Question 1 :
Check whether the following is a quadratic equation: $(x – 3)(2x +1) = x(x + 5)$

Question 3 :
State True or False whether the following quadratic equation has two distinct real roots : $\left(x-\sqrt{2}\right)^2-2\left(x+1\right)=0$

Question 5 :
Two water taps together can fill a tank in $9{\frac{3}{8}}$ hours. The tap of larger diameter takes 10 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.

Question 7 :
Find the roots of the following quadratic equation (by the factorisation method): $21x^2-2x+\frac{1}{21}=0$

Question 8 :
Values of $k$ for which the quadratic equation $2x^2–kx+k=0$ has equal roots is

Question 10 :
Justify why the following quadratic equation has no two distinct real roots: $x^2-3x+4=0$

Question 11 :
Find the roots of the following quadratic equation (by the factorisation method): $3x^2+5\sqrt{5}x-10=0$

Question 12 :
Find the roots of the quadratic equations, if they exist, by applying quadratic formula: $4x^2+4\sqrt{3}x+3=0$

Question 14 :
Had Ajita scored 10 more marks in her mathematics test out of 30 marks, 9 times these marks would have been the square of her actual marks. The marks scored by her are?

Question 15 :
The roots of the quadratic equation $ax^2 + bx + c = 0$ are given by $x = {-b \pm \sqrt{b^2-4ac} \over 2a}$. TRUE or FALSE ?

Question 16 :
A cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day that the cost of production of each article (in rupees) was 3 more than twice the number of articles produced on that day. If the total cost of production on that day was Rs. 90, find the cost of each article?

Question 17 :
At $t$ minutes past 2 pm, the time needed by the minutes hand of a clock to show 3 pm was found to be 3 minutes less than $\frac{t^2}{4}$ minutes. Find $t$.

Question 18 :
Find the roots of the quadratic equations, if they exist, by applying quadratic formula: $2x^2 – 7x + 3 = 0$

Question 19 :
Using method of completing the square , solve for x: $2x^2-5x+3=0$

Question 20 :
Check whether the following is quadratic equation : $(x+2)^3 = 2x (x^2 - 1)$