CBSE Class 11 Important Questions Maths

Important questions for Class 11 Maths are made to help students focus on the main topics and ideas that are most important for learning the subject well. These questions include key chapters from the CBSE Class 11 syllabus like Probability, Geometry, Trigonometry, and Statistics.

By practicing these questions, students can better understand the concepts, improve their problem-solving skills, and feel more confident for their exams. Solving important questions also helps students find out which topics they are weak in, so they can work on them and do better in the final exam.

20 Most Important Questions from Class 11 Maths Chapters

Q. If A={1,2,3},B={2,3,4}A = \{1, 2, 3\}, B = \{2, 3, 4\}A={1,2,3},B={2,3,4}, find A∪BA \cup BA∪B, A∩BA \cap BA∩B, A−BA - BA−B.
Solution:

A∪B={1,2,3,4}A \cup B = \{1, 2, 3, 4\}A∪B={1,2,3,4}

A∩B={2,3}A \cap B = \{2, 3\}A∩B={2,3}

A−B={1}A - B = \{1\}A−B={1}

Q. Show that the relation R={(a,b):a−b is even}R = \{(a,b): a - b \text{ is even} \}R={(a,b):a−b is even} on natural numbers is an equivalence relation.
Solution:

Reflexive: a−a=0a - a = 0a−a=0 (even) ✔

Symmetric: If a−ba - ba−b is even, so is b−ab - ab−a ✔

Transitive: If a−ba - ba−b and b−cb - cb−c are even ⇒ a−ca - ca−c is even ✔
Hence, R is an equivalence relation.

Q. If tan⁡θ=34\tan \theta = \frac{3}{4}tanθ=43, find sin⁡θ\sin \thetasinθ, cos⁡θ\cos \thetacosθ.
Solution:

Use identity: 1+tan⁡2θ=sec⁡2θ1 + \tan^2\theta = \sec^2\theta1+tan2θ=sec2θ
⇒ sec⁡θ=54\sec \theta = \frac{5}{4}secθ=45, then
cos⁡θ=45\cos \theta = \frac{4}{5}cosθ=54,
sin⁡θ=35\sin \theta = \frac{3}{5}sinθ=53

Q. Simplify 11+i+11−i\frac{1}{1 + i} + \frac{1}{1 - i}1+i1+1−i1.
Solution:
Rationalize each:
11+i=1−i2\frac{1}{1+i} = \frac{1-i}{2}1+i1=21−i,
11−i=1+i2\frac{1}{1-i} = \frac{1+i}{2}1−i1=21+i
Add: 1−i+1+i2=22=1\frac{1-i+1+i}{2} = \frac{2}{2} = 121−i+1+i=22=1

Q. Solve: x2+4x+13=0x^2 + 4x + 13 = 0x2+4x+13=0
Solution:
Discriminant D=16−52=−36D = 16 - 52 = -36D=16−52=−36
⇒ Complex roots:
x=−4±36i2=−2±3ix = \frac{-4 \pm \sqrt{36}i}{2} = -2 \pm 3ix=2−4±36i=−2±3i

Q. Solve: 3x−5<2x+13x - 5 < 2x + 13x−5<2x+1
Solution:
⇒ x<6x < 6x<6

Q. How many 3-digit numbers can be formed using digits 1, 2, 3, 4, 5 (no repetition)?
Solution:
5×4×3=605 \times 4 \times 3 = 605×4×3=60

Q. Find coefficient of x3x^3x3 in (2x−3)5(2x - 3)^5(2x−3)5
Solution:
Term: (53)(2x)3(−3)2=10×8x3×9=720x3\binom{5}{3}(2x)^3(-3)^2 = 10 \times 8x^3 \times 9 = 720x^3(35)(2x)3(−3)2=10×8x3×9=720x3
Coefficient = 720

