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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 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)

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.?

4 • A card is drawn at random from a well Shuffled pack of 52 playing cards .

Find the probability Of getting neither a red card nor a queen.

SECTION - B

Question numbers 5 to 10 carry 2 marks each,

5. If -5 is a root of the quadratic equation $2{x}^{2}+px-15=0$ and the quadratic

equation p(x

^{2}+x)+k=0 has equal roots, End the value of k.6. Let P and Q be the points of trisection of the line segment joining the points

A(2, —2) and B(—7, 4) such that P is nearer to A. Find the coordinates of

p and Q.

solve for x :root 3x

^{2- }2 root 2x- 2 root 3=0solve for x,

1 / x+1 + 2 / x+2 = 5 / x+4 , x is not equal to -1, -2, -4.

Find 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 .

If one root of a quadratic equation 3x

^{2}+ PX + 4 = 0 is 2/3, find the value of pTwo 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.

Solve this :13. If the arithmetic mean of two numbers 'a' and 'b' is 8 and ab = 9, then the quadratic equation whose roots are _________.

(a) x

^{2}- 16x + 9 = 0 (b) x^{2}+ 16x - 9 = 0(c) x

^{2}- 16x + 9 = 0 (d) x^{2}- 15x + 9 = 0Seven 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.

^{2}x^{2}- q^{2}=04x

^{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.

1) Solve for x: f) 10x

^{2}+ 3bx + a^{2}- 7ax- b^{2}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

if 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

The number of real values of x satisfying the equation 2(x² + (1/x²)) - 9(x + 1/x) + 14 = 0 is

1) 1 2) 2

3) 3 4) 4

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 .

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

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 k

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).

Write an equation which which has 1/5 as a root?

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'.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

if px^2+3x+q=0 has two roots x=-1 and x=-2 ,find the value of q - p .

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?

If alpha and beta are the roots of x

^{2 }+5x+a=0 and 2alpha +5beta= -1,then a is equal toA 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/d^{2}+ 6= 81sum 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?what do you mean by coincident roots?

if one root of a quadratic equation 3x

^{2}+ Px + 4 = 0 is 2/3 , find the value of pThe perimeter of a right triangle is 60cm. Its hypotenuse is 25cm.Find the area of the triangle.

^{2}-2x+3=0 are (i) real or distinct (ii) real or equal (iii) not real (iv) irrational and distinct. Explain by solving.sum of the areas of two squares is 640 m2.if the difference of their perimeters is64m,find the sides of the two squares.

Q.21. Solve $\sqrt{5}{x}^{2}+x+\sqrt{5}=0$.

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.

if the difference of the roots of equation x2 +kx+12=0 is 1,then find the positive value of k

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.The roots alpha and beta of the quadratic equation x2-5x +3(k-1) = 0 are such that alpha - beta= 11 . Find the value of k

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

solve for x - 2(2x-1/x+3)-3(x+3/2x-1)=5

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.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?

for what value of k will 7/3 be a root of 3x

^{2}-13x-k=0.Find the value of k for which the equation kx[x-2]+6=0 has equal roots.

Is there anything else in other chapters which is excluded from the current portions of CBSE syllabus Class 10

solve for x :-

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

(a)c

(b)2c

(c)3c

(d)2c+2b

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

solve by completing square:

^{x2 - (root2 + 1)x + root 2=0}A 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 for x :

9x

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

in 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.solve

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

a 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.

If the price of a book is reduced by Rs.5 ,a person can buy 5 more books for Rs.300 . Find the original list price of the article ?