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Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions

Important Questions for Class 10 Maths Chapter 4 Quadratic Equations with solutions includes all the important topics with detailed explanation that aims to help students to score more marks in Board Exams 2020. Students who are preparing for their Class 10 exams must go through Important Questions for Class 10 Math Chapter 4 Quadratic Equations.

Important Questions for Class 10 Maths Chapter 4 Quadratic Equations

Expert teachers at CBSETuts.com collected and solved 2 Marks and 4 mark important questions for Class 10 Maths Chapter 4 Quadratic Equations. All the solutions given in this page are solved based on CBSE marking scheme and NCERT guidelines.

2016

Short Answer Type Questions I [2 Marks]

Question 1.
If x= 2/3 and x = – 3 are roots of the quadratic equations ax2 + lx + b = 0, find the values of a and b.
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 1
Question 2.
If- 5 is a root of the quadratic equation 2x2 + px -15 = 0 and the quadratic equation p(x2 + x) + k = 0 has equal roots, find the value of k.
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions2
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 3
Question 3.
Solve for x: \(\sqrt { 2x+9 }\) + x = 13.
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 4

Question 4.
Solve for x :√3x2-2√2x-2√3=0 = 0.
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 5

Question 5.
A two digit number is four times the sum of the digits. It is also equal to 3 times the product of digits. Find the number.
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 5
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 7

Question 6.
Solve for x:√3x2 – 2√2x-2√3=0

Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 8

Question 7.
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 9
Solve for x:
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 10

Short Answer Type Questions II [3 Marks]

Question 8.

Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 11
Solve for x:
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 12
Question 9.

Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 13
Solve for x:
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 14

Question 10.
Solve the following quadratic equation for x:

Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 15
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 16
Question 11.

Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 17
Solve for x:
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 18

Question 12.
If the roots of the quadratic equation (a – b)x2 + (b – c)x + (c – a) = 0 are equal, prove that 2a = b + c.
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 19

The Completing The Square Calculator at online with the step-by-step procedure.

Question 13.
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
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 20

Question 14.
Two water taps together can fill a tank in 9 hours 36 minutes. The tap of larger diameter takes 8 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.
Solution :
Let x be the time taken by larger diameter tap.
x + 8 be the time taken by smaller diameter tap.

Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 21

Question 15.
Solve the given quadratic equation for x: 9x2 – 9(a + b)x + (2a2 + 5ab + 2b2 ) =0.
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 22

Question 16.

Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 23
Solve for x:
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 24

Question 17.

Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 25
Solve for x (in terms of a and b):
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 26

Long Answer Type Questions [4 Marks]

Question 18.
A passenger, while boarding the plane, slipped from the stairs and got hurt. The pilot took the passenger in the emergency clinic at the airport for treatment. Due to this, the plane got delayed by half an hour. To reach the destination 1500 km away in time, so that the passengers could catch the connecting flight, the speed of the plane was increased by 250 km/hour than the usual speed. Find the usual speed of the plane. What value is depicted in this question?
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 27

Question 19.
Find x in terms of a, b and c:

Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 28
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 29

Question 20.
The time taken by a person to cover 150 km was 2. 1/2 hours more than the time taken in the return journey. If he returned at a speed of 10 km/hour more than the speed while going, find the speed per hour in each direction.
Solution :

Let t1 and t2 be the time taken in going and returning respectively.
Also, v and v + 10 be the speed in going and returning respectively.
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 30
Question 21.
Solve for x:

Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 31
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 32

Question 22.
A motor boat whose speed is 24 km/h in still water takes 1 hour more to go 32 km upstream than to return downstream to the same spot. Find the speed of the stream.
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 33

Question 23.
A rectangular park is to be designed whose breadth is 3 m less than its length. Its area is to be 4 square metres more than the area of a park that has already been made in the shape of an isosceles triangle with its base as the breadth of the rectangular park and of altitude 12 m. Find the length and breadth of the rectangular park.
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 34

Question 24.
Two pipes running together can fill a tank in 11. 1/9 minutes. If one pipe takes 5 minutes more than the other to fill the tank separately, find the time in which each pipe would fill the tank separately.
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 35

