Practice Question Papers · with Answers

CBSE / NCERT Class 11 Maths Practice Question Papers

Download free CBSE / NCERT Class 11 Maths practice question papers with full answer keys. These are original Brain Grain model papers — built from our verified question bank to the real exam blueprint (sections, marks and solutions) — perfect for board revision and model tests.

Brain Grain · braingrain.in
Maths — Practice Paper · Set 1
Class: 11CBSE / NCERTMax Marks: 28
Name: ____________________Reg No: ____________
Part I — Short Answer Questions 14 × 2 = 28

Answer briefly. (Answer all questions.)

1.How many words, with or without meaning, each of 2 vowels and 3 consonants can be formed from the letters of the word DAUGHTER ?[2]
2.Find the area of the triangle formed by the lines joining the vertex of the parabola $x^2 = 12y$ to the ends of its latus rectum.[2]
3.Foci (± 4, 0), the latus rectum is of length 12[2]
4.$\dfrac{x^2}{100}+\dfrac{y^2}{400}=1$[2]
5.Find the derivative of (i) $2x-\dfrac34$ (ii) $(5x^3+3x-1)(x-1)$ (iii) $x^{-3}(5+3x)$ (iv) $x^5(3-6x^9)$ (v) $x^{-4}(3-4x^{-5})$ (vi) $\dfrac{2}{x+1}-\dfrac{x^2}{3x-1}$[2]
6.Find the distance between P (x1, y1) and Q (x2, y2) when : (i) PQ is parallel to the y-axis, (ii) PQ is parallel to the x-axis.[2]
7.Vertex (0,0), passing through (5,2) and symmetric with respect to y-axis.[2]
8.Find the equation of the lines through the point (3, 2) which make an angle of 45o with the line x – 2y = 3.[2]
9.Find the domain and the range of the real function f defined by $f(x)=|x-1|$ .[2]
10.State whether each of the following statement is true or false. Justify your answer. (i) { 2, 3, 4, 5 } and { 3, 6} are disjoint sets. (ii) { a, e, i, o, u } and { a, b, c, d }are disjoint sets. (iii) { 2, 6, 10, 14 } and { 3, 7, 11, 15} are disjoint sets. (iv) { 2, 6, 10 } and { 3, 7, 11} are disjoint sets.[2]
11.Intersecting the y-axis at a distance of 2 units above the origin and making an angle of 30o with positive direction of the x-axis.[2]
12.Passing through $\left(\dfrac{3}{2},2\right)$ and inclined with the x-axis at an angle of 75o.[2]
13.Find the lengths of the medians of the triangle with vertices A (0, 0, 6), B (0,4, 0) and (6, 0, 0).[2]
14.Let R be a relation from N to N defined by R = {(a, b) : a, b ∈N and a = b2}. Are the following true? (i) (a,a) ∈ R, for all a ∈ N (ii) (a,b) ∈ R, implies (b,a) ∈ R (iii) (a,b) ∈ R, (b,c) ∈ R implies (a,c) ∈ R. Justify your answer in each case.[2]
🔑 Show Answer Key — Set 1
  1. 1. $3600$ .
  2. 2. $18$ square units.
  3. 3. $\dfrac{x^2}{4}-\dfrac{y^2}{12}=1$ .
  4. 4. Foci $(0,\pm10\sqrt3)$ ; vertices $(0,\pm20)$ ; major axis length $40$ ; minor axis length $20$ ; eccentricity $\dfrac{\sqrt3}{2}$ ; latus rectum length $10$ .
  5. 5. (i) $2$ ; (ii) $20x^3-15x^2+6x-4$ ; (iii) $-\dfrac{15}{x^4}-\dfrac{6}{x^3}$ ; (iv) $15x^4-84x^{13}$ ; (v) $-12x^{-5}+36x^{-10}$ ; (vi) $-\dfrac{2}{(x+1)^2}-\dfrac{3x^2-2x}{(3x-1)^2}$ .
  6. 6. (i) $|y_2-y_1|$ ; (ii) $|x_2-x_1|$ .
  7. 7. $x^2=\dfrac{25}{2}y$ .
  8. 8. $3x-y-7=0$ and $x+3y-9=0$ .
  9. 9. Domain $=R$ and range $=[0,\infty)$ .
  10. 10. (i) false (ii) false (iii) true (iv) true.
  11. 11. $x-\sqrt3y+2\sqrt3=0$ .
  12. 12. $y-2=(2+\sqrt3)\left(x-\dfrac32\right)$ .
  13. 13. $7,\sqrt{34},7$ .
  14. 14. (i) false (ii) false (iii) false.
Brain Grain · braingrain.in
Maths — Practice Paper · Set 2
Class: 11CBSE / NCERTMax Marks: 28
Name: ____________________Reg No: ____________
Part I — Short Answer Questions 14 × 2 = 28

Answer briefly. (Answer all questions.)

