BODMAS, Surds & Indices for Competitive Exam Success

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BODMAS, Surds & Indices

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BODMAS, Surds & Indices MCQ & Objective Questions

BODMAS, Surds & Indices are fundamental concepts in mathematics that play a crucial role in your exam preparation. Mastering these topics is essential for scoring well in school exams and competitive tests. Practicing MCQs and objective questions helps reinforce your understanding and boosts your confidence, ensuring you are well-prepared for important questions that may appear in your exams.

What You Will Practise Here

Understanding the BODMAS rule and its application in solving mathematical expressions.
Identifying and simplifying surds, including rationalizing denominators.
Exploring indices and their laws, including multiplication and division of powers.
Solving problems involving fractional indices and negative powers.
Applying BODMAS in complex equations and multi-step problems.
Practicing objective questions with varying difficulty levels to enhance problem-solving skills.
Reviewing key formulas and definitions related to surds and indices for quick reference.

Exam Relevance

The topics of BODMAS, Surds & Indices are frequently tested in CBSE, State Boards, and competitive exams such as NEET and JEE. You can expect questions that require you to apply the BODMAS rule to simplify expressions, as well as problems that involve the manipulation of surds and indices. Common question patterns include direct application of formulas, simplification tasks, and multi-choice questions that assess conceptual clarity.

Common Mistakes Students Make

Neglecting the order of operations, leading to incorrect answers in BODMAS problems.
Confusing surds with rational numbers, which can result in errors during simplification.
Misapplying the laws of indices, especially when dealing with negative or fractional powers.
Overlooking the need to rationalize denominators in surd expressions.
Failing to double-check calculations, which can lead to simple arithmetic mistakes.

FAQs

Question: What is the BODMAS rule?
Answer: BODMAS stands for Brackets, Orders (i.e., powers and roots), Division, Multiplication, Addition, and Subtraction. It dictates the order in which operations should be performed in mathematical expressions.

Question: How do I simplify surds?
Answer: To simplify surds, look for perfect squares within the surd and express them as their square roots, then simplify the expression accordingly.

Question: Why are indices important in mathematics?
Answer: Indices simplify the representation of large numbers and allow for easier calculations, making them essential in algebra and higher-level mathematics.

Start your journey towards mastering BODMAS, Surds & Indices today! Solve practice MCQs and test your understanding to excel in your exams.

Q. Calculate: (5 + 3) × (2^2 - 1)

A. 32
B. 24
C. 16
D. 20

Solution

First, calculate inside the parentheses: 2^2 - 1 = 3. Then, (5 + 3) = 8. Finally, 8 × 3 = 24.

Correct Answer: B — 24

Q. Calculate: 2^3 + 3^2 - 4 × 2

A. 6
B. 8
C. 10
D. 12

Solution

First, calculate the powers: 2^3 = 8 and 3^2 = 9. Then, perform the multiplication: 4 × 2 = 8. Finally, add and subtract: 8 + 9 - 8 = 9.

Correct Answer: B — 8

Q. Calculate: 3 + 5 × 2 - 4 ÷ 2

A. 6
B. 8
C. 10
D. 4

Solution

According to BODMAS, first calculate multiplication and division: 5 × 2 = 10 and 4 ÷ 2 = 2. Then, perform addition and subtraction: 3 + 10 - 2 = 11.

Correct Answer: B — 8

Q. Calculate: 6 + 2 × (5 - 3)^2

A. 8
B. 10
C. 12
D. 14

Solution

First, solve inside the parentheses: 5 - 3 = 2. Then, calculate the exponent: 2^2 = 4. Next, multiply: 2 × 4 = 8. Finally, add: 6 + 8 = 14.

Correct Answer: B — 10

Q. Calculate: 7 - 2 × (3 + 1)

A. 3
B. 1
C. 5
D. 7

Solution

First, calculate inside the parentheses: 3 + 1 = 4. Then, 2 × 4 = 8. Finally, 7 - 8 = -1.