Question 25.
A pole has to be erected at a point on the boundary of a circular park of diameter 17 m in such a way that the differences of its distances from two diametrically opposite fixed gates where the pole is to be erected.
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 36
Question 26.
Find the positive value(s) of k for which quadratic equations x2 + kx + 64 = 0 and x2 -8X+ k = 0 both will have real roots.
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 37

Question 27.
If roots of the quadratic equation x2 + 2px + mn = 0 are real and equal, show that the roots of the quadratic equation x2 – 2(m + n)x + (m2 + n2 + 2p2 ) =0 are also equal.
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 38

Question 28.
The denominator of a fraction is one more than twice its numerator. If the sum of the fraction and its reciprocal 2. 16/21 find the fraction
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 39

2015

Very Short Answer Type Questions [1 Mark]

Question 29.
If x =-1/2 , is a solution of the quadratic equation 3x2 + 2kx -3 = 0, find the value of K .
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 40
Question 30.
If the quadratic equation px2 – 2√5px + 15 = 0 has two equal roots, then find the value of p.
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 41

Short Answer Type Questions I [2 Marks]

Question 31.
Solve the following quadratic equation for x: 4x2 – 4a2 x + (a4 – b4 ) = 0
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 42

Question 32.
Solve the following quadratic equation for x: 9x2 – 6b2 x – (a4 – b4 ) = 0
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 43

Question 33.
Solve the following quadratic equation for x: 4x2 + 4bx – (a2 – b2) = 0
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 44

Question 34.
Solve the following quadratic equation for x: x2 – 2ax – (4b2 -a2) = 0
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 45

Question 35.
Solve for x  .x2 -(√3+1)x+√3=0
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 46

Short Answer Type Questions II [3 Marks]

Question 36.
Find the value ofp for which the quadratic equation (p + l)x2 – 6(p + 1)x + 3(p + 9) = 0,p ≠ 1 has equal roots. Hence, find the roots of the equation.
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 47

Question 37.
Find that non-zero value of k, for which the quadratic equation kx2 + 1 – 2 (k – 1)x + x2= 0 has equal roots. Hence, find the roots of the equation.
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 48

Question 38.
Solve for x: √3x2 – 2√2x-2√3=0
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 49
Question 39.
Solve for x: 2x2 + 6√3-60 = 0
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 50
Question 40.
Solve for x: x2 + 5x – (a2 + a – 6) =0
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 51

Question 41.
Solve for x:
x2 -(2b- l)x + (b2 -b-20) = 0
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 52
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 53

Question 42.
Solve for a:
x2 + 6x – (a2 + 2a – 8) = 0
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 54

Long Answer Type Questions [4 Marks]

Question 43.

Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 55
Solve for x:
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 56

Question 44.

Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 57
Solve for x
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 58

Question 45.
The numerator of a fraction is 3 less than its denominator. If 2 is added to both the numerator and the denominator, then the sum of the new fraction and original  fraction is 29/20. Find the original fraction.
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 59
Question 46.
larger diameter is used for 4 hours and the pipe of smaller diameter for 9 hours, only half the pool can be filled. Find, how long it would take for each pipe to fill the pool separately, if the pipe of smaller diameter takes 10 hours more than the pipe of larger diameter to fill the pool.
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 60
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 61

Question 47.
The diagonal of a rectangular field is 16 metres more than the shorter side. If the longer side is 14 metres more than the shorter side, then find the lengths of the sides of the field.
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 62

Question 48.
A train travels at a certain average speed for a distance of 54 km and then travels a distance of 63 km at an average speed of 6 km/h more than the first speed. If it takes 3 hours to complete the total journey, what is its first speed?
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 63

Question 49.
A bus travels at a certain average speed for a distance of 75 km and then travels a distance of 90 km at an average speed of 10 km/h more than the first speed. If it takes 3 hours to complete the total journey, find its first speed.
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 64
Question 50.
A truck covers a distance of 150 km at a certain average speed and then covers another 200 km at an average speed which is 20 km per hour more than the first speed. If the truck covers the toal distance in 5 hours, find the first speed of the truck
Solution :

Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 65

Question 51.
Ifx = – 2 is a root of the equation 3x2 + 7x + p = 0, find the values of k so that the roots of the equation x2 + k(4x + k-1) + p = 0 are equal.
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 66

Question 52.
The total cost of a certain length of a piece of cloth is rs 200. If the piece was 5 cm longer and each metre of cloth costs rs 2 less, the cost of the piece would have remained unchanged. How long is the piece and what is its original rate per metre?
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 67

Question 53.
Ifx = 3 is root of the equation x2 -x + k = 0, find the value of p so that the roots of the equation x2 + k(2x + k +2)+ p = 0 are equal.
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 68
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 69

2014

Short Answer Type Questions I [2 Marks]

Question 54.
Solve the quadratic equation 2x2 + ax- a2= 0 for x.
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 70

Question 55.
Find the values of p for which the quadratic equation 4x2 + px + 3 = 0 has equal roots.
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 71
Question 56.
Find the values of k for which the quadratic equation 9x2 – 3kx + k = 0 has equal roots.
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 72

Question 57.
Find the value of p so that the quadratic equation px(x – 3) + 9 = 0 has equal roots.
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 73

Question 58.
Solve for x: √3x2-2√2x-2√3=0
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 74

Short Answer Type Questions lI [3 Marks]

Question 59.
Solve the equation:

Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 75
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 76

Question 60.
Solve the equation:

Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 77
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 78
Question 61.
Solve the equation:

Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 79
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 80
Question 62.
Solve for x:

Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 81
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 82

Question 63.
If- 5 is a root of the quadratic equation 2x2, +px-15 = 0 and the quadratic equation p(x2 + x) + k = 0 has equal roots, find the value of k.
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 83
Question 64.
If 2 is a root of the quadratic equation 3x2 + px – 8 = 0 and the quadratic equation 4x2– 2px + k = 0 has equal roots, find the value of k.
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 84
Question 65.
If 1 is a root of the quadratic equation 3x2 + ax – 2 = 0 and the quadratic equation a(x2 + 6x) – b = 0 has equal roots, find the value of b.
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 85

Long Answer Type Questions [4 Marks]

Question 66.
Find the value of p for which the quadratic equation (2p + l)x2 – (7p + 2)x + (7p – 3) = 0 has equal roots. Also find these roots.
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 86
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 87

Question 67.
Find the values of k for which the quadratic equation (3k + 1)x2 + 2(k + l)x + 1 = 0 has equal roots. Also find these roots.
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 88

Question 68.
Find the values of k for which the quadratic equation (k + 4)x2 + (k + l)x + 1 = 0 has equal roots. Also find these roots.
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 89
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 90

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Question 69.
The difference of two natural numbers is 5 and the difference of their reciprocals is 1/10. find the numbers.
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 91

Question 70.
The difference of two natural numbers is 3 and the difference of their reciprocal is 3/28. find the numbers.
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 92

Question 71.
The difference of two natural numbers is 5 and the difference of their reciprocal is 5/14. find the numbers.
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 93

Question 72.
Solve for x

Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 94
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 95

Question 73.
A motorboat whose speed in still water is 18 km/h, takes 1 hour more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream.
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 96

Question 74.

Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 97
Solve for x
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 98
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 99
Question 75.

Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 100
Solve for x
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 101
Question 76.
The sum of the squares of two consecutive odd numbers is 394. Find the numbers.
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 102

Question 77.

Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 103
Solve for x:
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 104
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 105
Question 78.
The sum of the squares of two consecutive even numbers is 340. Find the numbers.
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 106

Question 79.
Solve for x
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 107

Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 108

Question 80.
The sum of the squares of two consecutive multiples of 7 is 637. Find the multiples.
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 109
Question 81.
Solve for x :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 110

Solution :

Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 111

Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 112

2013

Short Answer Type Questions I [2 Marks]

Question 82.
Solve the following quadratic equation for x; 4√3x2 + 5x -2√3 = 0
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 113

Question 83.
Solve the following forjr. √2x2 + 7x + 5√2= 0
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 114
Question 84.
Solve for x: x2 – (√2 + 1) x + √2 = 0.
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 115

Short Answer Type Questions II [3 Marks]

Question 85.
For what value of k, are the roots of the quadratic equation kx(x – 2) + 6 = 0 equal?
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 116

Question 86.
For what value of k, are the roots of the quadratic equation kx(x – 2√5) + 10 = 0, equal?
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 117

Question 87.
For what value of k, are the roots of the quadratic equation(k + 4)x2 + (k + l)x + 1 = 0, equal?
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 118

Question 88.
For what value of k, are the roots of the quadratic equation (k – 12)x2 + 2(k – 12)x + 2 = 0 equal ?
Solution :

Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 119
Question 89.
For what value of A, are the roots of the quadratic equation y2 + k2 = 2(k + l)y equal?
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 120
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 121

Question 90.
For what value of k, are the roots of the quadratic equation (k – 4)x2 + (k – 4) x + 4 = 0 equal ?
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 122

Question 91.
For what value of k, are the roots of the quadratic equation x2 – (3k – l)x + 2k2 + 2k -11 = 0 equal?
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 123

Question 92.
For what value of m, are the roots of the quadratic equation x2 – 2x (1 + 3m) + 7 (3 + 2m) = 0 equal?
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 124
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 125

Long Answer Type Questions [4 Marks]

Question 93.
Solve for x:

Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 126

Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 127

Question 94.
Sum of the areas of two squares is 400 cm2. If the difference of their perimeters is 16 cm, find the sides of the two squares.
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 128

Question 95.
Solve for x

Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 129
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 130

Question 96.
Solve for x

Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 131
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 132

Question 97.
Solve for x
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 133

Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 134

Question 98.

Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 135
Solve for x:
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 136

Question 99.
The present age of a father is equal to the square of the present age of his son. One year ago, the age of the father was 8 times the age of his son. Find their present ages.
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 137
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 138

Question 100.
Solve the following quadratic equation in variable x : abx2 = (a + b)2 (x -1).
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 139

Short Answer Type Questions I [2 Marks]

Question 101.
Find the value(s) of k so that the quadratic equation 2x2 + kx + 3 = 0 has equal roots.
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 140

Question 102.
Find the value(s) of so that the quadratic equation x2 – 4kx +k = 0 has equal roots.
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 141

Question 103.
Find the value(s) of k so that the quadratic equation 3x2 – 2kx + 12 = 0 has equal roots
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 142

Question 104.
Find the value of m for which the roots of the equation mx(6x + 10) + 25 = 0, are equal.
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 143

Question 105.
Find the value of k for which the roots of the equation kx(3x – 4) + 4 = 0, are equal.
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 144

Question 106.
Find the value of ip’ for which the roots of the equation px(x – 2) + 6 = 0, are equal.
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 145
Question 107.
Find the value ofp for which the roots of the quadratic equation (p + 3) x2 + 2(p+3)x+ 4 = 0 are equal.
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 146
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 147

Question 108.
Find the value of* for which the roots of the quadratic equation (k – 4)x2 + 2(k – 4) x + 2 = 0 are equal.
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 148
Question 109.
Find the value of ‘a’ for which the roots of the quadratic equation 2(a + 5)x2 – (a + 5)x + 1 = 0 are equal.
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 149

Short Answer Type Questions II [3 Marks]

Question 110.
Solve for x: 4x2 – 4ax + (a2 – b2) = 0
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 150

Question 111.
Solve for x: 3x2 – 2-√6x + 2 = 0
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 151

Question 112.
If the sum of two natural numbers is 8 and their product is 15, find the numbers.
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 152

Question 113.
Solve for x: x2– 4ax – b + 4a2= 0.
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 153

Question 114.
Solve for x: x2– 5√5x + 30 = 0.
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 154

Question 115.
Solve for x: x2 + √5 x – 60 = 0
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 155
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 156

