12th cbse assignment 2021

NCERT Solutions for Class 6, 7, 8, 9, 10, 11 and 12

CBSE Class 12 Maths Question Paper 2021 (Term-I) with Solutions

May 10, 2024 by Sastry CBSE

Students can use CBSE Previous Year Question Papers Class 12 Maths with Solutions and CBSE Class 12 Maths Question Paper 2021 (Term-I) to familiarize themselves with the exam format and marking scheme.

Time Allowed: 3 hours Maximum Marks: 80

General Instructions:

• This Question paper comprises 50 questions out of which 40 questions are to be attempted as per instructions. All questions carry equal marks.
• This question paper consists three Sections — Section A, B and C.
• Section—A contains 20 questions. Attempt any 16 questions from Q. No. 1 to 20.
• Section—B also contains 20 questions. At tempt anti 16 questions from Q. No. 21 to 40.
• Section — C contains 10 questions including one Case Study. Attempt any 8 from Q. No. 41 to 50.
• There is only one correct option for every Multiple Choice Question (MC Q). Marks will not be awarded for answering more than one option.
• There is no negative marking.

Section – A

In this section, attempt any 16 questions out of Question 1-20. Each question is of one mark.

Question 1. Differential of log [log(log x 5 )] w.r.t. x is (a) \(\frac{5}{x \log \left(x^5\right) \log \left(\log x^5\right)}\) (b) \(\frac{5}{x \log \left(\log x^5\right)}\) (c) \(\frac{5 x^4}{\log \left(x^5\right) \log \left(\log x^5\right)}\) (d) \(\frac{5 x^4}{\log x^5 \log \left(\log x^5\right)}\) Solution: (a) \(\frac{5}{x \log \left(x^5\right) \log \left(\log x^5\right)}\)

Question 2. The number of all possible matrices of order 2 × 3 with each entry 1 or 2 is (a) 16 (b) 6 (c) 64 (d) 24 Solution: (c) 64

Order = 2 × 3 = 6 Each entry 1 or 2 i.e., 2 numbers ∴ Total possible matrices = 2 6 = 64

Question 3. A function f : R → R is defined as f(x) = x 3 + 1. Then the function has (a) no minimum value (b) no maximum value (c) both maximum and minimum values (d) neither maximum value nor minimum value Solution: (d) neither maximum value nor minimum value

Question 4. If sin y = x cos (a + y), then \(\frac{d x}{d y}\) is: (a) \(\frac{\cos a}{\cos ^2(a+y)}\) (b) \(\frac{-\cos a}{\cos ^2(a+y)}\) (c) \(\frac{\cos a}{\sin ^2 y}\) (d) \(\frac{-\cos a}{\sin ^2 y}\) Solution: (a) \(\frac{\cos a}{\cos ^2(a+y)}\)

Question 5. If radius of a spherical soap bubble is increasing at the rate of 0.2 cnVsec. Find the rate of increase of its surface area, when the radius is 7 cm. (a) 11.2π cm/sec (b) 11.2π cm 2 /sec (c) 11π cm 2 /sec (d) 11π cm 2 /sec Solution: (b) 11.2π cm 2 /sec

Given, radius, r = 7 cm and \(\frac{d r}{d t}\) = 0.2 cm/sec Surface area of Sphere, s = 4πr 2 Difference w.r.t, t i.e., time, we have ∴ \(\frac{d s}{d t}\) = 8πr\(\frac{d r}{d t}\) = 8π(7)(0.2) = 11.2 π cm 2 /sec

Question 6. Three points F(2x, x + 3), Q(0, x) and R(x + 3, x + 6) are collinear, then x is equal to (a) 0 (b) 2 (c) 3 (d) 1 Solution: (d) 1

