992 practice questions for CBSE Class 9 Mathematics, organised by NCERT chapter (8 chapters). Every question includes a written explanation. Pick a chapter below, or try the samples first.
In a survey of $400$ families in a colony, $260$ owned a car. Of the surveyed families that owned no car, exactly half owned a two-wheeler. The colony has $1600$ families in all. Using these estimates, how many families in the colony own neither a car nor a two-wheeler?
A$140$
B$280$
C$560$
D$1040$
Show answer and explanation
Correct answer: B - $280$
In the sample $400 - 260 = 140$ families had no car, an estimated probability of $\frac{140}{400} = 0.35$, so about $0.35 \times 1600 = 560$ colony families own no car. Half of those own a two-wheeler, leaving $\frac{560}{2} = 280$ families with neither. The value $560$ stops one step early, $1040$ is the predicted number of car owners, and $140$ is the sample's own count of families without a car.
Q2
medium
Assertion (A): If $AB$ subtends equal angles at two points $P$ and $Q$ lying on opposite sides of $AB$, then $A$, $B$, $P$ and $Q$ are concyclic. Reason (R): Angles subtended by a segment at two points on the same side of it are equal when all four points lie on one circle.
ABoth A and R are true, and R is the correct explanation of A
BBoth A and R are true, but R is not the correct explanation of A
CA is true, but R is false
DA is false, but R is true
Show answer and explanation
Correct answer: D - A is false, but R is true
(R) states the rule correctly, with the two points on the same side of the segment. (A) moves them to opposite sides, and there the test is different: concyclic points on opposite sides of $AB$ see it under angles that add to $180^\circ$, not under equal angles. So equal angles on opposite sides do not make the four points concyclic, and (A) is false while (R) is true.
Q3
medium
The term in position $n$ of a sequence is $7n - 2$. Which of these numbers is a term of the sequence?
A$60$
B$44$
C$50$
D$54$
Show answer and explanation
Correct answer: D - $54$
Solving $7n - 2 = 54$ gives $7n = 56$ and $n = 8$, so $54$ is the eighth term. For $50$, $60$ and $44$ the same working gives $7n = 52,\ 62$ and $46$, none of which is a multiple of $7$, so no position number fits them.
Q4
medium
A square park has each side $3$ units long. What is the exact length of the straight path across it from one corner to the opposite corner?
A$\sqrt{6}$ units
B$6$ units
C$3$ units
D$\sqrt{18}$ units
Show answer and explanation
Correct answer: D - $\sqrt{18}$ units
The diagonal satisfies $d^2=3^2+3^2=18$, so $d=\sqrt{18}$, which is about $4.24$ units. Multiplying the side by $2$ instead of squaring gives $\sqrt{6}$. A diagonal of $6$ units would be as long as two full sides laid end to end, and $3$ units is just the side itself.
Q5
easy
Are the three points $(0,\ 0)$, $(3,\ 0)$ and $(9,\ 0)$ collinear?
ANo, because the three points are all different from one another
BYes, because $0+3+9=12$
CIt cannot be decided without plotting them on graph paper
DYes, because all three lie on the $x$-axis, which is itself a straight line
Show answer and explanation
Correct answer: D - Yes, because all three lie on the $x$-axis, which is itself a straight line
Each of the three has second coordinate $0$, so all of them lie on the $x$-axis, and points sitting on one straight line are collinear. Being different points does not prevent them from lying on a line. The sum $12$ plays no part in the test, and once the shared second coordinate is noticed no plotting is needed.
Q6
medium
The point $M$ is the midpoint of the chord $AB$ of a circle with centre $O$, with $OM = 8\ \text{cm}$ and $MA = 6\ \text{cm}$. What is the radius of this circle?
A$12\ \text{cm}$
B$14\ \text{cm}$
C$2\ \text{cm}$
D$10\ \text{cm}$
Show answer and explanation
Correct answer: D - $10\ \text{cm}$
Since $M$ is the midpoint of the chord, $OM$ is perpendicular to $AB$, so triangle $OMA$ has a right angle at $M$ and the radius $OA$ is its hypotenuse. Then $OA = \sqrt{8^2 + 6^2} = \sqrt{100} = 10\ \text{cm}$. Adding the two legs gives $14\ \text{cm}$ and subtracting them gives $2\ \text{cm}$, neither of which is how a hypotenuse is found, and $12\ \text{cm}$ is just double $MA$, which is the whole chord.
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