Test: Algebraic Identities Quadratic

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This mock test of Test: Algebraic Identities Quadratic for Class 9 helps you for every Class 9 entrance exam. This contains 20 Multiple Choice Questions for Class 9 Test: Algebraic Identities Quadratic (mcq) to study with solutions a complete question bank. The solved questions answers in this Test: Algebraic Identities Quadratic quiz give you a good mix of easy questions and tough questions. Class 9 students definitely take this Test: Algebraic Identities Quadratic exercise for a better result in the exam. You can find other Test: Algebraic Identities Quadratic extra questions, long questions & short questions for Class 9 on EduRev as well by searching above.

QUESTION: 1

What should be subtracted to x²+2x+2 to make it a perfect square?

A.
1
B.
3
C.
2
D.
4

Solution:

By subtracting 1 from 2,you will get 1 that makes the whole square of (x+1)=1

QUESTION: 2

If a + b = 12 and a² + b² = 60, the value of a³ + b³ is:

A.
200
B.
150
C.
216
D.
310

Solution:

QUESTION: 3

One of the factors of (16y² – 1) + (1 -4y)² is

A.
(4y+1)
B.
(4-y)
C.
(4+y)
D.
8y

Solution:

QUESTION: 4

(101)² is equal to

A.
10201
B.
10211
C.
10001
D.
10011

Solution:

(100-1)²= (100)²+(1)²+2×100×1 10000+1+200 =10201

QUESTION: 5

Find the value of (9a + 10b)²

A.
81a + 180 ab + 100b
B.
81a² + 180 ab + 100b²
C.
81a² + 90 ab + 100b²
D.
9a² + 180 ab + 10b²

Solution:

QUESTION: 6

a² + b² + c² – ab – bc – ca equals:

A.
(a - b + c)²
B.
(a - b - c)²
C.
(a + b + c)²
D.

Solution:

= ( a² + b² + c² - ab - bc - ca )

By multiplying it by 2 and dividing it by 2.

= 2 ( a² + b² + c² - ab - bc - ca ) ÷ 2

= ( 2a² + 2b² + 2c² - 2ab - 2bc - 2ca ) ÷ 2

= ( a² + a² + b² + b² + c² + c² - 2ab - 2bc - 2ca ) ÷ 2

= ( a² + b² - 2ab + b² + c² - 2bc + a² + c² - 2ca ) ÷ 2

= [ ( a - b )² + ( b - c )² + ( a - c )² ] ÷ 2

Now , whatever is the value of ( a - b ) , ( b - c ) and ( a - c ) but its square will be always positive, and 2 is also a positive number.

So, the sum of ( a - b )², ( b - c )² and ( a - c )² will be a positive number and if a positive number is divided by a positive number then the result is also a positive number.

So, it is a positive number,hence it can't be a negative number.

QUESTION: 7

Evaluate 98 x 102.

A.
9899
B.
9988
C.
9996
D.
9898

Solution:

(100+2)×(100-2). [(a+b)(a-b)=a^2-b^2
100^2 - 2^2
10000 - 4
9996

QUESTION: 8

a² + b² is equal to

A.
(a + b)² – 2ab
B.
(a – b)² – 2xy
C.
(a + b)² – 2xy
D.
(a – b)² + 4 ab

Solution:

QUESTION: 9

Solve the equation x² + 6x - 7 = 0

A.
x = -5, x = -1
B.
x = -6, x = 7
C.
x = 6, x = -1
D.
x = 1, x = -7

Solution:

QUESTION: 10

If a - b = 3 and a² + b² = 29, find the value of ab.

A.
10
B.
12
C.
15
D.
18

Solution:

2ab = (a² + b²) - (a - b)²
= 29 - 9 = 20
⇒ ab = 10.

QUESTION: 11

What should be added to x²+2x+0.5 to make it a perfect square?

A.
0.1
B.
0.4
C.
0.6
D.
0.5

Solution:

QUESTION: 12

The missing figure in the expression
(5p +…)² = ….+ 40 pq + 16q² are:

A.
4q and 25p²
B.
4q and 25p
C.
16p and 5p²
D.
4q and 5p²

Solution:

QUESTION: 13

Factorise: x⁴-1

A.
(x²+1) (x – 1) (x+1)
B.
(x²+1)(x – 1)(x-1)
C.
(x²-1) (x -1)(x+1)
D.
(x²+1) (x +1)(x+1)

Solution:

QUESTION: 14

Factorise: x²– 81

A.
(x+9)(x+9)
B.
(x-9)(x-9)
C.
(x-9)(x+9)
D.
(x-81)(x+1)

Solution:

QUESTION: 15

What is the product of (x+a) and (x+b)?

A.
x² + (a+b)x + ab
B.
x² + (a+b)x - ab
C.
x² + (a+b)x - ab
D.
x²+ (a-b)x + ab

Solution:

QUESTION: 16

The value of 101 x 99 is

A.
8998
B.
1111
C.
9889
D.
9999

Solution:

(100+1)×(100 - 1) it is the formula of a²-b² so, (100)² -(1)² = 10000-1 = 9999.

QUESTION: 17

If 2x + 3y = 12 and xy = 5, find the value of 4x² + 9y².

A.
67
B.
98
C.
56
D.
84

Solution:

QUESTION: 18

Find the value of (109)²

A.
18181
B.
11881
C.
11181
D.
18811

Solution:

QUESTION: 19

(99)² is equivalent to

A.
8801
B.
9801
C.
9001
D.
9881

Solution:

QUESTION: 20

The expansion of (2a – 3b + 5c)².

Solution:

The expansion of (2a - 3b + 5c)² -: (2a)² + (- 3b)² + (5c)² + 2× 2a × (-3b) + 2× (-3b)× 5c + 2× 5c + 2a. = 4a² + 9b² + 25c² - 12ab - 30bc + 20ac

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Test: Algebraic Identities Quadratic

20 Questions MCQ Test Mathematics (Maths) Class 9 | Test: Algebraic Identities Quadratic

What should be subtracted to x²+2x+2 to make it a perfect square?

If a + b = 12 and a² + b² = 60, the value of a³ + b³ is:

One of the factors of (16y² – 1) + (1 -4y)² is

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20 Questions MCQ Test Mathematics (Maths) Class 9 | Test: Algebraic Identities Quadratic

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