\(\left|\begin{array}{ccc} 2 x & x+3 & 1 \\ 0 & x & 1 \\ x+3 & x+6 & 1 \end{array}\right|\) = 0 [∵ Points P, Q R are collinear. Expanding along C 1 , we have 2x(x – x – 6) + (x + 3) (x + 3 – x) = 0 ⇒ -12x + 3x + 9 = 0 ⇒ -9x = -9 ∴ x = 1

Question 7. The principal value of cos -1 \(\left(\frac{1}{2}\right)\) + sin -1 \(\left(-\frac{1}{\sqrt{2}}\right)\) is (a) \(\frac{\pi}{12}\) (b) π (c) \(\frac{\pi}{3}\) (d) \(\frac{\pi}{6}\) Solution: (a) \(\frac{\pi}{12}\)

Question 9. If a matrix A is both symmetric and skew symmetric, then A is necessarily a (a) Diagonal matrix (b) Zero square matrix (c) Square matrix (d) Identity matrix Solution: (b) Zero square matrix

A t = A (∵ A is a symmetric matrix) A t = -A (∵ A is a skew symmetric matrix) A = -A ⇒ 2A = 0 ⇒ A = 0 ∴ A is a zero square matrix.

Question 10. Let set X = {1, 2, 3} and a relation R is defined in X as: R = {(1, 3), (2, 2), (3, 2)}, then minimum ordered pairs which should be added in relation R to make it reflexive and symmetric are (a) {(1,1), (2, 3), (1, 2)} (b) {(3, 3), (3, 1), (1, 2)} (c) {(1, 1), (3, 3), (3, 1), (2, 3)} (d) {(1, 1), (3, 3), (3, 1), (1, 2)} Solution: (c) {(1, 1), (3, 3), (3, 1), (2, 3)}

Given. X = {1, 2, 3} Reflexive : {(1, 1), (2, 2), (3, 3)} Symmetric : {(1, 3), (3, 1), (3, 2), (2, 3)} R to makes it reflexive and symmetric then add = {(1, 1), (3, 3), (3, 1), (2, 3)}

Question 11. A Linear Programming Problem is as follows: Minimise z = 2x + y Subject to the constraints x ≥ 3, x ≤ 9, y ≥ 0 x – y ≥ 0, x + y ≤ 14 (a) 5 corner points including (0, 0) and (9, 5) (b) 5 corner points including (7, 7) and (3, 3) (c) 5 corner points including (14, 0) and (9, 0) (d) 5 corner points including (3, 6) and (9, 5) Solution: (b) 5 corner points including (7, 7) and (3, 3)

Question 13. If C ij denotes the cofactor of element P of the matrix P = \(\left[\begin{array}{rrr} 1 & -1 & 2 \\ 0 & 2 & -3 \\ 3 & 2 & 4 \end{array}\right]\), then the value of C 31 .C 23 is (a) 5 (b) 24 (c) -24 (d) -5 Solution: (d) -5

Cofactor of a 31 = C 31 = (-1) 3+1 \(\left|\begin{array}{rr} -1 & 2 \\ 2 & -3 \end{array}\right|\) = 3 – 4 = -1 Cofactor of a 23 = C 23 = (-1) 2+3 \(\left|\begin{array}{rr} 1 & -1 \\ 3 & 2 \end{array}\right|\) = -(2 + 3) = -5 ∴ C 31 . C 23 = (-1) (-5) = 5

Question 14. If function y = x 2 e -x is decreasing in the interval (a) (0, 2) (b) (2, ∞) (c) (-∞, 0) (d) (-∞, 0) ∪ (2, ∞) Solution: (d) (-∞, 0) ∪ (2, ∞)

Question 15. If R = {(x, y); x y ∈ Z, x 2 + y 2 ≤ 4) is a relation in set Z, then domain of R is (a) {0, 1, 2} (b) {-2, -1, 0, 1, 2} (c) {0, -1, -2} (d) {-1, 0, 1} Solution: (b) {-2, -1, 0, 1, 2}

