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.Show that A ∩ B = A ∩ C need not imply B = C.[2]
2.The first term of a G.P. is 1. The sum of the third term and fifth term is 90. Find the common ratio of G.P.[2]
3.Find n if ${}^{n-1}P_3 : {}^nP_4 = 1 : 9$[2]
4.Write the following sets in roster form: (i) A = {x : x is an integer and –3 ≤ x < 7} (ii) B = {x : x is a natural number less than 6} (iii) C = {x : x is a two-digit natural number such that the sum of its digits is 8} (iv) D = {x : x is a prime number which is divisor of 60} (v) E = The set of all letters in the word TRIGONOMETRY (vi) F = The set of all letters in the word BETTER[2]
5.The owner of a milk store finds that, he can sell 980 litres of milk each week at Rs 14/litre and 1220 litres of milk each week at Rs 16/litre. Assuming a linear relationship between selling price and demand, how many litres could he sell weekly at Rs 17/litre?[2]
6.Find the indicated terms in each of the sequences in Exercises 7 to 10 whose nth terms are: $a_n=\dfrac{n(n-2)}{n+3}; a_{20}$[2]
7.A solution of 8% boric acid is to be diluted by adding a 2% boric acid solution to it. The resulting mixture is to be more than 4% but less than 6% boric acid. If we have 640 litres of the 8% solution, how many litres of the 2% solution will have to be​ added?[2]
8.$\lim_{x\to0}\dfrac{ax+x\cos x}{b\sin x}$[2]
9.Find the values of the trigonometric functions in Exercises 6 to 10. cot $\left(-\dfrac{15\pi}{4}\right)$[2]
10.Insert two numbers between 3 and 81 so that the resulting sequence is G.P.[2]
11.If α and β are different complex numbers with $|\beta|=1$[2]
12.Vertices (0, ± 13), foci (0, ± 5)[2]
13.From the sets given below, select equal sets : A = { 2, 4, 8, 12}, B = { 1, 2, 3, 4}, C = { 4, 8, 12, 14}, D = { 3, 1, 4, 2} E = {–1, 1}, F = { 0, a}, G = {1, –1}, H = { 0, 1}[2]
14.How many 3-digit numbers can be formed by using the digits 1 to 9 if no digit is repeated?[2]
🔑 Show Answer Key — Set 1
  1. 1. Example: let $A=\{1\}$ , $B=\{1,2\}$ and $C=\{1,3\}$ . Then $A\cap B=A\cap C=\{1\}$ , but $B\ne C$ .
  2. 2. $r=3$ or $r=-3$ .
  3. 3. $n=9$ .
  4. 4. (i) $A = \{-3,-2,-1,0,1,2,3,4,5,6\}$ (ii) $B = \{1,2,3,4,5\}$ (iii) $C = \{17,26,35,44,53,62,71,80\}$ (iv) $D = \{2,3,5\}$ (v) $E = \{T,R,I,G,O,N,M,E,Y\}$ (vi) $F = \{B,E,T,R\}$
  5. 5. $1340$ litres.
  6. 6. $a_{20}=\dfrac{360}{23}$ .
  7. 7. More than $320$ litres but less than $1280$ litres of the 2% solution must be added.
  8. 8. $\dfrac{a+1}{b}$ .
  9. 9. $\cot\left(-\dfrac{15\pi}{4}\right)=1$ .
  10. 10. $9$ and $27$ .
  11. 11. $1$ .
  12. 12. $\dfrac{x^2}{144}+\dfrac{y^2}{169}=1$ .
  13. 13. $B=D$ and $E=G$ . No other listed sets are equal.
  14. 14. $504$ .
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.Three letters are dictated to three persons and an envelope is addressed to each of them, the letters are inserted into the envelopes at random so that each envelope contains exactly one letter. Find the probability that at least one letter is in its proper envelope.[2]
2.Out of 100 students, two sections of 40 and 60 are formed. If you and your friend are among the 100 students, what is the probability that (a) you both enter the same section? (b) you both enter the different sections?[2]
3.$x^2 + y^2 – 4x – 8y – 45 = 0$[2]
4.Prove the following: $\cos4x=1-8\sin^2x\cos^2x$[2]
5.Fill in the blanks: (i) The x-axis and y-axis taken together determine a plane known as_______. (ii) The coordinates of points in the XY-plane are of the form _______. (iii) Coordinate planes divide the space into ______ octants.[2]
6.$(x+\cos x)(x-\tan x)$[2]
7.Express each of the complex number given in the Exercises 1 to 10 in the form a + ib. $\left(-2-\dfrac{1}{3}i\right)^3$[2]
8.In what ratio, the line joining (–1, 1) and (5, 7) is divided by the line x + y = 4?[2]
9.If R is the set of real numbers and Q is the set of rational numbers, then what is R – Q?[2]
10.A die is rolled. Let E be the event “die shows 4” and F be the event “die shows even number”. Are E and F mutually exclusive?[2]
11.The length L (in centimetre) of a copper rod is a linear function of its Celsius temperature C. In an experiment, if L = 124.942 when C = 20 and L= 125.134 when C = 110, express L in terms of C.[2]
12.Vertex (0,0); focus (–2,0)[2]
13.Vertices (± 5, 0), foci (± 4, 0)[2]
14.$x^2 = – 16y$[2]
🔑 Show Answer Key — Set 2
  1. 1. $\dfrac23$ .
