📝 Quadratic Equations
Multiple Choice Questions
1. Which of the following is a quadratic equation?
(A) `x^2 + 2x + 1 = (4 – x)^2 + 3`
(B) ` –2x^2 = (5 – x)(2x -2/5)`
(C) `(k + 1)x^2 + 3/2 x = 7`, where `k = –1`
(D) `x^3 – x^2 = (x – 1)^3`
2. Which of the following is not a quadratic equation?
(A) `2(x – 1)^2 = 4x^2 – 2x + 1`
(B) `2x – x^2 = x^2 + 5`
(C) `(sqrt2x + sqrt3)^2 + x^2 = 3x^2 -5x`
(D) (`x^2 + 2x)^2 = x^4 + 3 + 4x^3`
3. Which of the following equations has 2 as a root?
(A) `x^2 – 4x + 5 = 0`
(B) `x^2 + 3x – 12 = 0`
(C) `2x^2 – 7x + 6 = 0`
(D) `3x^2 – 6x – 2 = 0`
4. If `1/2` is a root of the equation `x^2 + kx – 5 /4 = 0`, then the value of `k` is
(A) 2
(B) – 2
(C) `1/4`
(D) `1/2`
General Questions
1. Ajita had 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. How many marks did she get on the test?
2. 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, what is its original average speed?
3. Find a natural number whose square diminished by 84 is equal to thrice of 8 more than the given number.
4. A natural number, when increased by 12, equals 160 times its reciprocal. Find the number.
5. A train, travelling at a uniform speed of 360 km, would have taken 48 minutes less to travel the same distance if its speed were 5 km/h more. Find the original speed of the train.
6. If Zeba were younger by 5 years than what she really is, then the square of her age (in years) would have been 11 more than five times her actual age. What is her age now?
7. At present Asha’s age (in years) is 2 more than the square of her daughter Nisha’s age. When Nisha grows to her mother’s present age, Asha’s age would be one year less than 10 times the present age of Nisha. Find the present ages of both Asha and Nisha.
8. If Ritu were younger by 5 years than what she really is, then the square of her
age would have been 11 more than five times her present age. What is her
present age?
9. Solve for `x: 9x^² - 6px + (p² - q²) = 0`
10. Find the value of `m` so that the quadratic equation `mx(5x-6) = 0` has two
equal roots.
Case Studies
The speed of a motorboat is 20 km/hr. For covering the distance of 15 km the boat took 1 hour more upstream than downstream.
1. Let speed of the stream be x km/hr. then speed of the motorboat in upstream will be
a) 20 km/hr
b) (20 + x) km/hr
c) (20 - x) km/hr
d) 2 km/hr
2. What is the relation between speed ,distance and time?
a) speed = (distance )/time
b) distance = (speed )/time
c) time = speed × distance
d) speed = distance × time
3. Which is the correct quadratic equation for the speed of the current?
a) `x^2+ 30x − 200 = 0`
c) `x^ 2+ 30x − 400 = 0`
d) `x^2− 20x − 400 = 0`
a) `x^2+ 30x − 200 = 0`
c) `x^ 2+ 30x − 400 = 0`
d) `x^2− 20x − 400 = 0`
b) `x^2+ 20x − 400 = 0`
4. What is the speed of current ?
a) 20 km/hour
b) 10 km/hour
c) 15 km/hour
d) 25 km/hour
5. How much time boat took in downstream?
a) 90 minute
b) 15 minute
c) 30 minute
d) 45 minute
ANSWERS:
1. c) (20 – x)km/hr
2. b) distance=(speed)/ time
3. c) x 2+ 30x – 400= 0
4. b) 10 km/hour
5. c) 45 minute
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