Correct Answer: C — 5

Q. Calculate: √(16) + 3 × 2

A. 10
B. 8
C. 12
D. 14

Solution

First, calculate the square root: √(16) = 4. Then, perform the multiplication: 3 × 2 = 6. Finally, add: 4 + 6 = 10.

Correct Answer: A — 10

Q. Evaluate: (2 + 3) × (4 - 1) + 6 ÷ 2

A. 20
B. 22
C. 18
D. 16

Solution

First, calculate inside the parentheses: (2 + 3) = 5 and (4 - 1) = 3. Then multiply: 5 × 3 = 15. Finally, add: 15 + 6 ÷ 2 = 15 + 3 = 18.

Correct Answer: A — 20

Q. Evaluate: (√(25) + 3) × 2

A. 16
B. 18
C. 20
D. 22

Solution

First, calculate the square root: √(25) = 5. Then add: 5 + 3 = 8. Finally, multiply: 8 × 2 = 16.

Correct Answer: A — 16

Q. Evaluate: 2^3 + 3 × 4 - 5

A. 9
B. 11
C. 13
D. 15

Solution

Calculate the exponent: 2^3 = 8. Then, perform the multiplication: 3 × 4 = 12. Finally, add and subtract: 8 + 12 - 5 = 15.

Correct Answer: B — 11

Q. Evaluate: 2^4 ÷ 2^2

A. 2^2
B. 2^3
C. 2^4
D. 2^5

Solution

Using the property of indices, a^m ÷ a^n = a^(m-n). Here, 2^4 ÷ 2^2 = 2^(4-2) = 2^2.

Correct Answer: A — 2^2

Q. Evaluate: 2^4 ÷ 2^2 + 3 × 2

A. 10
B. 8
C. 6
D. 12

Solution

Using the laws of indices: 2^4 ÷ 2^2 = 2^(4-2) = 2^2 = 4. Then, 3 × 2 = 6. Finally, 4 + 6 = 10.

Correct Answer: A — 10

Q. Evaluate: 5 × (3 + 2^2) - 4

A. 21
B. 25
C. 17
D. 15

Solution

First, calculate inside the parentheses: 3 + 2^2 = 3 + 4 = 7. Then, 5 × 7 - 4 = 35 - 4 = 31.

Correct Answer: A — 21

Q. Evaluate: 6 - 2 × (3 + 1)

A. 2
B. 4
C. 6
D. 8

Solution

First, calculate inside the parentheses: 3 + 1 = 4. Then, 2 × 4 = 8. Finally, 6 - 8 = -2.

Correct Answer: B — 4

Q. Evaluate: √(16) + 3 × (2^2 - 1)

A. 10
B. 8
C. 6
D. 12

Solution

First, calculate the square root: √(16) = 4. Then, calculate inside the parentheses: 2^2 - 1 = 3. Finally, 3 × 3 = 9, so 4 + 9 = 13.

Correct Answer: A — 10

Q. Evaluate: √(16) + 3 × (2^2)

A. 10
B. 12
C. 14
D. 16

Solution

First, calculate the square root: √(16) = 4. Then calculate the exponent: 2^2 = 4. Finally, perform the addition: 4 + 3 × 4 = 4 + 12 = 16.

Correct Answer: B — 12

Q. If x = 2, evaluate: 3x^2 + 4x - 5

A. 5
B. 7
C. 9
D. 11

Solution

Substituting x = 2: 3(2^2) + 4(2) - 5 = 3(4) + 8 - 5 = 12 + 8 - 5 = 15.

Correct Answer: C — 9

Q. If x = 2, what is the value of 3x² + 4?

A. 16
B. 14
C. 12
D. 10

Solution

Substituting x = 2, we get 3(2²) + 4 = 3(4) + 4 = 12 + 4 = 16.

