Basic Algebra MCQs with Answers (FREE)

1: Simplify the following equation and choose the result from the given options: √(x3y3/a6b5)

A. (x2y2√b)/[a3b3√(xy)]

B. (x2y3√b)/[a3b3√(xy)]

C. (x2y2√b)/[a3b2√(xy)]

D. (x2y2)/[a3b3√(xy)]

2: Which of the following is equal to 1/(√3+2i)?

A. ( √3-2i)/7

B. ( √3-2i)

C. 7( √3-2i)

D. 14( √3-2i)

3:

Simplify the following equation using its LCM:

a/xp + b/yq + c/zr=0

A.

(cxpyq + axpyq + bxpzr)/(xpyqzr)=0

B.

(cxpyq + ayqzr + bxpzr)/(xpyqzr)=0

C.

(cxpyq + ayqzr + bxpyq)/(xpyqzr)=0

D.

(ayqzr + czryq + bxpzr)/(xpyqzr)=0

4: What is the cube of (ax + by) for a=2 and b=3?

A. 8x3 + 27y3 + 12x2y + 54xy2

B. 8x3 + 27y3 + 6xy(2x + 3y)

C. 8x3 + 27y3 + 6x2y + 6xy2

D. 8x3 + 27y3 + 36x2y + 54xy2

5: Simplify (5i+4)(2i-3) and choose the answer from the options given below.

A. -(22+7i)

B. -(22-7i)

C. 22+7i

D. -22+7i

6:

Select the correct answer from the options given below that is equal to:

√(81×36)

A.

9√64

B.

12√9

C.

18√9

D.

√16

7:

Find the value in the following equation:

3x/4y=?/xy

A.

3x/4

B.

3x2/4x

C.

9x2/12

D.

9x2/4

8:

One number is 4/5th of the another number. The sum of the reciprocals of the two numbers is 45. Find the two numbers.

One number is 4/5thof the another number. The sum of the reciprocals of the two numbers is 45. Find the two numbers.

A.

±18

B.

±64

C.

±8

D.

±24

9:

What is the result after solving the following expression:

4 × 63 + 24 / 8 - 4 × 29 + 65 / 10

A.

125

B.

144.5

C.

145.5

D.

145.6

10: Find the square of (3x + 4y + 2z).

A. 9x2 + 16y2 + 4z2 + 24xy + 8yz + 12xz

B. 9x2 + 16y2 + 4z2 + 12xy + 16yz + 24xz

C. 9x2 + 16y2 + 4z2 + 24xy + 16yz + 12xz

D. 9x2 + 16y2 + 4z2 + 12xy + 16yz + 24xz

11:

Which of the following equations on expanding will result in the given equation:

15ax + 9a + 6ay + 10x + 6 + 4y + 5bx + 3b + 2by

A.

(3a + 3 + 5b)(5x + 2 + 2y)

B.

(3a + 3 + b)(5x + 1 + 2y)

C.

(5a + 3 + 5b)(3x + 1 + 2y)

D.

(3a + 2 + b)(5x + 3 + 2y)

12:

Find the correct set of answers for the following expressions:

I) a + ( b × 4 )

II) a× ( b + 3 )

III) ( a× b)+ 3

given that a = 14 and b = 23.

A.

106,304,507

B.

106,362,325

C.

140,364,107

D.

106,364,325

13: What will be the value of the expression 2a5×3a2 for a=2?

A. 456

B. 768

C. 786

D. 678

14:

Evaluate the following expression and choose the correct answer from the options given below:

( 4× 5 ) / 8 + 2 - ( 3 / 4 )

A.

3

B.

3.75

C.

3.25

D.

3

15: Ron bought 4 books B1, B2, B3 and B4 for $450. The price of two books, B1 and B3 is the same. The price of B2 is twice the price of B1. Find the price of book B4 if the price of Book B1 is $75.

A. 70

B. 150

C. 100

D. 50

16:

Evaluate the expression:

3a - 4b + 6c + a - 2b - 2a + 3b - 4c + a + 2c

A.

3a + 3b + 4c

B.

2a - 3b - 4c

C.

3a - 4b + 4c

D. 3a - 3b + 4c

E.

17: What will be the answer after the negation of 365, 450 - 472, - (340 - 288 ), and ( 689 - 340 ) respectively?

A. - 365, - 22,-52,-349

B. -365,22, - 52, - 349

C. - 365,22,52,349

D. - 365,22,52, - 349

18:

Check whether the equation is valid or not:

5a - 2b + 6c = 3a + 30

for a = 2,b = 2,c = 5.

A.

Yes

B.

No

19:

What will be the value after solving the expression:

4 × 1 / 4 + 1 / 4a

for a = 2 ?

A.

1.25

B.

1.5

C.

1.125

D.

1.725

20: Find a + b for a = 21.5 and b = 32.9.

A. 54.3

B. 54.34

C. 54.4

D. 53.4

21:

Find the value of x from the given equation:

ax2+ 2bx2+ √cx2=2080 where a=1, b=2,c=0.04

A.

√30

B.

±20

C.

√40

D.

±40

22:

Find the solution to the following equation:

9a + 4bx + 3cy = 2bx2 + 2cy

for x = 2,y = 4.

A.

9a = - 4c

B.

9a = 4c

C.

9a + 2b + 4c = 0

D.

9a - 2b + 2c = 0

23: Symond deals in diamonds. He bought 3 diamonds for $4500. The price of the first diamond is half the price of the second diamond. The price of the second diamond is 1/3rd of the price of the third diamond. Find the cost of the first, second, and third diamond respectively.

