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

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}\$  

•  $x=\frac{a^2+b^2}{2}$  

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

Multiple Select

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

• -8

• 8

• -20

• 20

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

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)