Parallel and Intersecting Lines MCQs for UPSC Prelims
115 practice questions covering Parallel and Intersecting Lines, organised into 2 topics.
115 questions include a written explanation.
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Assertion (A): The distance between two parallel lines is measured along a line drawn perpendicular to them. Reason (R): Parallel lines never meet, however far they are extended.
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: B - Both A and R are true, but R is not the correct explanation of A
A is true: the gap is always taken along the perpendicular, since a slanting path between the lines is longer and changes with its slant. R is also a true property of parallel lines. But never meeting does not say why the perpendicular is chosen for measuring, so R is not the explanation of A.
Q2
easy
A transversal cuts two parallel lines and one of the eight angles formed is a right angle. What are the other seven angles?
AThey are $90^\circ$ and $180^\circ$ turn by turn
BFour are $90^\circ$ and three are $45^\circ$
CAll seven are $90^\circ$
DThey cannot be found from this information
Show answer and explanation
Correct answer: C - All seven are $90^\circ$
A right angle at one crossing makes all four angles there $90^\circ$, and the corresponding angles at the other crossing repeat them, so every one of the eight is $90^\circ$. Nothing halves an angle to $45^\circ$. An angle of $180^\circ$ is a straight angle, not one of these eight, and the parallel properties settle the answer completely.
Q3
medium
A transversal cuts lines $l$ and $m$ at two different points. Of the eight angles formed, how many lie in the region between $l$ and $m$?
A$2$
B$4$
C$6$
D$8$
Show answer and explanation
Correct answer: B - $4$
At each crossing, two of the four angles open towards the other line, so $2 + 2 = 4$ angles lie between the lines. The remaining four lie outside that region. Two counts only one crossing, and six or eight would leave too few angles outside.
Q4
medium
Assertion (A): When two straight lines intersect, each pair of vertically opposite angles is equal. Reason (R): Two vertically opposite angles together form a linear pair.
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: C - A is true, but R is false
Vertically opposite angles are indeed equal, so A is true. A linear pair is made of two adjacent angles on a straight line, and vertically opposite angles are not adjacent, so R is false. Since R is false it can neither explain A nor stand on its own.
Q5
medium
Three straight lines are drawn so that no two of them are parallel and no single point lies on all three. How many points of intersection are formed?
A$3$
B$6$
C$1$
D$2$
Show answer and explanation
Correct answer: A - $3$
Each pair of lines gives one crossing, and three lines make three pairs, so there are $3$ points. One point would happen only if all three passed through the same point, which is ruled out. Two points would need a parallel pair. Six is the count for four such lines, not three.
Q6
medium
Lines $l$ and $m$ are parallel and a transversal cuts them, meeting the upper line $l$ at $P$ and the lower line $m$ at $Q$. The interior angle at $P$ on the left of the transversal is $125^\circ$. Find the interior angle at $Q$ on the left of the transversal.
A$125^\circ$
B$35^\circ$
C$55^\circ$
D$65^\circ$
Show answer and explanation
Correct answer: C - $55^\circ$
The two angles are interior and on the same side of the transversal, so they are co-interior and add to $180^\circ$, giving $180^\circ - 125^\circ = 55^\circ$. Repeating $125^\circ$ would treat them as alternate interior angles, which lie on opposite sides. Subtracting from $160^\circ$ gives $35^\circ$ and from $190^\circ$ gives $65^\circ$.
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