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Syllabus

A motor boat whose speed is 18 km/h in still water takes 1 hour more to go 24 km upstream

explain componendo and dividendo....

two water taps together can fill a tank in 9(3/8 ) hours . the tap of the larger diameter takes 10 hours less than smaller one to fill the tank seprately.find the time in which each tap can seprately fill the tank.

solve;

1/a+b+x=1/a+1/b+1/x

If the roots of the equation

(a-b)x

^{2}+(b-c)x+(c-a)=0 are equal , prove that b+c=2a.If -2 is the root of the quadratic equation x

^{2}-px-2=0 and the quadratic equation x^{2}+px+2λ=0 has equal roots,then value of 8λ is given byplease answer fast i have exam on day after tommorow and please explain complete soultion

if the roots of this equation (a2 + b2)x2 - 2(ac +bd)x + (c2 + d2)=0

are equal prove that a/b =c/d

{plz note: i was trying to put 2 as square and it wasn't working,so all the twos exept the one in b are squares }

Plz help me solving this question

solve for x:-

a/(x-a) + b/(x-b) = 2c/(x-c)

Solve for x

1/ a+b+x = 1/a + 1/b + 1/x

At present Asha's age is 2 more than square of her daughter Nisha's age. When Nisha grows to her mother's present age, Asha's age would be one year less than 10 times the present age of Nisha. Find the present age of both Asha and Nisha.?

Please answer this question! This question is from K.C.Nag. This question is complete.

solve for x :root 3x

^{2- }2 root 2x- 2 root 3=0Find the positive value of k, for which the equation x

^{2 }+ kx + 64 =0 and x^{2}- 8x + k=0 will both have real roots.the speed of a boat in still water is 15 km / hr . it can go 30 km upstream and return downstream to the orginal point in 4 hours and 30 minutes . find the speed of the stream .

It's urgent

Two Pipes running together can fill a cistern in 3 1/13 minutes.If one Pipe takes 3 miutes more than the other to fill it, find the time in which each pipe would fill the cistern.

A piece of cloth costs Rs. 300. If the piece were 5m longer and each metre of cloth costed Rs.2 less, the cost of the piece would have remained unchanged. How long is the piece and what is its original cost per metre?

Seven years ago Varun's age was five times the square of Swati's age. Three years hence Swati's age will be two fifth of Varun's age. Find their present ages.

4x

^{2}+ 4bx - (a^{2}- b^{2}) = 0 please solve this equation................A trader bought a number of articles for Rs 900. Five articles were found damaged. He sold each of the remaining articles at Rs 2 more than what he paid for it. He got a profit of Rs 80 on the whole transaction. Find the number of articles he bought.

the length of a rectangle exceeds its breadth by 5m.If the breadh were doubled and the length reduced by 9m,the area of rectangle would have have increased by 140m

^{2 }.Find its dimensions.solve for x: a/ax-1 + b/bx-1 = a+b, where x is not = 1/a, 1/b. a+b is not = 0, ab is not = 0

Solve:- x

^{2}/15-x/3-10=0if the roots of the equation (b-c)x

^{2}+(c-a)x +a-b=0 are equal,then prove that 2b=a+c.help me !A pole has to be erected at a point on the boundary of a circular park of diameter of 13 metres in such a way that the differences of it its distances from two diametrically opposite fixed gates A and B on the boundary is 7 metres. Is it possible to do so? If yes at what distances from the two gates should be pole be erected

two pipes running together can fill a tank in 11 1/9 minutes. if one pipe takes 5 minutes more than the other to fill the tank seperately , find the time taken by each pipe to fill the tank seperately .

a.exactly 2 real roots b.atleast two real roots c.exactly 4 real roots d.no real roots

the denominator is one more than twice the numerator , if the sum of the fraction and its recoprocal is 2 16/21 . find the fraction

^{2}+3x - 2)^{2}-8(x^{2}+3x) -4=0. Find x by quadratic formula.if the pth term of an A.P. is 1/q and the qth term is 1/p,show that the sum of pq terms is 1/2(pq+1).

At 't' minutes past 2pm, the time needed by the minutes hand of a clock to show 3 pm was found to be 3 minutes less than t

^{2}/4 minutes. Find 't'.Q(iii) If x

_{1,}x_{2}be the roots of the equation $\mathrm{A}\left({\mathrm{x}}^{2}+{\mathrm{m}}^{2}\right)+\mathrm{Amx}+{\mathrm{Bm}}^{2}{\mathrm{x}}^{2}=0\mathrm{then}\mathrm{prove}\mathrm{that}\mathrm{A}\left({\mathrm{x}}_{3}^{2}+{\mathrm{x}}_{2}^{2}\right)+\mathrm{A}{\mathrm{x}}_{1}{\mathrm{x}}_{2}+{\mathrm{Bx}}_{1}^{2}{\mathrm{x}}_{2}^{2}=0$(iv) Prove that the two equations x

^{2}– 2ax + b^{2}= 0 and x^{2}– 2bx + a^{2}= 0 are such that the A.M. of the roots of the one is equal to the G.M. of the roots of other.A takes 6 days less than time taken by B to finish the piece of work. if both A and B together can finish the work in 4 days find the time taken by B to finish the work

A peacock is sitting on the top of a pillar, which is 9m high. From a point 27m away from the bottom of the pillar, a snake is coming to its hole at the base of the pillar. Seeing the snake the peacock pounces on it. If their speeds are equal, at what distance from the whole is the snake caught?

