simplifying-algebraic-expressions MCQs for UPSC Prelims

26 practice questions on simplifying-algebraic-expressions from the Expressions using Letter-Numbers section of the UPSC Prelims syllabus. 26 come with a written explanation. Try the sample set below - the answer stays hidden until you ask for it.

8 Easy 13 Medium 5 Hard

Sample questions

Q1
easy
Simplify $10y-4y$.
  1. A $40y$
  2. B $6$
  3. C $14y$
  4. D $6y$
Show answer and explanation

Correct answer: D - $6y$

Taking four lots of $y$ away from ten lots leaves six lots, which is $6y$. Adding instead gives $14y$, dropping the letter gives $6$, and $40y$ multiplies the coefficients.
Q2
medium
Simplify $10-(x+4)$.
  1. A $6-x$
  2. B $6+x$
  3. C $14-x$
  4. D $10-x+4$
Show answer and explanation

Correct answer: A - $6-x$

The minus sign in front of the bracket applies to both terms inside, so $10-(x+4)=10-x-4=6-x$. Ignoring the sign on the $4$ gives $14-x$ or $10-x+4$, and $6+x$ keeps the wrong sign on $x$.
Q3
medium
Read these two statements. Statement I: $6m$ and $m$ are like terms. Statement II: $6m$ and $6n$ are like terms. Which of them is correct?
  1. A Neither I nor II
  2. B Only II
  3. C Both I and II
  4. D Only I
Show answer and explanation

Correct answer: D - Only I

Both $6m$ and $m$ carry the letter $m$, so they are like terms and Statement I is true. The terms $6m$ and $6n$ carry different letters, so they stay unlike however similar their coefficients look, making Statement II false.
Q4
easy
Check the simplification $4a+3a=7a$ by taking $a=2$. What values do the two sides give?
  1. A $12$ and $14$
  2. B $7$ and $14$
  3. C $14$ and $12$
  4. D $14$ and $14$
Show answer and explanation

Correct answer: D - $14$ and $14$

With $a=2$ the left side is $4\times 2+3\times 2=8+6=14$, and the right side is $7\times 2=14$, so the two agree and the simplification is correct. None of the mismatched pairs can come from this substitution.
Q5
easy
How can you check whether $3x+2x$ really simplifies to $5x$?
  1. A Put the same number in place of $x$ in both expressions and compare the values
  2. B Add the coefficients to the letters
  3. C Count the letters in each expression
  4. D Compare how many terms each expression has
Show answer and explanation

Correct answer: A - Put the same number in place of $x$ in both expressions and compare the values

Two expressions are the same only when they give equal values for every value of the letter, so substituting a number is a genuine test. Counting letters or terms says nothing about value, and adding a coefficient to a letter is not a valid operation.
Q6
hard
Which expression is already fully simplified, with no like terms left to combine?
  1. A $4y-y+7$
  2. B $5x+3y-2$
  3. C $5x+3x-2$
  4. D $8+3-2m$
Show answer and explanation

Correct answer: B - $5x+3y-2$

In $5x+3y-2$ the three terms carry $x$, $y$ and no letter, so no two of them can be joined. The second has $5x$ and $3x$, the third has $4y$ and $-y$, and the fourth has the constants $8$ and $3$, each of which can still be combined.
Q7
easy
Terms that carry different letters are called:
  1. A Constant terms
  2. B Like terms
  3. C Coefficients
  4. D Unlike terms
Show answer and explanation

Correct answer: D - Unlike terms

Terms count as alike only when their letter parts match, so terms with different letters are unlike terms. Constant terms carry no letter at all, and a coefficient is simply the number written in front of a letter.
Q8
medium
Rani simplifies $2(x+5)$ to $2x+5$. Substituting $x=1$ into both, what does she find?
  1. A $12$ and $7$, so her simplification is wrong
  2. B $12$ and $12$, so her simplification is right
  3. C $7$ and $7$, so her simplification is right
  4. D $6$ and $7$, so her simplification is wrong
Show answer and explanation

Correct answer: A - $12$ and $7$, so her simplification is wrong

With $x=1$ the original gives $2\times 6=12$ while her answer gives $2+5=7$, and the two disagree, so she is wrong; the correct expansion is $2x+10$. The matching pairs cannot arise here, and the original never gives $6$.

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