writing-algebraic-expressions MCQs for UPSC Prelims
30 practice questions on writing-algebraic-expressions from the Expressions using Letter-Numbers section of the UPSC Prelims syllabus.
30 come with a written explanation.
Try the sample set below - the answer stays hidden until you ask for it.
9 Easy15 Medium6 Hard
Sample questions
Q1
medium
Find the value of $5xy$ when $x=2$ and $y=3$.
A$10$
B$15$
C$30$
D$523$
Show answer and explanation
Correct answer: C - $30$
The expression means $5\times x\times y$, so substituting gives $5\times 2\times 3=30$. The value $10$ multiplies by $x$ alone, $15$ multiplies by $y$ alone, and $523$ simply joins the digits together.
Q2
medium
A taxi fare is given by $50+9d$, where $d$ is the distance in kilometres. Which part of this expression does not change with the distance?
AThe distance $d$
B$50$
C$9d$
DThe whole expression
Show answer and explanation
Correct answer: B - $50$
The number $50$ is a constant term, so it stays the same however far the journey goes. The term $9d$ grows with the distance, $d$ is the distance itself and clearly changes, and the whole expression changes because $9d$ does.
Q3
hard
The perimeter of a rectangle is $2l+2b$. If the length is $3$ metres more than the breadth, which expression gives the perimeter using $b$ alone?
A$4b+3$
B$2b+6$
C$4b+6$
D$4b+12$
Show answer and explanation
Correct answer: C - $4b+6$
Writing the length as $b+3$ gives a perimeter of $2(b+3)+2b=2b+6+2b=4b+6$. The expression $4b+3$ counts the extra three metres only once, $2b+6$ leaves out one pair of sides, and $4b+12$ doubles that extra length too many times.
Q4
easy
What is the coefficient of $y$ in the term $y$?
A$y$
B$1$
CThere is none
D$0$
Show answer and explanation
Correct answer: B - $1$
Writing $y$ on its own means one lot of $y$, so the coefficient is $1$ even though it is not written down. A coefficient of $0$ would wipe the term out, a letter is not its own coefficient, and every term does have one.
Q5
easy
Which of these is the correct short form of $9\times t$?
A$9+t$
B$9\div t$
C$9t$
D$t9$
Show answer and explanation
Correct answer: C - $9t$
The number is written first and the letter straight after it with no sign between, giving $9t$. Writing $t9$ reverses the accepted order, and the last two options change the operation altogether.
Q6
easy
In the expression $4x+9$, which part is the constant term?
A$4$
B$9$
C$x$
D$4x$
Show answer and explanation
Correct answer: B - $9$
A constant term carries no letter, so its value never changes, and here that term is $9$. The term $4x$ changes as $x$ changes, $4$ is only the coefficient inside that term, and $x$ is the variable itself.
Q7
hard
Ravi's savings are $8w$ rupees and Sita's are $5w$ rupees, where $w$ is the number of weeks they have been saving. What do the coefficients tell you?
ARavi saves ₹$8$ a week and Sita saves ₹$5$ a week
BRavi saves ₹$8$ more each week than Sita
CRavi saved for $8$ weeks and Sita for $5$ weeks
DRavi has ₹$8$ in total and Sita has ₹$5$
Show answer and explanation
Correct answer: A - Ravi saves ₹$8$ a week and Sita saves ₹$5$ a week
In each expression the letter $w$ counts the weeks, so the coefficient is the amount saved per week: ₹$8$ for Ravi and ₹$5$ for Sita. The number of weeks is $w$, the totals are the whole expressions, and the weekly gap between them is ₹$3$, not ₹$8$.
Q8
medium
Write "$6$ subtracted from twice a number $p$" as an expression.
A$6-2p$
B$2p-6$
C$2(p-6)$
D$6p-2$
Show answer and explanation
Correct answer: B - $2p-6$
Twice the number is $2p$, and subtracting six from that gives $2p-6$. The expression $6-2p$ subtracts the other way round, $2(p-6)$ subtracts before doubling, and $6p-2$ swaps the two numbers.
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