Question 1 :
Represent the following situation in the form of quadratic equations: Rohan’s mother 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 2 :
Represent the following situation in the form of quadratic equations: The product of two consecutive positive integers is 306. We need to find the integers.
Question 3 :
Represent the following situation in the form of quadratic equations : The area of a rectangular plot is $528 m^2$. The length of the plot (in metres) is one more than twice its breadth. We need to find the length and breadth of the plot.
Question 4 :
Check whether the following is a quadratic equation: $x^3 – 4x^2 – x + 1 = (x – 2)^3$
Question 5 :
Check whether the following is a quadratic equation: $x^2 + 3x + 1 = (x – 2)^2$
Question 6 :
Check whether the following is a quadratic equation: $(x – 2)(x + 1) = (x – 1)(x + 3)$
Question 7 :
Represent the following situation in the form of quadratic equations: A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/h less, then it would have taken 3 hours more to cover the same distance. We need to find the speed of the train.
Question 8 :
Check whether the following is a quadratic equation: $(x + 2)^3 = 2x (x^2 – 1)$
Question 9 :
Check whether the following is a quadratic equation: $(x + 1)^2 = 2(x – 3)$
Question 10 :
Find the roots of the following quadratic equation by factorisation: $100x^2 – 20x + 1 = 0$
Question 11 :
The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides.
Question 12 :
Find the roots of the following quadratic equation by factorisation: $2x^2 – x + \frac{1}{8} = 0$
Question 13 :
Find two consecutive positive integers, sum of whose squares is 365.
Question 14 :
Find two numbers whose sum is 27 and product is 182.
Question 15 :
Find the roots of the following quadratic equation by factorisation: $\sqrt{2}x^2+7x+5\sqrt{2}=0$
Question 16 :
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 17 :
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 18 :
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 19 :
Find the roots of the following quadratic equation by factorisation: $2x^2 + x – 6 = 0$
Question 20 :
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. Find out how many marbles they had to start with.
Question 21 :
Find the roots of the following quadratic equation by factorisation: $x^2 – 3x – 10 = 0$
Question 22 :
Find the roots of the quadratic equations, if they exist, by the method of completing the square: $2x^2 + x + 4 = 0$
Question 23 :
Find the roots of the quadratic equations, if they exist, by the method of completing the square: $2x^2 – 7x + 3 = 0$
Question 24 :
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 25 :
The difference of squares of two numbers is 180. The square of the smaller number is 8 times the larger number. Find the two numbers.
Question 28 :
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 29 :
Find the roots of the quadratic equations, if they exist, by applying quadratic formula: $4x^2+4\sqrt{3}x+3=0$
Question 30 :
Find the roots of the quadratic equations, if they exist, by applying quadratic formula: $2x^2 + x + 4 = 0$
Question 31 :
Find the roots of the quadratic equations, if they exist, by the method of completing the square: $4x^2+4\sqrt{3}x+3=0$
Question 32 :
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 33 :
Find the roots of the quadratic equations, if they exist, by applying quadratic formula: $2x^2 – 7x + 3 = 0$
Question 34 :
In a class test, the sum of Shefali’s marks in Mathematics and English is 30. Had she got 2 marks more in Mathematics and 3 marks less in English, the product of their marks would have been 210. Find her marks in the two subjects.
Question 35 :
Sum of the areas of two squares is $468 m^2$. If the difference of their perimeters is 24 m, find the sides of the two squares.
Question 36 :
Find the roots of the quadratic equations, if they exist, by applying quadratic formula: $2x^2 + x – 4 = 0$
Question 37 :
The diagonal of a rectangular field is 60 metres more than the shorter side. If the longer side is 30 metres more than the shorter side, find the sides of the field.
Question 38 :
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 39 :
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 passenger train.
Question 40 :
Find the roots of the quadratic equations, if they exist, by the method of completing the square: $2x^2 + x – 4 = 0$
Question 41 :
Is the following situation possible? If so, determine their present ages.The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48.
Question 42 :
Find the nature of the roots of the following quadratic equation: $2x^2 – 6x + 3 = 0$
Question 43 :
Find the values of k for each of the following quadratic equations, so that they have two equal roots: $kx (x – 2) + 6 = 0$
Question 44 :
Find the nature of the roots of the following quadratic equation: $2x^2 – 3x + 5 = 0$.
Question 45 :
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 46 :
Find the values of k for each of the following quadratic equations, so that they have two equal roots: $2x^2 + kx + 3 = 0$
Question 47 :
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 48 :
Find the nature of the roots of the following quadratic equation: $3x^2 – 4\sqrt{3}x + 4 = 0$
Question 49 :
Find the roots of the following quadratic equation: $3x^2 – 4\sqrt{3}x + 4 = 0$.
Question 50 :
Find the roots of the following quadratic equation: $2x^2 – 6x + 3 = 0$.