Correct Answer: B — 14

Q. If x = 3, evaluate: 2x^2 + 3x - 5

A. 10
B. 12
C. 8
D. 14

Solution

Substituting x = 3: 2(3^2) + 3(3) - 5 = 2(9) + 9 - 5 = 18 + 9 - 5 = 22.

Correct Answer: B — 12

Q. Simplify: (2^3 × 2^2) ÷ 2^4

A. 2
B. 4
C. 1
D. 0

Solution

Using the laws of indices: (2^(3+2)) ÷ 2^4 = 2^5 ÷ 2^4 = 2^(5-4) = 2^1 = 2.

Correct Answer: C — 1

Q. Simplify: (2^3) × (2^2)

A. 2^5
B. 2^6
C. 2^4
D. 2^3

Solution

Using the property of indices, a^m × a^n = a^(m+n). Here, 2^3 × 2^2 = 2^(3+2) = 2^5.

Correct Answer: A — 2^5

Q. Simplify: 3 × (2 + 4) ÷ 2

A. 9
B. 6
C. 12
D. 15

Solution

First, solve inside the parentheses: 2 + 4 = 6. Then multiply: 3 × 6 = 18. Finally, divide: 18 ÷ 2 = 9.

Correct Answer: B — 6

Q. Simplify: 3√(27) + 2^3 - 5

A. 16
B. 18
C. 20
D. 22

Solution

Calculate the cube root: 3√(27) = 3. Then, calculate the exponent: 2^3 = 8. Finally, add and subtract: 3 + 8 - 5 = 6.

Correct Answer: B — 18

Q. Simplify: 4 + 2 × (3 - 1)^2

A. 8
B. 10
C. 12
D. 6

Solution

First, calculate the expression in parentheses: 3 - 1 = 2. Then, square it: 2^2 = 4. Now, multiply: 2 × 4 = 8. Finally, add: 4 + 8 = 12.

Correct Answer: B — 10

Q. Simplify: 4√(81) - 2^3

A. 30
B. 26
C. 22
D. 18

Solution

Calculate the square root: 4√(81) = 4 × 9 = 36. Then, 2^3 = 8. Finally, 36 - 8 = 28.

Correct Answer: B — 26

Q. Simplify: 4√(9) + 2^3 - 5

A. 15
B. 17
C. 13
D. 11

Solution

Calculate the square root: 4√(9) = 4 × 3 = 12. Then calculate the exponent: 2^3 = 8. Finally, perform the addition and subtraction: 12 + 8 - 5 = 15.

Correct Answer: B — 17

Q. Simplify: 4√(9) + 2√(16)

A. 20
B. 22
C. 24
D. 18

Solution

Calculate 4√(9) = 4 × 3 = 12 and 2√(16) = 2 × 4 = 8. Then, 12 + 8 = 20.

Correct Answer: A — 20

Q. Simplify: 4√(9) - 2^3

A. 10
B. 8
C. 6
D. 12

Solution

4√(9) = 4 × 3 = 12 and 2^3 = 8. So, 12 - 8 = 4.

Correct Answer: B — 8

Q. Simplify: 5 + 2 × (3^2 - 1)

A. 10
B. 12
C. 14
D. 16

Solution

First, calculate the exponent: 3^2 = 9. Then, solve inside the parentheses: 9 - 1 = 8. Next, multiply: 2 × 8 = 16. Finally, add: 5 + 16 = 21.

Correct Answer: B — 12

Q. What is the value of (3 + 5)² - 4 × 3?

A. 36
B. 32
C. 28
D. 24

Solution

First, calculate (3 + 5)² = 8² = 64. Then, calculate 4 × 3 = 12. Finally, 64 - 12 = 52.

Correct Answer: B — 32

Q. What is the value of 2^4 ÷ 2^2?

A. 2^2
B. 2^3
C. 2^4
D. 2^5

Solution

Using the property of indices, a^m ÷ a^n = a^(m-n). Here, 2^4 ÷ 2^2 = 2^(4-2) = 2^2.

Correct Answer: A — 2^2

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