Quadratic Equations - CBSE Class 10

Quadratic Equations - CBSE Class 10

Multiple Choice

Find the roots of the equation

 $x^2-3x-m\left(m+3\right)=0$ where m is a constant. (2011 OD)

• x = m-3, x=m

• x = m+2, x=-m

• x = m-2, x=-m

• x = m+3, x=-m

Fill in the Blank

If 1 is a root of the equations  $ay^2+ay+3=0$  and  $y^2+y+b=0$ , then find the value of ab. (2012D)

Fill in the Blank

If the quadratic equation $px^2–2\sqrt{5}px+15=0$  has two equal roots, then find the value of p. (2015OD)

Multiple Select

Find the value of p so that the quadratic equation px(x – 3) + 9 = 0 has two equal roots. (2011D, 2014OD)

• 0

• 2

• 3

• 4

Multiple Select

Solve the following quadratic equation for x:  $4x^2-4a^2x+\left(a^4-b^4\right)=0$  . (2015D)

•  $x=\frac{a^2-b^2}{2}\$  

•  $x=\frac{b^2-a^2}{2}\$  

•  $x=\frac{a^2+b^2}{2}$  

•  $x=\frac{a^2+b^2-\left(a+b\right)}{2}$  

Fill in the Blank

Find the value of p, for which one root of the quadratic equation  $px^2-14x+8=0$   is 6 times the other. (20170D)

Multiple Select

Solve for x:   $\sqrt{\left(2x+9\right)}+x=13$ . (20160D)

• -8

• 8

• -20

• 20

Fill in the Blank

Three consecutive natural numbers are such that the square of the middle number exceeds the difference of the squares of the other two by 60. Find the numbers. (2016OD)

[ENTER ANSWER IN ASCENDING ORDER - COMMA SEPERATED]

Fill in the Blank

A shopkeeper buys some books for 80. If he had bought 4 more books for the same amount, each book would have cost ₹ 1 less. Find the number of books he bought. (2012D)

Fill in the Blank

Sum of the areas of two squares is  $400\ cm^2$  . If the difference of their perimeters is 16 cm, find the sides of the two squares. (2013D)

[ENTER ANSWER IN ASCENDING ORDER - COMMA SEPERATED]

Fill in the Blank

The diagonal of a rectangular field is 16 metres more than the shorter side. If the longer side is 14 metres more than the shorter side, then find the lengths of the sides of the field. (2015OD)

[ENTER ANSWER IN ASCENDING ORDER - COMMA SEPERATED]

Multiple Choice

The sum of three numbers in A.P. is 12 and sum of their cubes is 288.

[select answer in the order of series]

• 2 , 4 , 6

• 3 , 5 , 7

• 6 , 4 , 2

• 7 , 6 , 5

Fill in the Blank

The perimeter of a right triangle is 60 cm. Its hypotenuse is 25 cm. Find the area of the triangle. (2016D)

Multiple Select

The numerator of a fraction is 3 less than its denominator. If 1 is added to the denominator, the fraction is decreased by  $\frac{1}{15}$  . Find the fraction. (20120D)

•  $\frac{2}{5}$  

•  $\frac{2}{3}$  

•  $\frac{5}{2}$  

•  $\frac{5}{3}$  

BONUS QUESTION 1

Two pipes running together can fill a tank in   $11\frac{1}{9}$  minutes. If one pipe takes 5 minutes more than the other to fill the tank separately, find the time in which each pipe would fill the tank separately. (2016OD)

BONUS QUESTION 2

To fill a swimming pool two pipes are to be used. If the pipe of larger diameter is used for 4 hours and the pipe of smaller diameter for 9 hours, only half the pool can be filled. Find, how long it would take for each pipe to fill the pool separately, if the pipe of smaller diameter takes 10 hours more than the pipe of larger diameter to fill the pool. (2015D)