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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....

solve for x,

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

what do you mean by coincident roots?

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.

a flight was scheduled to go from delhi to mumbai covering 1200 km but to engine problem its speed was reduced to 3/4th of the original. therefore it reached the destination 60 min late. what is the original speed and original time of the journey?

solve;

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

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

If the roots of the equation

(a-b)x

^{2}+(b-c)x+(c-a)=0 are equal , prove that b+c=2a.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

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

find the discriminate of quadratic equation 4x

^{2}-2/3 x -1/16=0solve 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.?

^{2}-2x+3=0 are (i) real or distinct (ii) real or equal (iii) not real (iv) irrational and distinct. Explain by solving.solve for x :root 3x

^{2- }2 root 2x- 2 root 3=0^{2}are always real.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 alpha and beta are the roots of x

^{2 }+5x+a=0 and 2alpha +5beta= -1,then a is equal toTwo 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.

If one root of a quadratic equation 3x

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

use quadratic formula to solve :

x

^{2}+2ax+(a_{2}-b^{2})=04x

^{2}+ 4bx - (a^{2}- b^{2}) = 0 please solve this equation................x

^{2}-2(a^{2}+b^{2})x+(a^{2}-b^{2})=0A 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.

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 by completing square:

^{x2 - (root2 + 1)x + root 2=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 !^{2}– 5x – 11 = 0A 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 .

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

root x/1-x + root 1-x/x = 13/ 6 solve this equations by splitting the middle term

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).

solve:

x/x-1 + x-1/x =4

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

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 one root of a quadratic equation 3x

^{2}+ Px + 4 = 0 is 2/3 , find the value of pA 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?

Find the discriminant of the quadratic equation 2x

^{2}-4x+3=0 and hence find the nature of its rootsA 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/dsum 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?^{2}-z^{2 }= b(c-a)/z^{2}-x^{2}= c(a-b)/x^{2}-y^{2}Please answer this question! This question is from K.C.Nag. This question is complete.

The perimeter of a right triangle is 60cm. Its hypotenuse is 25cm.Find the area of the triangle.

Ruchir was aked his age by his friend. Ruchir said ''The number you get when you subtract 25 times my age from twice the square of my age will be thrice your age. If the friend's age is 14, then the age of Ruchir is

(a) 20

(b) 22

(c) 28

(d) 14

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

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.

^{2}-x-3/5=0solve by FACTORISATION method ONLY

^_^

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 -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 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

9x

^{2}-3[a^{2}+b^{2}]x+a^{2}b^{2}=0 using quadratic formula solve for x^{2}x^{2}- q^{2}=0what is the formula of (a+b) whole cube

If roots of the equation ax

^{2}+bx+c=0 are (k+1) / k and (k+2) / (k+1) then the value of (a+b+c)^{2}is how much? Options: (a) b^{2}+4ac(b) -b

^{2}+ 4ac(c) b

^{2}- 4ac(d) None of these

Please explain in detail

Solve : (k+4)x

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

^{ 2}x^{2}+ 8(a^{2}- b^{2}) x +16 (a-b)^{2}= 0solve for x.

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.

The angle of depression of a car, standing on the ground, from the top of a 75 m high tower, is 30

[Marks:1]A.B.C.D.2]^{o}. The distance of the car from the base of the tower (in m.) is:The probability of getting an even number, when a die is thrown once, is:

[Marks:1]A.B.C.D.3]A box contains 90 discs, numbered from 1 to 90. If one disc is drawn at random from the box, the probability that it bears a prime-number less than 23, is:

[Marks:1]A.B.C.D.4]In fig., a circle with centre O is inscribed in a quadrilateral ABCD such that, it touches the sides BC, AB, AD and CD at points P, Q, R and S respectively, If AB = 29 cm, AD = 23 cm,B = 90

[Marks:1]A.^{o}and DS = 5 cm, then the radius of the circle (in cm) is:18

B.6

C.15

D.11

5]In fig., PA and PB are two tangents drawn from an external point P to a circle with centre C and radius 4 cm. If PAPB, then the length of each tangent is:

[Marks:1]A.3 cm

B.5 cm

C.6 cm

D.4 cm

6]In fig., the area of triangle ABC (in sq. units) is:

[Marks:1]A.2.5

B.10

C.15

D.7.5

7]If the difference between the circumference and the radius of a circle is 37 cm, then using, the circumference (in cm) of the circle is:

[Marks:1]A.7

B.14

C.154

D.44

8]The common difference of AP... is:

[Marks:1]A.q

B.-q

C.2

D.-2

9]Prove that the parallelogram circumscribing a circle is a rhombus.

[Marks:2]10]Two circular pieces of equal radii and maximum area, touching each other are cut out from a rectangular card board of dimensions 14 cm7 cm. Find the area of the remaining card board.

