CBSE Class 10 Mathematics Important Questions for Exam 2023 (Chapter - Quadratic Equations)

 

Important Mathematics Questions of  Class X Chapter {Quadratic Equations} for CBSE      Examination 2023

 

1)      Solve the following equation by factorization method:-

(i)                  A²X² – 3ABX + 2B² = 0

(ii)              4√3X² + 5X - 2√3 = 0

(iii)            AX² + (4A² – 3B)X – 12AB = 0

2)      Solve the following equation by completing the square method:-

(i)                 5x² – 6x – 2 = 0

(ii)              2x² – 5x + 3 = 0

(iii)            X² - 2√2x + 1 = 0

(iv)             9x² – 15x + 6 = 0

3)      Solve the following equation by quadratic formula:-

(i)                 √2x² + 7x + 5√2 = 0

(ii)              5x² – 6x – 2 = 0

(iii)            A²X² – 3ABX + 2B² = 0

(iv)             36x² – 12ax + (a² – b²) = 0

4)      Find two consecutive odd natural numbers, sum of whose squares is 130.

5)      Find the value of k for which the quadratic equation 9x² – 3kx + k = 0 has equal roots.

6)      The sum of two numbers is 11 and the sum of their reciprocal is 11/28. Find the numbers.

7)       The numerator of a fraction is 3 less than its denominator. If 1 is added to the denominator, the fraction is decreased by 1/15. Find the fraction.

8)      The sum of a number and its reciprocal is 10/3. Find the number.

9)   Three consecutive natural numbers are such that the square of the middle number exceeds the difference of the squares of the other two by 60. Find the numbers.

10)  Solve for x :- x² + 5x – (a² + a – 6) = 0

11) The perimeter of a right triangle is 60 cm. its hypotenuse is 25 cm. Find the area e triangle.

12)  If the equation (1 + m²)x² + (2mc)x + (c² – a²) = 0 has equal roots show that 

       c² = a² (1 + m²)

13)  Solve for x : √2x² + 7x + 5√2 = 0

14)  The sum of two numbers is 9 and the sum of their reciprocal is ½.  Find the numbers.

15)  Find the value of m for which the roots of the equation mx(6x + 10) + 25 = 0, are equal.

16)  The numerator of a fraction is 3 less than its denominator. If 1 is added to the denominator, the fraction is decreased by 1/15. Find the fraction.

17)  For what value of k the equation 4x² – 2(k + 1)x + (k + 1) = 0 has real and equal roots.

18) If the roots of the quadratic equation (a-b)x² + (b – c)x + (c – a) = 0 are equal prove that 

       2a = b + c

19)  If x = 2/3 and x = -3 are roots of the quadratic equations ax² + 7x + b = 0 find the value of a and b.

20)  The time taken by a person to cover 150 km was 2 ½ hours more than the time taken in the return journey. If he returned at a speed of 10 km/hr more than the speed while going, find the speed per hour in each direction.

21)  Three consecutive natural numbers are such that the square of the middle number exceeds the difference of the squares of the other two by 60. Find the numbers.

22)   For what value of k are the roots of the quadratic equation (k + 4)x² + (k + 1)x + 1 = 0 equal?

23)  Rs. 6500 is divided equally among a certain number of persons. There had been 15 more persons , each would have got Rs. 30 less. Find the original number of persons.

24)  Find two positive numbers whose squares have the difference 48 and the sum of the numbers is 12.

25)  The sum of the number and its positive square root is 6/25. Find the number.

26)  The product of digits of a two digit positive number is 24. If 18 is added to the number, then the digit of the number are interchanged. Find the number.

27)  A motor boat whose speed is 24 km/hr in still water takes 1 one hour more to go 32 km upstream than to return downstream to the same spot. Find the sped of the stream.

28)  The sum of the square of two consecutive multiples of 7 is 637. Find the multiples.

29)  The sum of the square of two consecutive odd numbers is 394. Find the numbers.

30)  The difference of two natural numbers is 5 and the difference of their reciprocals is 1/10. Find the numbers.

31)  Find the value of p for which the quadratic equation (2p + 1)x² – (7p + 2)x + (7p – 3) = 0 has equal roots. Also find these roots.

32)  A shopkeeper buys some books for Rs. 80. If he had bought 4 more books for the same amount, each book would have cost Rs 1 less. Find the number of books he bought.

33)  In a flight of 2800 km, an aircraft was slowed down due to bad weather. Its average speed is reduced by 100 km/hr and time increased by 30 minutes. Find the original duration of the flight.