A. 550, 950, 3000

B. 450, 1500, 2550

C. 500, 1000, 3000

D. 400, 1100, 3000

24: Check if 72/105 is equal to 2/3

A. Yes

B. No

25: Find the value of x from the equation (2x + 3)2=36.

A. -1.5, 4.5

B. -1.5, 2.5

C. 2.5, -4.5

D. 1.5, -4.5

26:

Simplify the following equation:

2/(x-3) + 3/(x-4) and also find the value for x=2.

A.

(x-7)/(x2-4x + 12), Value of expression at x=2 is 3

B.

(x-7)/(x2-7x + 12), Value of expression at x=2 is -2.5

C.

(x-7)/(x2-7x + 12), Value of expression at x=2 is 1.5

D.

(5x-17)/(x2-7x + 12), Value of expression at x=2 is -3.5

27: Which of the following is the correct inverse of 356a + 489b = 2?

A. 356a = 2 + 489b

B. 489b = -2 + 356a

C. 489b = -356a - (-2)

D. -2 = -356a + (-(-489b))

28: Which of the following represents the square of (3x + 2y)?

A. 6xy + 9x2 + 4y2

B. 12xy + 9x2 + 8y2

C. 12xy + 9x2 + 4y2

D. 9x2 + 4y2 + 6xy

29: Sandy had some money with her. She saved ½ of the money, spent 1/3rd of the remaining money on shopping, spent 1/4th of the remaining money for paying electricity bill, and at the end, she was left with $60. Find the money that she had initially before spending or saving.

A. 300

B. 500

C. 200

D. 240

30:

What is the number of factors in the third term of the following expression:

a + bx+ ( c + d)× 3

A.

2

B.

3

C.

4

D.

1

31:

Find the value of x from the following equation:

5x3=625

A.

5

B.

25

C.

125

D.

15

32:

What is the value of the expression:

- 4 × 5 + ax / bx2 - 55 / ( - 11 )

for a = 2, x = 5, b = 1?

A.

14.4

B.

- 14.8

C.

- 14.6

D.

14.6

33: Solve a3(1 + a) for a=2 and also find the correct form of distributive rule for the given expression. The solution and the distributive form are given in the options respectively.

A. 8, a4 + a3

B. 8, a + a4

C. 24, a + a4

D. 24, a3 + a4

34: Find the value of 134.

A. 28564

B. 28561

C. 28651

D. 28971

35:

Find the value of the following expressions respectively:

- 111/ 3, - 135/ - 5, 456 / - 8

A.

37,27, - 57

B.

- 37,27, - 57

C.

35, - 27,57

D.

- 37,29, - 57

36:

Find all the integer values of x for which the following inequality is satisfied.

|x - 1| > 4

A.

x > 5

B.

x ≤ 5

C.

x > 5 and x < - 4

D.

x > 5 and x ≤ - 4

37: Find the square root of √(-256x2) for x=2.

A. 16i

B. -32i

C. 32i

D. 16

38:

What will be the value of the following expressions respectively?

16 / | - 4| , - 16 / |4| , 3 / | - 2|

A.

- 4,4,1.5

B.

4, - 4,1.5

C.

4, - 4, - 1.5

D.

- 4,4,1.5

39:

Find the value of x from the equation:

3x + 2y + 7 = 0

where y = 2.2.

A.

- 3.8

B.

3.8

C.

- 4.62

D.

4.62

40:

Find the value of x from the equation:

3x/4 + 2x/3=51

A.

12

B.

36

C.

17

D.

34

41:

Find the values of x from the following equation:

i23x+x2+3=31 where i is a complex number.

A.

7,-4

B.

-7,4

C.

-4,-7

D.

4,7

42: The sum of the age of person A and twice the age of person B is greater than the age of Person C. Find the inequality that depicts the given statement.

A. C - 2B > A

B. C - A > 2B

C. A + ( - 2B)< C

D. C - 2B < A

43:

What will be the result after solving the fraction:

(-3x2/4y-3)-3

A.

-64/(27x6y9)

B.

64/(27x6y9)

C.

-64/(9x6y9)

D.

-64/(27x-6y9)

44: 2/3rd of a number is added to 3/5th of the same number and the result is equal to 6. Find the approximate value of the number.

A. 4.74

B. 4.54

C. 3.82

D. 5.53

45: What is the square root of 2401?

A. 51

B. 49

C. 39

D. 41

46: Evaluate: √(3×20×12×5)

A. 120

B. 40

C. 60

D. 80

47: Which of the following is equal to (12x) / (√3√4), for x=1/2?

A. √12/4

B. (√3√4)/2

C. √3√4

D. ( √3√4)/4

48: Find the cube of (1.0x + 1.0y + 3.0z).

A. (1.0x + 1.0y + 3.0z)(x2 + y2 + 9z2 + 6xy + 2yz + 6xz)

B. (x + y + 3z)(x2 + y2 + 9z2 + 2xy + 6yz + 6xz)

C. (x + y + 3z)(x2 + y2 + 9z2 + 6xy + 6yz + 6xz)

D. (1.0x + 1.0y + 3.0z)(x2 + y2 + 9z2 + 2xy + 2yz + 6xz)

49: Find the value of -(-11)3

A. -1211

B. 1331

C. -1331

D. -1131

50:

How many terms are there in the following expression:

ax + (b + 2y)+(c+9)

A.

3

B.

1

C.

2

D.

5

Basic Algebra MCQs