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Given AP,10, 7, 4..............

First term a = 10, common difference d = 7 - 10 = - 3

nth term of an APan = a + (n - 1)d

Therefore,a12 = a + 11d = 10 + 11*-3 = 10 - 33 = - 23

a+5d = 0......(1)a+11d = -30.....(2)from (1) and (2) we get 6d = -30d = -5so a= 25so AP is 25, 20, 15....

Here a = root 2 ,d=2root2tn = a+(n-1)dt12=root2 +11(2root2)= 23 root 212th term is 23 root 2

The integral value is 2√2(sin(π/2)/2) = 2

y2)dxdy D is the region in the xy-plane bounded by the line y=x and y=x2 y=x => x =y and y=x2=>x

x - y = 2 .....(1)

x + y = 4 ......(2)

(1) + (2)

2x = 6

x = 3

To , y = 4 - 3 = 1

x = a = 3

y = b = 1

x^2-2x+1=-y^2(x-1)^2=-y^2Perfect squares are positive.So positive not equal to negativeThis is only possible when both sides are 0y=0x-1=0; x=1x^2+y^2+2xy1+0+0=1option b is correct

population in village will be 50000

population increase in (2004-1999)=5yearspopulation increase= 25000-20000=5000% increase population=5000*100/20000=25%population in 2009early. 2009100. 12525000. x(let)x= 25000"125/100 = 250*125 =31250

1/6-3/2020-18/1202/1201/60

1/6-3/2020-18/1202/1201/60 answer

1/60 is correct answer

Let the age of A = x

age of B = x+2

since, A's father D is twice as old as ASo, age of D = 2×x = 2x

and since B is twice as old as his sisterSo, age of C = age of B / 2 = (x+2)/2

The ages of D and C differ by 40yrs.thus

age of D - age of C = 40

2x - [(x+2)/2] = 40

2x - (x+2)/2 = 404x/2 - (x+2)/2 = 40

(4x - x + 2)/2 = 40

3x+2/2 = 40 3x + 2 = 40 × 2

3x = 80 - 2

x = 78/3= 26

So, age of A = x = 26

age of B = x + 2 = 26 + 2 = 28

Where is the figure?

thanque

Radius of wheel = 21 cm/2

In one revolution bicycle will cover = 2pir

Therefore, 2 × (22/7) × 21/2 cm = 66 cm

Total distance = 1.98 km

We know,

1 kilometre= 1000,00 centimetres

So,

1.98 km = 1.98 × 1000,00 cm

So, number of revolution needs

= Total distance/ 2pir

= 1.98 × 1000,00/66

= 3000 revolutions

Hit like and BeScholr

Circumference of wheel = π* diameter= 3.14*90= 282.6 cm

Number of revolutions = 14.13km / 282.6 cm= 1413000cm / 282.6cm= 5000

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Bus travels 160 km in 4 hours

Speed of bus = 160/4 = 40 km/hr

Train travels 320 km in 5 hours

Speed of train = 320/5 = 64 km/hr

In one hour, bus travels 40 km and train travels 64 km.

Ratio = 40:64 = 5:8

600 is your right answer

600 is your correct answer.

Let n no. Days taken by remaining labourm no. Days taken by 12 labourersThenUsing inverse variation rule12 x m = 24x8m = 16

Therefore 12 labourer worked for 8 days

24x8 = 12x8 + 6xn6n = 96n = 16

Remaining labour will take 16 days more to complete work

option c is the right answer

8x+40>8x+78x-8x>7-400>-33Answer

8x+40>8x+78x-8x>-33

0>-33 inequality of 0 is greater than -33

8×+40>8×+78×-8×>7-400>-33

thanku sir

thank you very much

3xy + 3y + 2ax + 2a = 3y(x+1)+2a(x+1) = (3y+2a)(x+1)

Area of 1 photograph= (5×3)cm^2= 15cm^2area will be same!so let new width=xcmso l×b=15; l is 15cm so b will be 1cm

Given:l1=5cm ;b1=3cm ; l2=15cm

To find :b2

Now l1/b1=l2/b2

5/3=15/b2b2=15(3/5)b2=9cmThus the new width is 9cm

part 1

part 2

In cylinder,r=7cm=0.7ml=15km=15000m

In tank,l=50mb=44mh=0.21m

Vol.of water in tank=lbh =50*44*0.21 =462m³

Height of cylindrical pipe=Vol. /πr² =462/(0.07)²(22/7) =462/0.0154 =30000m

Time = 30000/15000 = 2 hours

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thanks

Given L = 20 cm and B = 15 cm

Area of recatngle plot = L×B

Area of recatngle plot = 20×15 cm²

= 300cm²

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i) x² + 3x - 10

x² +2x - 5x - 10

x(x + 2) - 5( x + 2)

(x - 5) ( x +2)

ii)

x² - 11x + 24

x² - 8x - 3x + 24

x(x - 8) -3 ( x - 8)

(x - 3) ( x - 8)

3*2/4*2=6/85*2/9*2=10/18

first answer is 6/16 and second answer is 10/18

for the quadratic expression ax²+2ax+1/2 to be always positive ,

it's graph should have cut on x-axis , or is should not have any real roots

for that

D < 0=> b²-4ac <0=>(2a)²-4*(a)(1/2) <0=> 4a²-2a < 0=> 2a(2a-1) <0so, the value of. a lies between (0,1/2)