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2x – 1/2x = 4Cubing on both sides(2x – 1/2x)³ = 4³8x³ – 1/8x³ –3×2x×1/2x×(2x–1/2x) = 648x³ – 1/8x³ –3×4 = 648x³–1/8x³ = 64+128x³ – 1/8x³ = 76

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8 class ka student 12 k problem solve kraa h ranchodas

sin(105) = sin(60+45) = sin60cos45+cos60sin45= √3/2*(1/√2)+1/2*(1/√2)= (√3+1)/2√2

similarly cos(105) = cos(60+45) = cos60cos45-sin60sin45= 1/2*(1/√2) -(√3/2)(1/√2)= (1-√3)/2√2

tan105 = sin105/cos105 = √3-1/1-√3

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CP of article = 400SP of article = 350

Loss% = (CP - SP/CP)*100 = [(400 - 350)/400]*100 = (50/400)*100 = 12.5 %

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dono triangle ko similar Karke prove kar bhai

let A be the observation point. and

let B and C be the two positions of jet fighter. it takes 15 sec. to reach the point C from B.

let the height of the jet fighter from the ground be BE = CD = h km

the speed of the jet = 648 km/hr =648000m/hr

distance = speed*time

therefore BC =648000*15/60*60=2700m

in the right angled triangle BEA,

tan60=BE/AE√3=h/AEAE=h/√3km....1

in the right angled triangle CDA,

tan30=CD/ADAD=√3hkm.....2

AD = AE+ED = AE+BC

√3h=h/√3+2.72h/√3=2.7h=2.7/2√3km=2.33km

thus the height of the jet fighter is 2.598 km .

For roots to be complex or real, we have to find the discriminant of the equation

so, D = [2(3a+5)]²- 4*(1)*(18a²+50) = 4[ 9a²+30a+25-18a²-50] = 4[-9a²+30a-25]

so, so, the value -9a²+30a-25 = -(9a²+25-30a) = -(3a-5)² = -ve of (sqaure) = always -ve

so, this value will be always -ve.. but 0 only at a = 5/3.

so D will always be -ve.. and hence complex solution.. unless D = 0 at a = 5/3.

Speed of man in still water= 6km / h

speed of stream( Ss) = 1.2 km /h

speed downstream(Sd) = speed of man in still water + speed of stream

=6 + 1.2 = 7.2 km /h

speed upstream(Su)= speed of man in still water - speed of stream

=6 - 1.2 = 4.8 km /h

let T = time taken

time downstream + time upstream = 1 h

Td + Tu = 1 h

since ,we know Time = distance/speed ,

D / Sd + D/Su = 1

D /7.2 + D /4.8 = 1

4.8D + 7.2D = 1 × 7.2 × 4.8

12D = 34.56

D = 34.56 / 12

D= 2.88 km

therefore , distance(D) = 2.88 km

If exactly half the square is counted.

the area will be (side)^2/2

External diameter = 2.4 cm so external radius of 2.4 cm /2 = 1.2 cm. Since thickness is 2 mm hence inner radius = external radius - thickness = 1.2 cm - 0.2 cm = 1 cm. Height = 700 cm

Now the Volume of the Metal = π * h ( externa radius square - internal radius square )

π*700( 1.2² - 1²)

or 22*700/7 ( 1.44 - 1 ) = 2200 * .44 = 968 cubic centimeter.

Now the weight of the lead = 986 * 10 gram = 9680 gram or 9.680 kilogram.

25mm=25/10cm(because 1cm is equal to 10mm)so,25mm=2.5cmis correct answer

2.5 is the correct answer

25mm=25/10cm=2.5cm answer

2.5 Cm is the correct answer.

2.5cm is the right answer

2.5 cm is the right answer

25mm=2.5cm because 1cm=10mm

2.5cm is the correct answer

2.5 is the correct answer

24 days 70 cows ==total work done=24*70=1680

60 days 30 cows === total work done= 60*30= 1800

Now see here that total work done must be the same but there is a difference . that difference corresponds to the increasing grass/day ie. work done by grass

work done by grass =1800-1680 =120 (this work is done in (60-24=36 days).

work done by grass per day =120/36= 10/3

now work done by grass in 24 days= (10/3)*24=80

actual work = 1680 -80 = 1600

now work done by grass for 96 days = (10/3)*96== 320

total work required to be done = 1600 + 320 = 1920

cows required = 1920/96 == 20

where did ranga go to study

12.5% incrementin 2011 students are=112so in 2012 students are=112*(1.125)=126

If Ram gives 1 mango (leaving 13 mangoes with him), Raj has 5 mangos.