Q. Find the sum of first 10 terms of AP: 3, 7, 11,...
Solution:
d = 4, a = 3
Sum = 102(2⋅3+9⋅4)=5(6+36)=210\frac{10}{2}(2 \cdot 3 + 9 \cdot 4) = 5(6 + 36) = 210210(2⋅3+9⋅4)=5(6+36)=210

Q. Sum of first 5 terms of GP: 2, 4, 8,...
Solution:
a = 2, r = 2
Sum = 2(25−12−1)=2(31)=622\left(\frac{2^5 - 1}{2 - 1}\right) = 2(31) = 622(2−125−1)=2(31)=62

Q. Find the slope and intercept of line 3x−2y+6=03x - 2y + 6 = 03x−2y+6=0
Solution:
Convert to y=mx+cy = mx + cy=mx+c:
y=32x+3y = \frac{3}{2}x + 3y=23x+3
Slope = 32\frac{3}{2}23, y-intercept = 3

Q. Find the center and radius of circle: x2+y2−4x+6y−12=0x^2 + y^2 - 4x + 6y - 12 = 0x2+y2−4x+6y−12=0
Solution:
Complete squares:
Center = (2, -3), Radius = 25=5\sqrt{25} = 525=5

Q. Find the distance between points A(1,2,3)A(1,2,3)A(1,2,3), B(4,6,8)B(4,6,8)B(4,6,8)
Solution:
Distance = (4−1)2+(6−2)2+(8−3)2=9+16+25=50=52\sqrt{(4-1)^2 + (6-2)^2 + (8-3)^2} = \sqrt{9 + 16 + 25} = \sqrt{50} = 5\sqrt{2}(4−1)2+(6−2)2+(8−3)2=9+16+25=50=52

Q. Evaluate: lim⁡x→0sin⁡xx\lim_{x \to 0} \frac{\sin x}{x}limx→0xsinx
Solution:
Answer = 1 (standard limit)

Q. Find f′(x)f'(x)f′(x) of f(x)=x2f(x) = x^2f(x)=x2 using first principle
Solution:
f′(x)=lim⁡h→0(x+h)2−x2h=lim⁡h→02xh+h2h=2xf'(x) = \lim_{h \to 0} \frac{(x+h)^2 - x^2}{h} = \lim_{h \to 0} \frac{2xh + h^2}{h} = 2xf′(x)=limh→0h(x+h)2−x2=limh→0h2xh+h2=2x

Q. A die is thrown. Find probability of getting an even number.
Solution:
Favorable outcomes = 3 (2, 4, 6), Total = 6
Probability = 36=12\frac{3}{6} = \frac{1}{2}63=21

Q. Find mean for data: x: 10, 20, 30 | f: 1, 3, 2
Solution:
xˉ=10⋅1+20⋅3+30⋅26=10+60+606=1306≈21.67\bar{x} = \frac{10 \cdot 1 + 20 \cdot 3 + 30 \cdot 2}{6} = \frac{10 + 60 + 60}{6} = \frac{130}{6} ≈ 21.67xˉ=610⋅1+20⋅3+30⋅2=610+60+60=6130≈21.67

Q. Write the contrapositive of: “If it rains, then I stay home.”
Solution:
Contrapositive: “If I do not stay home, then it does not rain.”

Q. Find modulus and argument of z=1+iz = 1 + iz=1+i
Solution:
Modulus = 12+12=2\sqrt{1^2 + 1^2} = \sqrt{2}12+12=2,
Argument = tan⁡−1(1)=π4\tan^{-1}(1) = \frac{\pi}{4}tan−1(1)=4π

Q. Graph: x+y≤5x + y \leq 5x+y≤5, x,y≥0x, y \geq 0x,y≥0
Solution:

• Draw line x+y=5x + y = 5x+y=5,

Benefits of Solving Important Questions for Class 11 Maths

1. Improves Conceptual Understanding: Solving important questions strengthens key mathematical concepts such as functions, trigonometry, coordinate geometry, and algebra. It enables students to connect theory with real problem scenarios.