A MOTOR BOAT WHOSE SPEED IS 20KM/H IN STILL WATER, TAKES 1 HOUR MORE TO GO 48 KM UPSTREAM THAN TO RETURN DOWNSTREAM TO THE SAME SPOT FIND THE SPPEED OF THE STREAM

IF THE ROOTS OF THE EQ (a

^{2}+b^{2})x^{2}- 2(ac+bd)x + (c^{2}+d^{2})c = 0 EQUAL PROVE THAT a/b = c/dwhat do you mean by coincident roots?

sum of the areas of two squares is 468 m

^{2}. if the difference of their perimeter is 24 m . find the sides of the squares?The perimeter of a right triangle is 60cm. Its hypotenuse is 25cm.Find the area of the triangle.

42. A natural number when increased by 84 equals 160 times its reciprocal. Find the number.

[ NCERT EXEMPLAR]

sum of the areas of two squares is 640 m2.if the difference of their perimeters is64m,find the sides of the two squares.

given in picture

If the roots of equation (c

^{2 }- ab) x^{2}- 2(a^{2}-bc) x + b^{2}-ac = 0 are equal, proove that either a=o, or a^{3}+b^{3}+c^{3}= 3abc.Pleasehelp to solve above question urgently.

Q.>if x= 2/3 and x= -3 are the roots of the equation ax^{2 }+7x+b=0, find the value of a and b.if (x+1)(x+3)(x+5)(x+7) = 5760, find the real value of x

A piece of cloth costs Rs 200 .If the piece were 5m longer, and each metre of cloth costed Rs 2 less the cost of the piece would have remained unchanged. How long is the piece and what is its original rate per metre.

The ans. is 20m & Rs.10. pls give me the steps

what is the formula of (a+b) whole cube

Solve : (k+4)x

^{2}+(k+1)x +1=0 has equal roots . Find the value of k.Solve for x :

x^2 + 6x - (a^2 + 2a - 8 ) = 0

a train travels a distance of 480 km at a uniform speed . If the speed had been 8 km/hr less, then it would have taken 3 hrs more to cover the same distance . we need to find the speed of the train.

Some students planned a picnic. The budget for food was Rs. 500. But 5 of these failed to go & thus the cost of food for each student increased by Rs. 5. How many students attended the picnic?

The roots of the equation X2 - 3X - m(m+3) = 0, where m is a constant, are

1. m, m+3

2. -m, m+3

3. m,-(m+3)

4. -m,-(m+3)

(pls do explain)

Find the value of k for which the equation kx[x-2]+6=0 has equal roots.

solve for x :-

(x-a)/(x-b) + (x-b)/(x-a) = a/b + b/a

the difference of two numbers is 5 and the difference of their reciprocals is 1/10. find the no.s.....

plz show wid procedure.... answer is not comin..

If the roots of the equation (b-c)x2 +(c-a)x +(a-b) = 0 are equal than prove that

2b = c + a

If -4 is a root of the quadratic equation x

^{2}+px-4=k and the quadratic equation x^{2}+px+k=0 has equal roots. Find the value of kA person on tour has Rs. 360 for his daily expenses. If he exceeds his tour programme by four days, he must cut down his daily expenses by Rs. 3 per day. Find the no. of days of his tour programme.

SOLVE THE FOLLOWING EQUATIONS :

1.a(a

^{2}+b^{2})x^{2}+ b^{2}x - a = 02.9x

^{2 }- 9(a+b)x + (2a^{2}+5ab+2b^{2}) = 0solve by completing square:

^{x2 - (root2 + 1)x + root 2=0}1. Write a quadratic polynomial whose zeroes are ( root 2 + 1) ( root 2 - 1).

2.Show that one zero of 8x

^{2}+30x+27 is the square of the other.3.If one zero of the polynomial 2x

^{2}+3x+lamda= 1/2,find the value of lamda and the other zero.Solve for x :

9x

^{2}- 9( a + b )x + ( 2a^{2}+ 5ab + 2b^{2})Solve this by both factorisation and by using quadratic formula.

m/nx

^{2}+n/m =1-2xin a flight of 2800 km, an aircraft was slowed down due to bad weather. its average speed is reduced by 100km/h and time increased by 30 mins. find the original duration.

Solve : x

^{2}-(root3+1)x+root3=0 by the method of completing the square.The numerator of a fraction is one less than its denominator.If three is added to each of the numerator and denominator,the fraction is increased by 3/28.find the fraction

solve

p2x2+(p2-q2)x-q2=0

^{2}-(a+b+c)x+a=0a train travels 360 km at uniform speed . if the speed had been 5 km / hr more it would have taken 1 hour less for the same journey. find the speed of the train.