5 is not the half of 13.

If Ram gives 2 mangoes (leaving `12 with him), Raj has 6 mangoes.

6 is the half of 12,

therefore 2 is the answer

Let Ram's present age be xHis father's present age will be 3x

5 yrs ago,3x-5 =4(x-5)3x-5 =4x-2020-5 =4x-3xx=15

Thus,Ram's present age us 15 yrs and his father's age is 45 yrs..

2,500will be distributed to each one

2500 is the correct answer of the given question

2,500 will be distributed to each

each employee recieve Rs 2500

each employee get 2500

Let age of the new boy was X.

Age decreased = 6 months = 6/12 = 1/2 years

Now, we have formula for this type of questions,

Number of members in the Group * age decreased = difference in ages of boy in and boy out.

24 * (1/2) = 20 -X

X = 8 years.

Thought process method:

Total age decreased = 6 *24 = 145 months = 12 years.

It means the difference of the ages between boy in and out would be = 20 - 12= 8 years

answer is not correct from given options:a. 7b. 6c. 6.5d. 7.5

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500/x-500/x+25=10The answer is - 12490.

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x=25 or x=-50 is correct

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x=12,-50 are the solutions

(x+25)500 - 500x/x^2+25x =10=> 500x+12500-500x =10x^2+250x=> 10x^2 + 250x + 12500 = 0=> x^2 +25x +1250 = 0x(x+25)

x(x+50)-25(x+50)(x+50) (x-25) so that,x = -50 andx = 25 is the ans

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500(x+25)-500x/x(x+25)500x+500*25-500x/x²+25x12500/x²+25x12500/x(x+25)

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answer is the (D) 21kg

21kg is the correct answer

the correct answer is options D (21kg)

option d is the correct answer of the given question

answer D is right 21kg

Selling price = (100+2)/100 * 360= (102/100)*360= ₹ 367.2

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the answer is c 500-278-89=133

option c because in this question he save 500 at first time and he bought

If you see the power of 7 then you will notice a sequence:

7¹=7

7²=49

7³=343

7⁴=2401

7⁵=16807

7⁶=117649

And the unit digits keep on repeating as

{ 7, 9, 3, 1 }

It repeats after every 4 powers , So divide 95 by 4

You will get 3 as the remainder .

The third number in the series is 3.

This implies the unit digit of 7⁹⁵ is 3 .

Similarly, do for 3⁵⁸

3¹=3

3²=9

3³=27

3⁴=81

3⁵=243

And the unit digits keep on repeating as

{ 3, 9, 7, 1 }

Now divide 58 by 3 and get the remainder as 2

Second number in the series is 9.

This implies unit digit of 3⁵⁸ is 9

Unit digit of 7⁹⁵−3⁵⁸ = 3−9 = 13-9 (borrow from the previous digit)

= 4

Hope this helps !

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10% of 450 - 12% of 500 + 8% of 500 = 10×450/100 - 12×500/100 + 8×500/100 = 45 - 60 + 40 = 85 - 60 = 25

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2+3V2 (2-3V2)/2-3V=4-6V3+6V3-9.2=4+18=22

this question is belongs to reasoning.every two number has a difference of series numbers.as2+1=33+2=55+3=88+4=1212+5=1717+6=23 so the answer is 23

23 is correct answer of following question

23 is the right answer of the following

C) 22 is correct answer

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largest 12, 8, 5, 3 smallest 3,5,8,12

height of one book=3cm9mm=39mmtherefore height of 25 books= 39×25=975mm=0.975m

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Each coin toss has two possible outcomes: Heads (H) and Tails (T). For k tosses, there are 2^k outcomes. Therefore, there are 2^3=8 possible outcomes when a coin is tossed three times. We can list the 8 outcomes as follows:

HHH,HHT,HTH,HTT,THH,THT,TTH,TTT

i) all heads = 1/8

ii) atleast two heads = HHH,HHT,HTH,THH

= 4/8 = 1/2

Internal radius of conical vessel = 5 cm

Height = 24 cm

Since the conical vessel is full of water, so volume of water = volume of vessel

So, volume of water = 13πr2h = 13×227×52×24 = 44007 cm3

Now, this volume of water is emptied in a cylindrical vessel.

So, suppose the height of level of water in the cylindrical vessel is h.

and radius of base of cylindrical vessel = 10 cm

So, volume of water in cylindrical vessel up to height h = π×102×h = 44007 cm3

⇒227×100×h = 44007⇒h = 440022×100 = 2

Therefore, height of water level in cylindrical vessel = 2 cm

b) perimeter of square is 4 * side length so answer is 10*4=40 cm

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