1.The cable of a uniformly loaded suspension bridge hangs in the form of a parabola. The roadway which is horizontal and 100 m long is supported by vertical wires attached to the cable, the longest wire being 30 m and the shortest being 6 m. Find the length of a supporting wire attached to the roadway 18 m from the middle.[2]
2.Without using the Pythagoras theorem, show that the points (4, 4), (3, 5) and (–1, –1) are the vertices of a right angled triangle.[2]
3.Ends of major axis (± 3, 0), ends of minor axis (0, ± 2)[2]
4.Find the derivative of the following functions from first principle: (i) $-x$ (ii) $(-x)^{-1}$ (iii) $\sin (x + 1)$ (iv) $\cos \left(x - \dfrac{\pi}{8}\right)$[2]
5.The number lock of a suitcase has 4 wheels, each labelled with ten digits i.e., from 0 to 9. The lock opens with a sequence of four digits with no repeats. What is the probability of a person getting the right sequence to open the suitcase?[2]
6.Prove that: $(\sin3x+\sin x)\sin x+(\cos3x-\cos x)\cos x=0$[2]
7.Express each of the complex number given in the Exercises 1 to 10 in the form a + ib. $\left(\dfrac{1}{3}+3i\right)^3$[2]
8.Solve the inequalities in Exercises 5 to 16 for real x. 3(x – 1) ≤ 2 (x – 3)[2]
9.Prove the following: $\dfrac{\sin x-\sin3x}{\sin^2x-\cos^2x}=2\sin x$[2]
10.Find the degree measures corresponding to the following radian measures (Use $\pi=\dfrac{22}{7}$ ). (i) $\dfrac{11}{16}$ (ii) – 4 (iii) $\dfrac{5\pi}{3}$ (iv) $\dfrac{7\pi}{6}$[2]
11.Expand each of the expressions in Exercises 1 to 5. $(1-2x)^5$[2]
12.The mean and variance of eight observations are 9 and 9.25, respectively. If six of the observations are 6, 7, 10, 12, 12 and 13, find the remaining two observations.[2]
13.Given 5 flags of different colours, how many different signals can be generated if each signal requires the use of 2 flags, one below the other?[2]
14.For the function $f(x)=\dfrac{x^{100}}{100}+\dfrac{x^{99}}{99}+...+\dfrac{x^2}{2}+x+1$ . Prove that $f'(1)=100f'(0)$ .[2]
🔑 Show Answer Key — Set 2
  1. 1. $\dfrac{5694}{625}$ m, approximately $9.11$ m.
  2. 2. They form a right angled triangle, right-angled at $(4,4)$ .
  3. 3. $\dfrac{x^2}{9}+\dfrac{y^2}{4}=1$ .
  4. 4. (i) $-1$ ; (ii) $\dfrac{1}{x^2}$ ; (iii) $\cos(x+1)$ ; (iv) $-\sin\left(x-\dfrac{\pi}{8}\right)$ .
  5. 5. $\dfrac1{5040}$ .
  6. 6. The identity is proved.
  7. 7. $-\dfrac{242}{27}-26i$ .
  8. 8. $x\le-3$ .
  9. 9. The identity is proved.
  10. 10. (i) $39.375^\circ$ or $39^\circ22'30''$ (ii) $-\dfrac{2520}{11}^\circ$ (iii) $300^\circ$ (iv) $210^\circ$ .
  11. 11. $1-10x+40x^2-80x^3+80x^4-32x^5$ .
  12. 12. $4$ and $8$ .
  13. 13. $20$ .
  14. 14. $f'(1)=100f'(0)$ .
Brain Grain · braingrain.in
Maths — Practice Paper · Set 3
Class: 11CBSE / NCERTMax Marks: 28
Name: ____________________Reg No: ____________
Part I — Short Answer Questions 14 × 2 = 28

Answer briefly. (Answer all questions.)