[Marks:2]11]In fig., a circle is inscribed in triangle ABC touches its sides AB, BC and AC at points D, E and F respectively. If AB = 12 cm, BC = 8 cm and AC = 10 cm, then find the length of AD, BE and CF.

[Marks:2]12]How many three-digit natural numbers are divisible by 7?

[Marks:2]13]Solve the following quadratic equation for x:

[Marks:2]14]A card is drawn at random from a well shuffled pack of 52 playing cards. Find the probability that the drawn card is neither a king nor a queen.

[Marks:2]15]A vessel is in the form of hemispherical bowl surmounted by a hollow cylinder of same diameter. The diameter of the hemispherical bowl is 14 cm and the total height of the vessel is 13 cm. Find the total surface area of the vessel.

[Marks:3]16]A wooden toy was made by scooping out a hemisphere of same radius from each end of a solid cylinder. If the height of the cylinder is 10 cm, and its base is of radius 3.5 cm, find the volume of wood in the toy.

[Marks:3]17]In a circle of radius 21 cm, an arc subtends an angle of 60

[Marks:3]18]^{o}at the centre. Find: (i) the length of the arc (ii) area of the sector formed by the arc.In Fig., AB and CD are two diameters of a circle with centre O, which are perpendicular to each other. OB is the diameter of the smaller circle. If OA = 7 cm, find the area of the shaded region.

[Marks:3]19]Find the ratio in which the y-axis divides the line segment joining the points (-4, -6) and (10, 12). Also, find the coordinates of the point of division.

[Marks:3]20]The horizontal distance between two poles is 15 m. The angle of depression of the top of first pole as seen from the top of second pole is 30

[Marks:3]21]^{o}. If the height of the second pole is 24 m, find the height of the first pole.For what values of k, the roots of the quadratic equation (k + 4) x

[Marks:3]22]^{2}+ (k + 1)x + 1 = 0 are equal?The sum of first n terms of an AP is 3n

[Marks:3]23]^{2}+ 4n. Find the 25^{th}term of this AP.Construct a tangent of a circle of radius 4 cm from a point on the concentric circle of radius 6 cm.

[Marks:3]24]Show that the points (-2, 3), (8, 3) and (6, 7) are the vertices of a right triangle.

[Marks:3]25]Water is flowing through a cylindrical pipe, of internal diameter 2 cm, into a cylindrical tank of base radius 40 cm, at the rate of 0.4 m/s. Determine the rise in level of water in the tank in half an hour.

[Marks:4]26]A Group consists of 12 persons, of which 3 are extremely patient, other 6 are extremely honest and rest are extremely kind. A person from the group is selected at random. Assuming that each person is equally likely to be selected, find the probability of selecting a person who is (i) extremely patient (ii) extremely kind or honest. Which of the above values you prefer more?

[Marks:4]27]A bucket open at the top, and made up of a metal sheet is in the form of a frustum of a cone. The depth of the bucket is 24 cm and the diameters of its upper and lower circular ends are 30 cm and 10 cm respectively. Find the cost of metal sheet used in it at the rate of Rs 10 per 100 cm

[Marks:4]28]^{2}.In fig., l and m are two parallel tangents to a circle with centre O, touching the circle at A and B respectively. Another tangent at C intersects the line l at D and m at E. Prove that

[Marks:4]29]Sum of the areas of two squares is 400 cm

[Marks:4]30]^{2}. If the difference of their perimeters is 16 cm, find the sides of the two squares.Solve that following for x:

[Marks:4]31]Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact.

[Marks:4]32]Find the number of terms of the AP -12, -9, -6,... 12. If 1 is added to each term of this AP, then find the sum of all terms of the AP thus obtained.

[Marks:4]33]Two poles of equal heights are standing opposite each other on either side of the roads, which is 80 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 60

[Marks:4]34]^{o}and 30^{o}respectively. Find the height of the poles and the distances of the point from the poles.If the area of triangle ABC formed by A(x,y), B(1,2) and C(2,1) is 6 square units, then prove that x + y = 15.

[Marks:4]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?

solve for x ; 2(2x+3/x-3)-25(x-3/2x+3) = 5

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

"there is no integral value of t such that roots of equation 7x2 + tx - 3 = 0 are real and equal"

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.

^{2}+bx+c=0 and bx^{2}+cx+a=0 have a common root, then prove that a+b+c=0 and a=b=c.Solve for x :

9x

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

find 2 consecutive positive integers , sum of whose squares is 925 ?

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.

Why there minus symbol is used instead of plus....

Solve : x

^{2}-(root3+1)x+root3=0 by the method of completing the square.Solve 3x

^{2}- 6x + 2 = 0 by factorisation...solve

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

solve x+1/x =25 1/25 * (25 1/25 is mixed fraction)

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.

^{2}- √11x + 1=0If 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 ?

Solve for x; 1/x-3 - 1/x+5=1/6 , x is not equal to 3,-5