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.
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