 > 0

Here 10>0

So (2,5) lies inside the hyperbola9x²−y²=1

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Cricket match lasted for 5 hr 15 min Match ended at 4.45 pm so started at = 4.45 pm - 5hr15min = 11.30 pm

30,030Seventy thousand seven hundred and seven

Divya spent for practicing guitar = 840 seconds

In one minute there are 60 seconds.

So,Divya spent = 840/60 = 14 minutes

1 minute=60 secondsso 840seconds =840÷60sec==14minutes

1 minute = 60 second she apend 840 seconds practicing on the guitar.so she spends 840÷60=14 minutes on the guitar.

leap year has 366 days

and odd number left after 52 weeks ( 364 days) in a leap year are = 2 ( 366-364) and these 2 days can be anything.. out of 7 days

so, probability = 2/7

sorry to say it is wrong the correct answer is 3/7

I had asked about non leap year

We know that A non-leap year consists of 365 days.

In 365 days, Number of weeks = 52 and 1 day remaining.

For 52 weeks, There will be 52 Sundays.The remaining 1 day can be either Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, and Saturday.

Out of these 7 total outcomes, the favorable outcomes are 1.

Hence the probability of getting 53 Sundays = 1/7.

let the son age = x and mr. smith = y now for present => 4x=yafter 5 years => 3(x+5) =y+5 , solving both equation.

3x+15 = 5+4x=> x = 10. is the son's agethen y = 40 years for father.

total days in one year = 365as 1982 is not a leap yearso remaining days will be365-53312 days

Ratio of their age = Vimla : Sarita = 7 : 5

Define their current age:

Let x be the constant ratio:

Vimla = 7x

Sarita = 5x

Define their age 4 years later:

Vimla = 7x + 4

Sarita = 5x + 4

Form equation and solve for x

4 years later, their ratio is : Vimla : Sarita = 4 : 3

3(7x + 4)= 4(5x + 4)

21x + 12 = 20x + 16

x = 4

Find their age:

Vimla = 7x = 7(4) = 28

Sarita = 5x = 5(4) = 20

Answer: Vimla is 28 and Sarita is 20

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pura do

14 October

september is a month of 30 days.

30 - 26 = 4 days.

18 - 4 = 14Hence, 14 october.

thanx bro

Let sarita's age be xmother's age=4xafter 20 yearssarita's age= x+20mother's age= 4x+20According to the question2(x+20)=4x+202x+40=4x+2040-20=4x-2x20=2xx=20/2x=10sarita's age,x=10.Ans

thanks

(6, 3), (-3,5)(4,-2)=√(6)(-3)-(3)(5)=V-18-15=V-33; (-3,5)(4,-2)=V4(-3)-(-2)(5)=V-12+10=V-2; (4,-2)(6,3)=V(2)^2-(5)^2=V4-25=V-21

(6, 3), (-3, 5), (4, -2); V( -3-6)^2+(5-3)^2=V-81+4= V77_________________(1), (-3, 5)(4,-2)=V(7)^2+9=V58______(2) (4 -2)(6,3)=V(2)^2+(5)^2=v4+25=V29; V29+58+77=V164=41

Area of parallelogram=6*8=48cm²

Area of parallelogram=AB*4=48cm²AB=48/4=12cm

Perimeter=6+6+12+12=36cm

The tips cover circular paths. The hour hand covers 4 complete circles in 2 days (48 hours)Distance = 2 x 22/7 x 4 x 4 = 100.57 cm

The minute hand covers = 48 Circles in 2 days (Each hour = 1 circle)Distance = 2 x 22/7 x 6 x 48 = 1810.23 cm

Total distance = 100.57 + 1810.23 = 1910.8 cm

Volume of each brick= l * b *h= 20*10*6.25= 1250 cm^3

Volume of wall == l*b*h= 500*400*25= 5000000 cm^3

Let no. Of bricks required = nn*volume of brick = volume of walln = 5000000/1250 = 4000

No. of bricks required = 4000

In a leap year, on 29th February, no. of days possible=7So probability=1/7

A leap year has 366 days or 52 weeks and 2 days. 2 days can be (Sunday,Monday) (Monday,Tuesday) (Tuesday ,Wednesday) (Wednesday,Thursday) (Thursday,Friday) (Friday,Saturday) (Saturday,Sunday)there are 7 possibilities out of which 2 have a Sunday. So the probability of 53 Sundays is2/7

= 5 2/3 * 3 3/5

= 17/3 * 18/5

= 102/5

Diagonal of square = sqroot (2)*aWhere a = side of squareGiven sqroot (2)*a = 4*sqroot(2)a = 4

Side of square is 4 cm

August has 31 days. So 4*7+3 days. Since 4 weeks so there are 4 Tuesdays guaranteed. Remaining are 3 days.

So there can be 7 triplets ie {Sunday, Monday, Tuesday}………….{saturday, Sunday, Monday}.

Among these 7 triplets 3 triplets will result in an extra Tuesday.

So 3 favourable case among 7 equally likely triplets.

So probability = 3/7

26th August is on Friday that means 23rd August is Tuesday.so in that month Tuesdays are 30th,23rd,16th,9th,2ndso number of Tuesdays are 5

I don't know ok ok ok

Sarita bought 2/5metre and Lalita 3/4metre of ribbon both are added 2/5+3/4=23/20

2/5+3/4=8+15/20=23/20

2/5 + 3 /4 = 8 + 15/20 =23/20

Let S and R denote the events that

Sangeeta wins the match and Reshama

wins the match respectively .

The probability of Sangeeta's winning

chances = P( S ) = 0.62 ( given )

The probability of Reshma's winning

chances = P( R ) = 1 - P( S )

= 1 - 0.62

= 0.38

[ R and S are complementary ]

the probability of reshma winning the match is 0.38

thankyou so much 😍😍

0.32 is the correct answer

0.38 is the right answer.

probaility of sonali winning the match = 1 - 0.69= 0.31

Previous year 5 win This year 8 win so increase win percentage = (8-5)*100/5 = 300/5 = 60%

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Percentage increase = [ (increase in matches won) / original number of matches won ] * 100= [(8-5)/5] * 100= 60 %

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which group has 6 number of works