Introduction to Linear Polynomials MCQs for UPSC Prelims
125 practice questions covering Introduction to Linear Polynomials, organised into 0 topics.
125 questions include a written explanation.
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Sample questions
Q1
easy
The sum of two numbers is $50$ and their difference is $10$. What is the smaller number?
A$20$
B$25$
C$30$
D$40$
Show answer and explanation
Correct answer: A - $20$
Taking the difference away from the sum gives twice the smaller number, $50 - 10 = 40$, so the smaller is $20$ and the larger is $30$. The answer $30$ is the larger number. The answer $25$ splits the sum equally and ignores that the numbers differ. The answer $40$ stops at $50 - 10$ without halving it.
Q2
medium
The line $y = -x + 6$ is to be drawn on graph paper. Statement I: It meets the vertical axis at the point $(0, 6)$. Statement II: It meets the horizontal axis at the point $(-6, 0)$. Which is correct?
AOnly Statement II is true
BNeither statement is true
COnly Statement I is true
DBoth statements are true
Show answer and explanation
Correct answer: C - Only Statement I is true
Putting $x = 0$ gives $y = 6$, so the line meets the vertical axis at $(0, 6)$ and Statement I is true. Putting $y = 0$ gives $0 = -x + 6$, so $x = 6$ and the crossing point is $(6, 0)$, not $(-6, 0)$; Statement II is false. So only the first of the two holds, and they are certainly not both false.
Q3
medium
The length of a rectangular garden is $5\ \text{m}$ more than its width, and its perimeter is $46\ \text{m}$. What is the width?
A$9\ \text{m}$
B$11.5\ \text{m}$
C$14\ \text{m}$
D$18\ \text{m}$
Show answer and explanation
Correct answer: A - $9\ \text{m}$
With width $w$ the length is $w + 5$, so $2(2w + 5) = 46$, giving $4w = 36$ and $w = 9\ \text{m}$, with length $14\ \text{m}$. The answer $14$ is the length, not the width. The answer $11.5$ divides the perimeter by $4$ as if the shape were a square. The answer $18$ stops at $2w = 18$ after halving only once.
Q4
medium
The lines $y = 2x$ and $y = 9x$ are drawn on the same graph. Statement I: Both lines pass through the origin. Statement II: For positive values of $x$, the line $y = 2x$ is the steeper of the two. Which is correct?
AOnly Statement II is true
BBoth statements are true
CNeither statement is true
DOnly Statement I is true
Show answer and explanation
Correct answer: D - Only Statement I is true
Both equations give $y = 0$ when $x = 0$, so Statement I is true. At $x = 1$ the heights are $2$ and $9$, so $y = 9x$ climbs faster and Statement II is false. Only the first of the two holds, so the choices that accept Statement II do not fit, and they are not both false.
Q5
medium
Which pair of points both lie on the line $y = 3x - 4$?
A$(0, 4)$ and $(2, 2)$
B$(0, -4)$ and $(2, -2)$
C$(1, 3)$ and $(2, 6)$
D$(0, -4)$ and $(2, 2)$
Show answer and explanation
Correct answer: D - $(0, -4)$ and $(2, 2)$
Putting $x = 0$ gives $y = -4$ and putting $x = 2$ gives $y = 6 - 4 = 2$, so both of those points fit. The pair starting $(0, 4)$ has the wrong sign on the constant. The pair ending $(2, -2)$ subtracts $4$ from $-6$ instead of from $6$. The pair $(1, 3)$ and $(2, 6)$ belongs to $y = 3x$ and ignores the $-4$ altogether.
Q6
easy
Find the value of $s^2 + 3$ when $s = 4$.
A$11$
B$16$
C$19$
D$49$
Show answer and explanation
Correct answer: C - $19$
Squaring first gives $4^2 = 16$, and adding $3$ gives $19$. The value $16$ stops after the squaring and never adds $3$. The value $11$ doubles $4$ instead of squaring it. The value $49$ adds first and then squares, working out $(4 + 3)^2$, which reverses the order the expression asks for.
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