Mathematics (HOT's SUMS) notes for class 10th (ALL BOARDS)

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Showing posts with the label Quadratic Equation

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Solve: 216x^6 - 793x^3 + 216 = 0

September 30, 2018

A man travels by boat 36 km down a river and back in 8 hours. If the speed of his boat in still water is 12 km per hour, find the speed of the river current.

September 30, 2018

If the sum of the roots of the quadratic equation ax²+bx+c=0 is equal to the sum of the squares of their reciprocals. Show that bc², ca², ab² are in A.P.

September 30, 2018

Find the value of p, if the equations 3x²-2x+p=0 and 6x²-17x+12=0 have a common root.

September 30, 2018

Find the condition that the equations ax²+bx+c=0 and a1x²+b1x+c1=0 may have a common root. Find this common root, when it exists

September 30, 2018

From the quadratic equation whose roots are the squares of the sum of roots and square of the difference of roots of the equation 2x²+2x(m+n)+m²+n²=0.

September 30, 2018

If the sum of the roots of the quadratic equation ax²+bx+c=0 is equal to the sum of the squares of their reciprocals then, Prove that: 2a²c= c²b + b²a.

September 30, 2018

If the roots of the quadratic equation ax²+bx+c=0 are in the ration p:q. Show that √(p/q)+√(q/p)+√(c/a) = 0.

September 30, 2018

A businessman bought some items for Rs. 600, keeping 10 items for himself he sold the remaining items at a profit of Rs. 5 per item. From the amount received in this deal he could buy 15 more items. Find the original price of each item.

September 30, 2018

One tank can be filled up by two taps in 6 hours. The smaller tap alone takes 5 hours more than the bigger tap alone. Find the time required by each tap to fill the tank separately.

September 30, 2018

Tinu takes 9 days more than his father to do a certain piece of work. Together they can do the work in 6 days. How many days tinu take to do that work.

September 30, 2018

An express train takes 30 min less for a journey of 440 km, if its usual speed is increased by 8 km/hr. Find its usual speed.

September 30, 2018

A man riding on a bicycle cover a distance of 60km in a direction of wind and come back to his original position in 8 hours. If the speed of the wind is 10 km/hr. Find the speed of the bicycle.

September 30, 2018

Around a square pool there is a footpath of width 2km. If the area of the footpath is (5/4) times that of the pool. Find the area of pool.

September 30, 2018

From the same place at 7cm 'A' started walking in the north at the speed of 5km/hr. After 1 hour B started cycling in the east at a speed of 16km/hr. At what time they will be at distance of 52km apart from each other.

September 30, 2018

The divisor and quotient of the number 6123 are same and the remainder is half the divisor. Find the divisor.

September 30, 2018

Two years ago my age was 4(1/2) times the age of my son. Six years ago, my age was twice the square of the age of my son. What is the present age of son.

September 30, 2018

One diagonal of a rhombus is greater than other by 4cm. If the area of the rhombus is 96cm², find the side of the rhombus.

September 30, 2018

The sum of the areas of two squares is 400sq.m. If the difference between their perimeters is 16m, find the sides of the square.

September 30, 2018

Exterior angle of a regular polygon having n-sides is more than that of the polygon having n² sides by 50°. Find the number of the sides of each polygon.

September 30, 2018

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Mathematics (HOT's SUMS) notes for class 10th (ALL BOARDS)

Posts

Solve: 216x^6 - 793x^3 + 216 = 0

A man travels by boat 36 km down a river and back in 8 hours. If the speed of his boat in still water is 12 km per hour, find the speed of the river current.

If the sum of the roots of the quadratic equation ax²+bx+c=0 is equal to the sum of the squares of their reciprocals. Show that bc², ca², ab² are in A.P.

Find the value of p, if the equations 3x²-2x+p=0 and 6x²-17x+12=0 have a common root.

Find the condition that the equations ax²+bx+c=0 and a1x²+b1x+c1=0 may have a common root. Find this common root, when it exists

From the quadratic equation whose roots are the squares of the sum of roots and square of the difference of roots of the equation 2x²+2x(m+n)+m²+n²=0.

If the sum of the roots of the quadratic equation ax²+bx+c=0 is equal to the sum of the squares of their reciprocals then, Prove that: 2a²c= c²b + b²a.

If the roots of the quadratic equation ax²+bx+c=0 are in the ration p:q. Show that √(p/q)+√(q/p)+√(c/a) = 0.

A businessman bought some items for Rs. 600, keeping 10 items for himself he sold the remaining items at a profit of Rs. 5 per item. From the amount received in this deal he could buy 15 more items. Find the original price of each item.

One tank can be filled up by two taps in 6 hours. The smaller tap alone takes 5 hours more than the bigger tap alone. Find the time required by each tap to fill the tank separately.

Tinu takes 9 days more than his father to do a certain piece of work. Together they can do the work in 6 days. How many days tinu take to do that work.

An express train takes 30 min less for a journey of 440 km, if its usual speed is increased by 8 km/hr. Find its usual speed.

A man riding on a bicycle cover a distance of 60km in a direction of wind and come back to his original position in 8 hours. If the speed of the wind is 10 km/hr. Find the speed of the bicycle.

Around a square pool there is a footpath of width 2km. If the area of the footpath is (5/4) times that of the pool. Find the area of pool.

From the same place at 7cm 'A' started walking in the north at the speed of 5km/hr. After 1 hour B started cycling in the east at a speed of 16km/hr. At what time they will be at distance of 52km apart from each other.

The divisor and quotient of the number 6123 are same and the remainder is half the divisor. Find the divisor.

Two years ago my age was 4(1/2) times the age of my son. Six years ago, my age was twice the square of the age of my son. What is the present age of son.

One diagonal of a rhombus is greater than other by 4cm. If the area of the rhombus is 96cm², find the side of the rhombus.

The sum of the areas of two squares is 400sq.m. If the difference between their perimeters is 16m, find the sides of the square.

Exterior angle of a regular polygon having n-sides is more than that of the polygon having n² sides by 50°. Find the number of the sides of each polygon.

Arithmetic Progression