EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Quadratic Equations
Grade : SSC Grade X
License : Non Commercial Use
Question
1
1.
A number is of two digits. The digit in unit's place is the square of the digit in ten's place. The number formed by reversing the digits exceeds twice the number by 15 . Find the number
(i)
40
(ii)
41
(iii)
36
(iv)
39
(v)
38
Question
2
2.
Solve :
18
x
2
+
19
a
b
x
+
5
a
2
b
2
= 0
(i)
−
a
b
4
,
−
5
a
b
11
(ii)
a
b
2
,
−
a
b
3
(iii)
−
3
a
b
2
,
−
7
a
b
9
(iv)
−
a
b
2
,
−
5
a
b
9
(v)
−
a
b
,
−
5
a
b
7
Question
3
3.
Solve the quadratic equation
x
−
5
=
36
x
(i)
(
11
,
-6
)
(ii)
(
9
,
-4
)
(iii)
(
10
,
-4
)
(iv)
(
10
,
-5
)
(v)
(
11
,
-5
)
Question
4
4.
The sum of the numerator and denominator of a fraction is
21
.
If
9
is added to both the numerator and denominator,
the fraction is increased by
9
34
. Find the fraction
(i)
4
17
(ii)
4
15
(iii)
6
17
(iv)
17
4
(v)
2
17
Question
5
5.
Solve :
35
x
2
b
2
+
34
a
x
b
+
8
a
2
= 0
(i)
−
4
a
5
b
,
−
6
a
7
b
(ii)
−
2
a
5
b
,
−
4
a
7
b
(iii)
−
2
a
3
b
,
−
4
a
5
b
(iv)
−
2
a
7
b
,
−
4
a
9
b
(v)
0
,
−
2
a
7
b
Question
6
6.
Find two natural numbers which differ by 14 and the sum of whose squares is 2020
(i)
(
23
,
37
)
(ii)
(
26
,
41
)
(iii)
(
24
,
38
)
(iv)
(
25
,
39
)
(v)
(
21
,
35
)
Question
7
7.
Solve :
63
x
2
+
52
a
2
b
x
+
5
a
4
b
2
= 0
(i)
a
2
b
9
,
−
3
a
2
b
7
(ii)
−
a
2
b
3
,
−
a
2
b
(iii)
−
a
2
b
11
,
−
5
a
2
b
9
(iv)
−
a
2
b
9
,
−
5
a
2
b
7
(v)
−
a
2
b
7
,
−
a
2
b
Question
8
8.
Find the roots of the quadratic equation
(
36
x
2
+
6
x
−
12
)
=
0
(i)
(
1
4
,
-2
)
(ii)
(
1
2
,
(
-2
3
)
)
(iii)
(
1
4
,
(
-2
3
)
)
(iv)
(
3
2
,
-2
)
(v)
(
3
2
,
(
-4
3
)
)
Question
9
9.
Find the roots of the quadratic equation
(
36
x
2
+
12
x
)
=
0
(i)
(
1
,
-1
)
(ii)
(
1
,
(
-1
3
)
)
(iii)
(
0
,
(
-1
3
)
)
(iv)
(
2
,
-1
)
Question
10
10.
Solve :
(
x
−
9
)
(
x
−
8
)
+
(
x
−
6
)
(
x
−
4
)
=
29
21
(i)
(
12
,
86
15
)
(ii)
(
13
,
6
)
(iii)
(
10
,
6
)
(iv)
(
9
,
74
13
)
(v)
(
11
,
76
13
)
Question
11
11.
The sum of the squares of two consecutive odd numbers is 514. Find the numbers
(i)
(-17)
,
(-15)
or
17
,
15
(ii)
(-19)
,
(-18)
or
19
,
18
(iii)
(-18)
,
(-16)
or
18
,
16
(iv)
(-14)
,
(-12)
or
14
,
12
(v)
(-16)
,
(-14)
or
16
,
14
Question
12
12.
Solve :
(
4
x
+
2
)
(
3
x
+
1
)
=
(
25
x
+
2
)
(
18
x
+
1
)
(i)
(
3
,
5
)
(ii)
(
-2
,
0
)
(iii)
(
-1
,
2
)
(iv)
(
0
,
-3
)
(v)
(
0
,
3
)
Question
13
13.
