CBSE Class 11 Maths MCQs, chapter by chapter

1,067 practice questions for CBSE Class 11 Mathematics, organised by NCERT chapter (14 chapters). Every question includes a written explanation. Pick a chapter below, or try the samples first.

Practice by chapter

Sets

75 questions in timed practice

Relations and Functions

75 questions in timed practice

Trigonometric Functions

75 questions in timed practice

Complex Numbers and Quadratic Equations

76 questions in timed practice

Linear Inequalities

75 questions in timed practice

Permutations and Combinations

75 questions in timed practice

Binomial Theorem

75 questions in timed practice

Sequences and Series

75 questions in timed practice

Straight Lines

79 questions in timed practice

Conic Sections

75 questions in timed practice

Introduction to Three Dimensional Geometry

75 questions in timed practice

Limits and Derivatives

75 questions in timed practice

Statistics

87 questions in timed practice

Probability

75 questions in timed practice

Sample questions

Q1
medium
Assertion (A): $\dfrac{d}{dx}(\cos x) = -\sin x$. Reason (R): $\dfrac{d}{dx}(\sin x) = -\cos x$.
  1. A Both A and R are true, and R is the correct explanation of A
  2. B Both A and R are true, but R is not the correct explanation of A
  3. C A is true, but R is false
  4. D A is false, but R is true
Show answer and explanation

Correct answer: C - A is true, but R is false

A is true, and it fits the graph: just to the right of $0$ the cosine curve is falling, so its derivative is negative there. R is false, because the derivative of $\sin x$ is $+\cos x$; the minus sign belongs only to the cosine. So A is true with R false, the third rung.
Q2
easy
Find the sum of the first 20 terms of the arithmetic progression $2, 5, 8, \dots$
  1. A $640$
  2. B $1180$
  3. C $590$
  4. D $610$
Show answer and explanation

Correct answer: D - $610$

With $a = 2$, $d = 3$ and $n = 20$, the sum is $\frac{20}{2}[2(2) + 19(3)] = 10(4 + 57) = 610$. Using $20d$ instead of $19d$ gives $640$, and writing $a$ in place of $2a$ gives $590$. The value $1180$ is $20$ times the 20th term $59$, which would only be right if every term were $59$.
Q3
medium
A fan blade makes $180$ complete revolutions in one minute. Through how many radians does it turn in one second?
  1. A $360\pi$
  2. B $3\pi$
  3. C $6\pi$
  4. D $180\pi$
Show answer and explanation

Correct answer: C - $6\pi$

In one second the blade makes $\frac{180}{60} = 3$ revolutions, and each revolution is $2\pi$ radians, so the turn is $6\pi$ radians. The value $3\pi$ counts only $\pi$ per revolution, $180\pi$ uses the whole minute's count with $\pi$ per revolution, and $360\pi$ mixes up $360^\circ$ with the number of revolutions.
Q4
hard
An ellipse has centre at the origin and major axis along the $x$-axis. Its eccentricity is $\frac{3}{5}$ and its two foci are $6$ units apart. Find its semi-major axis $a$ and semi-minor axis $b$.
  1. A $a=10,\ b=8$
  2. B $a=5,\ b=4$
  3. C $a=3,\ b=5$
  4. D $a=5,\ b=3$
Show answer and explanation

Correct answer: B - $a=5,\ b=4$

The foci are $(\pm c,\ 0)$, so the distance between them is $2c=6$ and $c=3$. From $e=\frac{c}{a}$ we get $a=\frac{3}{3/5}=5$, and then $b^2=a^2-c^2=25-9=16$, so $b=4$. Taking $c=6$ instead of $3$ gives the pair $a=10$, $b=8$. Reporting $b=3$ confuses $b$ with $c$, and $a=3$, $b=5$ swaps the two axes.
Q5
hard
A point $P$ is reflected in the $xy$-plane and the image is $Q(3, -5, 2)$. This point $Q$ is then reflected in the $yz$-plane to give a point $R$. Find $P$ and $R$.
  1. A $P(3, 5, -2)$ and $R(-3, 5, 2)$
  2. B $P(-3, -5, 2)$ and $R(3, -5, -2)$
  3. C $P(3, -5, 2)$ and $R(-3, -5, 2)$
  4. D $P(3, -5, -2)$ and $R(-3, -5, 2)$
Show answer and explanation

Correct answer: D - $P(3, -5, -2)$ and $R(-3, -5, 2)$

Reflection in the $xy$-plane reverses $z$, and undoing it from $Q(3, -5, 2)$ gives $P(3, -5, -2)$. Reflection in the $yz$-plane reverses $x$, so $R = (-3, -5, 2)$. Taking $P(3, -5, 2)$ forgets to undo the first reflection, taking $P(-3, -5, 2)$ undoes the wrong coordinate, and $P(3, 5, -2)$ with $R(-3, 5, 2)$ also reverses $y$, which neither reflection touches.
Q6
easy
Let $U = \{1, 2, 3, 4, 5, 6, 7, 8, 9\}$ and $A = \{2, 4, 6, 8\}$. Find $A'$.
  1. A $\{1, 3, 5, 7, 9, 10\}$
  2. B $\{1, 3, 5, 7\}$
  3. C $\{2, 4, 6, 8\}$
  4. D $\{1, 3, 5, 7, 9\}$
Show answer and explanation

Correct answer: D - $\{1, 3, 5, 7, 9\}$

The complement holds every element of the universal set that is missing from $A$, which here means the odd numbers $1, 3, 5, 7$ and $9$. The option $\{1, 3, 5, 7\}$ forgets $9$, which is in $U$ and not in $A$. The set $\{2, 4, 6, 8\}$ repeats $A$ itself, and $\{1, 3, 5, 7, 9, 10\}$ adds $10$, which does not belong to $U$ at all.

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