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

Question 2 : A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less for the same journey. Find the speed of the train.

Question 4 : Check whether the following is quadratic equation : $(x+2)^3 = 2x (x^2 - 1)$

Question 5 : An express train takes 1 hour less than a passenger train to travel 132 km between Mysore and Bangalore (without taking into consideration the time they stop at intermediate stations). If the average speed of the express train is 11km/h more than that of the passenger train, find the average speed of the express train.

Question 7 : Represent the following situation in the form of a quadratic equation : Rohan’s mofher is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. We would like to find Rohan’s present age.

Question 8 : 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 9 : Using method of completing the square , $9x^2-15x+6=0$ can be written as ?

Question 10 : Does the following equation has the sum of its roots as 3? $-x^2+3x-3=0$

Question 11 : Check whether the following is a quadratic equation: $(x + 1)^2 = 2(x – 3)$

Question 12 : Is it possible to design a rectangular park of perimeter 80 m and area $400 m^2$ ? If so, find its length and breadth.

Question 13 : Justify why the following quadratic equation has two distinct real roots: $3x^2-4x+1=0$

Question 14 : A train travels at a certain average speed for a distance of 63 km and then travels a distance of 72 km at an average speed of 6 km/h more than its original speed. If it takes 3 hours to complete the total journey, original average speed of the train is?

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 : Check whether the following is a quadratic equation: $x(x + 1) + 8 = (x + 2) (x – 2)$

Question 17 : Find the roots of the following quadratic equation (by the factorisation method): $3x^2+5\sqrt{5}x-10=0$

Question 18 : Justify why the following quadratic equation has two distinct real roots: $2x^2+x-1=0$

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

Question 20 : Check whether the following is a quadratic equation: $(x + 2)^3 = x^3 – 4$

Question 21 : Find the roots of the quadratic equation (by using the quadratic formula): $-x^2+7x-10=0$

Question 22 : Using method of completing the square , solve for x: $5x^2-6x-2=0$

Question 23 : Find the roots of the quadratic equation $3x^2 - 2\sqrt{6}x+2=0$, by factorisation.

Question 24 : Values of $k$ for which the quadratic equation $2x^2–kx+k=0$ has equal roots is

Question 25 : Find the roots of the quadratic equation (by using the quadratic formula): $5x^2+13x+8=0$

Question 27 : Find the roots of the following quadratic equation by factorisation: $2x^2 + x – 6 = 0$

Question 28 : 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 number of articles produced.

Question 29 : Which constant should be added and subtracted to solve the quadratic equation $4x^2-\sqrt{3}x-5=0$ by the method of completing the square?

Question 30 : State True or False: Every quadratic equation has exactly one root.

Question 31 : The sum of the reciprocals of Rehman’s ages, (in years) 3 years ago and 5 years from now is $\frac{1}{3}$. Find his present age.

Question 32 : Check whether the following is quadratic equation : $x^2 + 3x + 1 = (x-2)^2$

Question 33 : Justify why the following quadratic equation has no two distinct real roots: $2x^2-6x+\frac{9}{2}=0$

Question 36 : State True or False whether the following quadratic equation has two distinct real roots: $2x^2+x-1=0$

Question 37 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b60273b23058497998d.png' /> In the centre of a rectangular lawn of dimensions $50m×40m$, a rectangular pond has to be constructed so that the area of the grass surrounding the pond would be 1184 $m^2$ in the above figure. Find the length of the pond.

Question 38 : Is it possible to design a rectangular mango grove whose length is twice its breadth,and the area is $800 m^2$ ? If so, find its length and breadth.

Question 39 : A cottage industry produces a certain number of toys in a day. The cost of production of each toy (in rupees) was found to be 55 minus the number of toys produced in a day. On a particular day, the total cost of production was Rs. 750. Write an equation to find out the number of toys produced on that day.

Question 41 : Find the roots of the following quadratic equation by factorisation: $\sqrt{2}x^2+7x+5\sqrt{2}=0$

Question 42 : Represent the following situation in the form of a quadratic equation : The product of two consecutive positive integers is 306. We need to find the integers.

Question 43 : John and Jivanti together have 45 marbles. Both of them lost 5 marbles each, and the product of the number of marbles they now have is 124. Write an equation to find out how many marbles they had to start with.

Question 44 : Check whether the following is a quadratic equation: $(x – 3)(2x +1) = x(x + 5)$

Question 45 : Check whether the following is a quadratic equation: $x^2 + 3x + 1 = (x – 2)^2$

Question 46 : A cottage industry produces a certain number of toys in a day. The cost of production of each toy (in rupees) was found to be 55 minus the number of toys produced in a day. On a particular day, the total cost of production was Rs. 750. Find out the number of toys produced on that day.

Question 47 : Does the following equation has the sum of its roots as 3? $\sqrt{2}x^2-\frac{3}{\sqrt{2}}x+1=0$

Question 49 : Find the roots of the quadratic equations, if they exist, by applying quadratic formula: $2x^2 + x – 4 = 0$

Question 50 : Justify why the following quadratic equation has no two distinct real roots: $x\left(1-x\right)-2=0$