Find the discriminant of the quadratic equation
(
x
2
−
2
x
+
1
)
=
0
(i)
3
(ii)
-1
(iii)
0
(iv)
1
(v)
-2
Question
14
14.
Find the number which is less than its square by 272
(i)
14
(ii)
19
(iii)
17
(iv)
16
(v)
18
Question
15
15.
A stream flows from A to B, a distance of 9.00 km. A man who can row in still water at 5.00 kmph, can row up and down in 5.62 hr . What is the speed of the stream?
(i)
3.00 kmph
(ii)
5.00 kmph
(iii)
1.00 kmph
(iv)
4.00 kmph
(v)
2.00 kmph
Question
16
16.
Solve :
48
x
2
−
2
a
x
−
a
2
= 0
(i)
−
a
10
,
a
8
(ii)
−
3
a
8
,
−
a
6
(iii)
a
8
,
a
2
(iv)
−
a
8
,
a
6
(v)
−
a
6
,
a
4
Question
17
17.
Find the roots of the quadratic equation
(
x
2
+
15
x
+
56
)
=
0
(i)
(
-6
,
-9
)
(ii)
(
-5
,
-10
)
(iii)
(
-7
,
-8
)
(iv)
(
-6
,
-8
)
(v)
(
-5
,
-9
)
Question
18
18.
Find the discriminant of the quadratic equation
(
−
12
x
2
−
35
x
−
41
)
=
0
(i)
-740
(ii)
-744
(iii)
-745
(iv)
-743
(v)
-742
Question
19
19.
Twice the square of a number exceeds 5 times the number by 462. Find the number
(i)
(-11)
(ii)
(-14)
(iii)
(-17)
(iv)
(-13)
(v)
(-15)
Question
20
20.
The denominator of a fraction exceeds the numerator by
1
.
The square of the fraction is equal to
256
289
. Find the fraction
(i)
16
19
(ii)
16
15
(iii)
14
17
(iv)
16
17
(v)
18
17
Question
21
21.
If the difference of two numbers is 8 and their product is 273, find the numbers
(i)
(-13)
,
(-21)
or
13
,
21
(ii)
(-14)
,
(-22)
or
14
,
22
(iii)
(-10)
,
(-19)
or
10
,
19
(iv)
(-16)
,
(-23)
or
16
,
23
(v)
(-12)
,
(-20)
or
12
,
20
Question
22
22.
57 is divided into two parts such that the sum of their reciprocals is
57
770
.
Find the two parts
(i)
(
34
,
23
)
(ii)
(
37
,
20
)
(iii)
(
33
,
24
)
(iv)
(
36
,
21
)
(v)
(
35
,
22
)
Question
23
23.
The sum of the ages of a father and his son is 42 years whereas two years ago, the product of their ages was 105. Find the current ages of the son and the father.
(i)
5 years , 37 years
(ii)
6 years , 36 years
(iii)
3 years , 39 years
(iv)
7 years , 35 years
(v)
4 years , 38 years
Question
24
24.
The product of two consecutive numbers is 72. Find the numbers
(i)
8 , 9 or -8,-9
(ii)
6 , 6 or -6 , -6
(iii)
10 , 12 or -10 , -12
(iv)
7 , 8 or -7 , -8
(v)
9 , 10 or -9 , -10
Question
25
25.
Solve :
2
(
x
−
2
)
−
5
(
−
x
−
3
)
=
3
(i)
2
√
5
,
(
−
3
√
5
)
(ii)
2
√
3
,
(
−
3
√
3
)
(iii)
2
√
4
,
(
−
3
√
4
)
(iv)
2
√
2
,
(
−
3
√
2
)
(v)
2
,
(
−
3
)
Assignment Key
1) (iv)
2) (iv)
3) (ii)
4) (i)
5) (ii)
6) (iii)
7) (iv)
8) (ii)
9) (iii)
10) (v)
11) (i)
12) (v)
13) (iii)
14) (iii)
15) (i)
16) (iv)
17) (iii)
18) (iv)
19) (ii)
20) (iv)
21) (i)
22) (v)
23) (i)
24) (i)
25) (v)