1.$\lim_{x\to\pi/2}\dfrac{\tan2x}{x-\dfrac{\pi}{2}}$[2]
2.Which term of the following sequences: (a) $2,2\sqrt2,4,...$ is 128 ? (b) $\sqrt3,3,3\sqrt3,...$ is 729 ? (c) $\dfrac13,\dfrac19,\dfrac1{27},...$ is $\dfrac1{19683}$ ?[2]
3.Which of the following are sets ? Justify your answer. (i) The collection of all the months of a year beginning with the letter J. (ii) The collection of ten most talented writers of India. (iii) A team of eleven best-cricket batsmen of the world. (iv) The collection of all boys in your class. (v) The collection of all natural numbers less than 100. (vi) A collection of novels written by the writer Munshi Prem Chand. (vii) The collection of all even integers. (viii) The collection of questions in this Chapter. (ix) A collection of most dangerous animals of the world.[2]
4.Find the multiplicative inverse of each of the complex numbers given in the Exercises 11 to 13. $\sqrt5+3i$[2]
5.An equilateral triangle is inscribed in the parabola $y^2 = 4 ax$ , where one vertex is at the vertex of the parabola. Find the length of the side of the triangle.[2]
6.In each of the following, determine whether the statement is true or false. If it is true, prove it. If it is false, give an example. (i) If x ∈ A and A ∈ B , then x ∈ B (ii) If A ⊂ B and B ∈ C , then A ∈ C (iii) If A ⊂ B and B ⊂ C , then A ⊂ C (iv) If A ⊄ B and B ⊄ C , then A ⊄ C (v) If x ∈ A and A ⊄ B , then x ∈ B (vi) If A ⊂ B and x ∉ B , then x ∉ A[2]
7.How many words, with or without meaning, can be formed using all the letters of the word EQUATION, using each letter exactly once?[2]
8.Using properties of sets, show that (i) A ∪ ( A ∩ B ) = A (ii) A ∩ ( A ∪ B ) = A.[2]
9.$\dfrac{x^2}{36}+\dfrac{y^2}{16}=1$[2]
10.Find $\lim_{x\to0}f(x)$ and $\lim_{x\to1}f(x)$ , where $f(x)=\begin{cases}2x+3,&x\le0\\3(x+1),&x>0\end{cases}$[2]
11.$\lim_{x\to-1}\dfrac{x^{10}+x^5+1}{x-1}$[2]
12.Write the relation R = {(x, x3) : x is a prime number less than 10} in roster form.[2]
13.Given the sets A = {1, 3, 5}, B = {2, 4, 6} and C = {0, 2, 4, 6, 8}, which of the following may be considered as universal set (s) for all the three sets A, B and C (i) {0, 1, 2, 3, 4, 5, 6} (ii) φ (iii) {0,1,2,3,4,5,6,7,8,9,10} (iv) {1,2,3,4,5,6,7,8}[2]
14.Prove the following: $\cos\left(\dfrac{3\pi}{2}+x\right)\cos(2\pi+x)\left[\cot\left(\dfrac{3\pi}{2}-x\right)+\cot(2\pi+x)\right]=1$[2]
🔑 Show Answer Key — Set 3
  1. 1. $2$ .
  2. 2. (a) 13th term (b) 12th term (c) 9th term.
  3. 3. (i), (iv), (v), (vi), (vii) and (viii) are sets. (ii), (iii) and (ix) are not sets.
  4. 4. $\dfrac{\sqrt5}{14}-\dfrac{3}{14}i$ .
  5. 5. $8\sqrt3a$ .
  6. 6. (i) false (ii) false (iii) true (iv) false (v) false (vi) true.
  7. 7. $40320$ .
  8. 8. (i) $A\cup(A\cap B)=A$ and (ii) $A\cap(A\cup B)=A$ .
  9. 9. Foci $(\pm2\sqrt5,0)$ ; vertices $(\pm6,0)$ ; major axis length $12$ ; minor axis length $8$ ; eccentricity $\dfrac{\sqrt5}{3}$ ; latus rectum length $\dfrac{16}{3}$ .
  10. 10. $\lim_{x\to0}f(x)=3$ and $\lim_{x\to1}f(x)=6$ .
  11. 11. $-\dfrac12$ .
  12. 12. $R=\{(2,8),(3,27),(5,125),(7,343)\}$ .
  13. 13. Only (iii) may be considered a universal set for all three sets.
  14. 14. The identity is proved.

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Class 11 does not have a public board examination, so there are no official board question papers for this class. The papers above are Brain Grain practice papers built to the standard exam pattern — ideal for unit tests, monthly tests and revision.

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