# CBSE HOTS Questions Mathematics (QUADRATIC EQUATIONS)

1. Solve by factorization

2.  By the method of completion of squares show that the equation 4×2+3x +5 = 0 has no real roots.
3. The sum of areas of two squares is 468m2 If the difference of their perimeters is 24cm, find the sides of the two squares.
4. A dealer sells a toy for Rs.24 and gains as much percent as the cost price of the toy.  Find the cost price of the toy.
5. A fox and an eagle lived at the top of a cliff of height 6m, whose base was at a distance of 10m from a point A on the ground.  The fox descends the cliff and went straight to the point A.  The eagle flew vertically up to a height x metres and then flew in a straight line to a point A, the distance traveled by each being the same.  Find the value of x.
6. A lotus is 2m above the water in a pond.  Due to wind the lotus slides on the side and only the stem completely submerges in the water at a distance of 10m from the original position. Find the depth of water in the pond
7. The hypotenuse of a right triangle is 20m.  If the difference between the length of the other sides is 4m.  Find the sides.
8. The positive value of k for which x2 +Kx +64 = 0 & x2 – 8x + k = 0 will have real roots .
9. A teacher on attempting to arrange the students for mass drill in the form of a solid square found that 24 students were left over.  When he increased the size of the square by one student he found he was short of 25 students.  Find the number of students.

• PROVE THAT: a4+b4+c4>=abc(a+b+c) [you are not able to do this question]

PREM on 11 Oct 2012
• 2^(2x) -3.2^(x+2) +32 =0 solve for x using factorization method, quadratic equations , class 10th, cbse

Reema on 11 Oct 2012
• If the sum of first 10 terms of an a.p is -80 and the sum of next 10 term is -260.form a.p

Rahul on 25 Jan 2013
• A lotus is 2m above the water in a pond. Due to wind the lotus slides on the side and only the stem completely submerges in the water at a distance of 10m from the original position. Find the depth of water in the pond

aman on 15 Feb 2013
• first convert this equation into quadratic equation then solve this equation:- 5 1-x +51+x=26

mohit.raninga on 28 Feb 2013
• a car travels a distance of 900km with a certain average speed. if after travelling half the distance the average speed of the car be increased by 15km/hr,the time required to travel 900km is reduced by 1.5hr.find the original average speed of the car.

monil on 13 Mar 2013
• A car travels a distance of 400 km and consumes x km per liter of fuel.Then the driver gets the engine serviced.The same car then travels a distance of 400 km but the fuel consumption by the car in the total journey?

monika jaggi on 18 Mar 2013
• Water in a canal,6m wide and 1.5m deep is flowing with a speed of 10km/hr.How much area will it irrigate i 30min.If 8cm of standing water is needed.

Rakesh on 18 Feb 2014