Previous Year Mathematics Question of Class X [Chapter - Quadratic Equations ]

 

Previous Year Mathematics Questions of Class 10 Chapter {Quadratic Equations } for Examination 2023

One mark Questions

1)  Value of the roots of the quadratic equation x² – x – 6 = 0 is ………………                        (CBSE 2020)

2)  The roots of the quadratic equation x² – 0.04 = 0 are …………..                                                 (CBSE 2020)

3)  Find the nature of the roots of the quadratic equation 4x² + 4√3 x + 3 = 0                                (CBSE 2019)

4)  Find the nature of the roots of the quadratic equation 2x² – 4x + 3 = 0                                     (CBSE 2019)

5)  If x = 3 is one root of the quadratic equation x² – 2kx – 6 = 0, then find the value of k.          (CBSE 2018)

6)  Find the values of k for which the quadratic equation 

    2x² – kx + k = 0 has two equal roots.            

Two mark Questions

1)  Determine the roots of the following quadratic equations 4√5x² – 17x + 3√5 = 0

2)  If roots of the quadratic equation (b – c)x² + (c – a)x + (a – b) = 0 are real and equal then prove that 2b = a + c

3)  Solve the quadratic equation √3x² + 10 x - 8√3 = 0.

4)  Solve the quadratic equation x² + x – (a + 1)(a + 2) = 0

5)  Find the value of a for which equation 5x² – kx + 1 = 0 has real roots (D ≥ 0).

6)  If the equation (1 + m²)x² + 2mcx + (c² – a²) = 0 has equal roots prove that c² = a²(1 + m²)

 

Three mark Questions

1)  Solve for x:1/x+4  -  1/x+7 = 11/30 ,  x ≠ - 4, 7                                                     (CBSE 2020)

2)  In a flight of 600 Km, an aircraft was slowed down due to bad weather. The average speed of the trip was reduced by 200 Km per hour and the time of flight increased by 30 minutes. Find the duration of flight.    (CBSE 2020)  

3)  A fast train takes 3 hours less than a slow train for a journey for 600 Km. If speed of the slow train is 10 Km per hour less than that of the fast train, find the speed of each train.                                     (CBSE 2020)

4)  Write all the values of p for which the quadratic equation x² + px + 16 = 0 has equal roots, find the roots of the equation so obtained.                                                                         (CBSE 2019)

5)  A plane left 13 minutes late than its scheduled time and in order to reach the destination 1500 km away in time, it had to increase its speed by 100 Km from the usual speed. Find its usual speed.

6)  Find the roots of the quadratic equations 4x² + 4bx – (a² – b²) = 0 by the completing the square method.

7)  Using quadratic formula solve the following quadratic equation in x:  p²x² + (p² – q²)x – q² = 0

Four mark Questions

1)  If the price of book is reduced by Rs. 5, a person can buy 4 more books for Rs. 600. Find the original price of the book.  (CBSE 2020)

2)  Three consecutive positive integers are such that the sum of the square of the first and the product of the other two is 46. Find the integers.                          (CBSE 2020)

3)  Solve the quadratic equation x² + 3x – (a² + a – 2) = 0      (CBSE 2019)

4)  In a class test the sum of Arun’s marks in Hindi and English is 30 had he got 2 marks more in Hindi and 3 marks less in English, the product of the marks would have been 210, find his marks in 2 subjects.          (CBSE 2019)

5)  A motor boat whose speed is 18 Km per hour in still water takes 1 hour more to go 24 km upstream then to return downstream to the same spot. Find the speed of the stream.                                        (CBSE 2018)

6)  A train travel at a certain average speed for a distance of 63 km and then travels at a distance of 72 km at an average speed of 6 km per hour more than its original speed, if it takes 3 hours to complete total journey. What is the original average speed?                              (CBSE 2018)

7) 2 water taps together can fill a tank in 31/10 hours the tap of smaller diameter take 2 hours more than the larger one to fill the tank separately. Find the time in which each tap can separately fill the tank.

8)  Find the positive value of k for which x² + kx + 64 = 0 and x² – 8x + k = 0 will have real roots.  

9)  Solve the quadratic equation by factorization method: 9x² – 9(a + b)x + (2a² + 5ab + 2b²) = 0

10)                    The denominator of a fraction is 1 more than twice the numerator if the sum of the fraction and its reciprocal is 16/11. Find the fraction.

11)        O Girl! Out of a group of swans 7/2 times the square root of the number are playing on the shore of a tank , the two remaining ones are playing with a morous fight in the water. What is the total number of swans?

12)                    If the price of a book is reduced by Rs. 5, a person can by 5 more books for Rs. 300. Find the original list price of the book.