  2. 2. (a) $\dfrac{17}{33}$ ; (b) $\dfrac{16}{33}$ .
  3. 3. Centre $(2,4)$ and radius $\sqrt{65}$ .
  4. 4. The identity is proved.
  5. 5. (i) XY-plane; (ii) $(x,y,0)$ ; (iii) eight.
  6. 6. $(1-\sin x)(x-\tan x)+(x+\cos x)(1-\sec^2x)$ .
  7. 7. $-\dfrac{22}{3}-\dfrac{107}{27}i$ .
  8. 8. $1:2$ .
  9. 9. $R-Q$ is the set of irrational numbers.
  10. 10. No, E and F are not mutually exclusive.
  11. 11. $L-124.942=\dfrac{0.192}{90}(C-20)$ , i.e. $L=124.899333\ldots+0.002133\ldots C$ .
  12. 12. $y^2=-8x$ .
  13. 13. $\dfrac{x^2}{25}+\dfrac{y^2}{9}=1$ .
  14. 14. Focus $(0,-4)$ ; axis: y-axis; directrix $y=4$ ; latus rectum length $16$ .
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.Find the equation of the circle passing through the points (2,3) and (–1,1) and whose centre is on the line x – 3y – 11 = 0.[2]
2.Draw appropriate Venn diagram for each of the following : (i) (A ∪ B)′, (ii) A′ ∩ B′, (iii) (A ∩ B)′, (iv) A′ ∪ B′[2]
3.$\lim_{x\to4}\dfrac{4x+3}{x-2}$[2]
4.Find the radian measures corresponding to the following degree measures: (i) 25° (ii) – 47°30′ (iii) 240° (iv) 520°[2]
5.Which term of the following sequences: (a) $2,2\sqrt2,4,...$[2]
6.IQ of a person is given by the formula IQ = $\dfrac{MA}{CA}\times100$[2]
7.Which of the following are examples of the null set (i) Set of odd natural numbers divisible by 2 (ii) Set of even prime numbers (iii) { x : x is a natural numbers, x < 5 and x > 7 } (iv) { y : y is a point common to any two parallel lines}[2]
8.Let S be the sum, P the product and R the sum of reciprocals of n terms in a G.P. Prove that $P^2R^n=S^n$[2]
9.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]
10.Find the sum to indicated number of terms in each of the geometric progressions in Exercises 7 to 10: $\sqrt7, \sqrt{21}, 3\sqrt7, ...$[2]
11.$36x^2 + 4y^2 = 144$[2]
12.Prove the following: $\sin(n+1)x\sin(n+2)x+\cos(n+1)x\cos(n+2)x=\cos x$[2]
13.Find the equation of the set of points P, the sum of whose distances from A (4, 0, 0) and B (– 4, 0, 0) is equal to 10.[2]
14.Draw a quadrilateral in the Cartesian plane, whose vertices are (– 4, 5), (0, 7), (5, – 5) and (– 4, –2). Also, find its area.[2]
🔑 Show Answer Key — Set 3
  1. 1. $\left(x-\dfrac72\right)^2+\left(y+\dfrac52\right)^2=\dfrac{65}{2}$ .
  2. 2. (i) Shade the region outside both $A$ and $B$ . (ii) Shade the region outside both $A$ and $B$ . (iii) Shade every region except the common part of $A$ and $B$ . (iv) Shade every region except the common part of $A$ and $B$ .
  3. 3. $\dfrac{19}{2}$ .
  4. 4. (i) $\dfrac{5\pi}{36}$ (ii) $-\dfrac{19\pi}{72}$ (iii) $\dfrac{4\pi}{3}$ (iv) $\dfrac{26\pi}{9}$ .
  5. 5. (a) 13th term (b) 12th term (c) 9th term.
  6. 6. $9.6\le MA\le16.8$ years.
  7. 7. (i), (iii) and (iv) are examples of the null set. (ii) is not a null set.
  8. 8. $P^2R^n=S^n$ .
  9. 9. (i) false (ii) false (iii) true (iv) false (v) false (vi) true.
  10. 10. $S_n=\dfrac{\sqrt7\left((\sqrt3)^n-1\right)}{\sqrt3-1}$ .
  11. 11. Foci $(0,\pm4\sqrt2)$ ; vertices $(0,\pm6)$ ; major axis length $12$ ; minor axis length $4$ ; eccentricity $\dfrac{2\sqrt2}{3}$ ; latus rectum length $\dfrac43$ .
  12. 12. The identity is proved.
  13. 13. $\dfrac{x^2}{25}+\dfrac{y^2}{9}+\dfrac{z^2}{9}=1$ .
  14. 14. The area is $\dfrac{121}{2}$ square units.

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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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