Question 116.
Solve for x: 4√3x2 + 5x- 2√3 = 0
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 157

long Answer Type Questions [4 Marks]

Question 117.
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.
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 158
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 159

Question 118.
The sum of two numbers is 9 and the sum of their reciprocals is 1/2. Find the numbers.
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 160

Question 119.
In a flight of 2800 km, an aircraft was slowed down due to bad weather. Its average speed is reduced by 100 km/h and time increased by 30 minutes. Find the original duration of the flight.
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 161
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 162

Question 120.
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.
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 163

Question 121.
A two-digit number is such that the product of its digits is 14. When 45 is added to the number, the digits interchange their places. Find the number.
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 164
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 201
Question 122.
Find two consecutive natural numbers, the sum of whose squares is 145
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 165

2011

Short Answer Type Questions I [2 Marks]

Question 123.
Find the value of p so that the quadratic equation px(x – 3) + 9 = 0 has two equal roots.
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 166

Question 124.
Find the value of & so that the quadratic equation kx(3x -10) + 25 = 0, has two equal roots.
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 167

Question 125.
Find the value of m so that the quadratic equation mx(5x – 6) + 9 = 0 has two equal roots.
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 168

Question 126.
Find the value of m so that the quadratic equation mx(x – 7) + 49 = 0 has two equal roots.
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 169

Question 127.
For what value of k does the quadratic equation (k – 5)x2+ 2(k – 5)x + 2 = 0 have equal roots?
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 170
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 171

Short Answer Type Questions II [3 Marks]

Question 128.
Find the roots of the following quadratic equation. 2√3x2-5x + √3 = 0
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 172

Question 129.
Find the roots of the following quadratic equation: x2– 3√5x + 10 = 0
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 173
Question 130.
Find the roots of the following quadratic equation:√3x2-2√2x-2√3=0
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 174
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 175
Question 131.
Find the roots of the following quadratic equation: 3x2 + 2 √5x — 5 = 0
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 176

Long Answer Type Questions [4 Marks]

Question 132.
A motor boat whose speed is 20 km/h in still water, takes 1 hour more to go 48 km upstream than to return downstream to the same spot. Find the speed of the stream.
Solution :
Let the speed of the stream = km/h
Speed of the boat in still water = 20 km/h
Now, speed of boat during downstream = (20 + x) km/h

Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 177

Question 133.
Find the roots of the equation:

Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 178
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 179

Question 134.
Find the roots of the equation:
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 180
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 181
Question 135.
A train travels 180 km at a uniform speed. If the speed had been 9 km/hour more, it would have taken 1 hour less for the same journey. Find the speed of the train.
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 182

Question 136.
Two water taps together can fill a tank in 6 hours. The tap of larger diameter takes 9 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 183

Question 137.
Solve the following equation for x:

Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 184
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 185

2010

Very Short Answer Type Questions [1 Mark].

Question 138.
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 186
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 187
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 188
Question 139.
If one zero of the polynomial x2 – 4x + 1 is 2 + √3, write the other zero.
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 189

Short Answer Type Questions I [2 Marks]

Question 140.
For what value of k, is -2 a zero of the polynomial 3x2 + 4x + 2k?
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 190

Question 141.
For what value of k, is 3 a zero of the polynomial 2x2 + x + k?
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 191

Question 142.
For what value of It, is 3 a zero of the polynomial x2 + 11x + k?
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 192

Long Answer Type Questions [4 Marks]

Question 143.
The difference of squares of two numbers is 88. If the larger number is 5 less than twice the smaller number, then find the two numbers.
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 193
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 194

Question 144.
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.
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 195
Question 145.
A girl is twice as old as her sister. Four years hence, the product of their ages (in years) will be 160. Find their present ages.
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 196

Question 146.
Solve the following equation for x.
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 197
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 198
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 199
Question 147.
Some students planned a picnic. The total budget for food was rs 2,000. But 5 students failed to attend the picnic and thus the cost of food for each member increased by rs 20. How many students attended the picnic and how much did each student pay for the food.
Solution :
Quadratic Equations Class 10 Maths CBSE Important Questions with Solutions 200

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