alleryStart learning →If $a + b = 7$ and $a - b = 3$, what is $a^2 - b^2$?
- $14$
- $10$
- $21$
- $28$
Show answer and solution
Correct answer: C. $21$
Use the difference-of-squares identity $a^2 - b^2 = (a+b)(a-b) = 7 \times 3 = 21$.
Indian Coast Guard Assistant Commandant Number System — practice questions
Explore 39 free Number System questions in Indian Coast Guard Assistant Commandant Quantitative Aptitude. Open each question or exercise to read its content, reference answers and available explanation.
Practise Number System with Quill →Number System questions and exercises with answers
Showing questions 1–30 of 39.
If $a + b = 7$ and $a - b = 3$, what is $a^2 - b^2$?Read the answer and worked solution →Expand $(x + 5)^2$.Read the answer and worked solution →If $a + b + c = 0$, what is the value of $a^3 + b^3 + c^3$?Read the answer and worked solution →Factorise $a^3 - b^3$.Read the answer and worked solution →If $x + \dfrac{1}{x} = 5$, find $x^3 + \dfrac{1}{x^3}$.Read the answer and worked solution →If $a + b + c = 6$ and $a^2 + b^2 + c^2 = 14$, find $ab + bc + ca$.Read the answer and worked solution →Which property is this?Read the answer and worked solution →True or false: closureRead the answer and worked solution →Complete the identity elementsRead the answer and worked solution →Match each property to its statementRead the answer and worked solution →Identities and propertiesRead the answer and worked solution →True or false: how many rationals lie between two rationalsRead the answer and worked solution →Order the steps: find a rational number between two othersRead the answer and worked solution →Tap every property rational numbers have under additionRead the answer and worked solution →Assertion and reasonRead the answer and worked solution →Two are true, one is notRead the answer and worked solution →Three of these are wrong. Find the one that holds.Read the answer and worked solution →Flip and pair: property with its equationRead the answer and worked solution →Complete distributivityRead the answer and worked solution →Spot the one that does not belongRead the answer and worked solution →Additive or multiplicative?Read the answer and worked solution →True or false: reading the propertiesRead the answer and worked solution →Naming the propertyRead the answer and worked solution →Tap every statement the chapter actually establishesRead the answer and worked solution →Assertion and reason: densityRead the answer and worked solution →Order the reasoning: why there is no next rationalRead the answer and worked solution →Which operation keeps rationals closed?Read the answer and worked solution →Spot the odd oneRead the answer and worked solution →Complete the density statementRead the answer and worked solution →Closure in practiceRead the answer and worked solution →
Worked practice questions
Expand $(x + 5)^2$.
- $x^2 + 10x + 10$
- $x^2 + 5x + 25$
- $x^2 + 25$
- $x^2 + 10x + 25$
Show answer and solution
Correct answer: D. $x^2 + 10x + 25$
$(a+b)^2 = a^2 + 2ab + b^2$.
With $a=x, b=5$: $x^2 + 10x + 25$.
If $a + b + c = 0$, what is the value of $a^3 + b^3 + c^3$?
- $3abc$
- $-3abc$
- $0$
- $abc$
Show answer and solution
Correct answer: A. $3abc$
The general identity $a^3+b^3+c^3 - 3abc = (a+b+c)(a^2+b^2+c^2-ab-bc-ca)$ collapses when $a+b+c = 0$: the RHS is zero, so $a^3+b^3+c^3 = 3abc$.
A frequent slip is to pick option A — that would require *all three* numbers to be zero, not just their sum.
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