Question 16. The system of linear equations 5x + ky = 5, 3x + 3y = 5; will be consistent if (a) k ≠ -3 (b) k = -5 (c) k = 5 (d) k ≠ 5 Solution: (d) k ≠ 5

For consistent, | A | ≠ 0 ∴ \(\left|\begin{array}{ll} 5 & k \\ 3 & 3 \end{array}\right|\) ≠ 0 ⇒ 15 – 3k ≠ 0 ⇒ -3k ≠ -15 ∴ k ≠ 5

Question 17. Find the point on the curve y 2 = 8x for which the abscissa and ordinate change at the same rate (a) (1, 2) (b) (2, 3) (c) (2, 4) (d) (1, 4) Solution: (c) (2, 4)

Question 18. If \(\left[\begin{array}{cc} 3 c+6 & a-d \\ a+d & 2-3 b \end{array}\right]\) = \(\left[\begin{array}{rr} 12 & 2 \\ -8 & -4 \end{array}\right]\) are equal, then value ab – cd (a) 4 (b) 16 (c) -4 (d) -16 Solution: (a) 4

Question 19. The principal value of tan -1 \(\left(\tan \frac{9 \pi}{8}\right)\) is (a) \(\frac{\pi}{8}\) (b) \(\frac{3 \pi}{8}\) (c) \(-\frac{\pi}{8}\) (d) \(-\frac{3 \pi}{8}\) Solution: (a) \(\frac{\pi}{8}\)

Question 20. For two matrices P = \(\left[\begin{array}{rr} 3 & 4 \\ -1 & 2 \\ 0 & 1 \end{array}\right]\) and Q T = \(\left[\begin{array}{rrr} -1 & 2 & 1 \\ 1 & 2 & 3 \end{array}\right]\) then, P – Q is (a) \(\left[\begin{array}{rr} 2 & 3 \\ -3 & 0 \\ 0 & -3 \end{array}\right]\) (b) \(\left[\begin{array}{rr} 4 & 3 \\ -3 & 0 \\ -1 & -2 \end{array}\right]\) (c) \(\left[\begin{array}{rr} 4 & 3 \\ 0 & -3 \\ -1 & -2 \end{array}\right]\) (d) \(\left[\begin{array}{rr} 2 & 3 \\ 0 & -3 \\ 0 & -3 \end{array}\right]\) Solution: (b) \(\left[\begin{array}{rr} 4 & 3 \\ -3 & 0 \\ -1 & -2 \end{array}\right]\)

Section – B

In this section, attempt any 16 questions out of Question 21-40. Each question is of one mark.

Question 21. The function f(x) = 2x 3 – 15x 2 + 36x + 6 is increasing in the interval (a) (-∞, 2) ∪ (3, ∞) (b) (-∞, 2) (c) (-∞, 2) ∪ (3, ∞) (d) [3, ∞) Solution: (a) (-∞, 2) ∪ (3, ∞)

Question 22. If x = 2 cos θ – cos 2θ and y = 2 sinθ – sin 2θ, then \(\frac{d y}{d x}\) is (a) \(\frac{\cos \theta+\cos 2 \theta}{\sin \theta-\sin 2 \theta}\) (b) \(\frac{\cos \theta-\cos 2 \theta}{\sin 2 \theta-\sin \theta}\) (c) \(\frac{\cos \theta-\cos 2 \theta}{\sin \theta-\sin 2 \theta}\) (d) \(\frac{\cos 2 \theta-\cos \theta}{\sin 2 \theta+\sin \theta}\) Solution: (b) \(\frac{\cos \theta-\cos 2 \theta}{\sin 2 \theta-\sin \theta}\)

Question 23. What is the domain of the function cos -1 (2x – 3)? (a) [-1, 1] (b) (1, 2) (c) (-1, 1) (d) [1, 2] Solution: (b) (1, 2)

-1 ≤ 2x – 3 ≤ 1 [Domain of cos -1 θ = -1 ≤ θ ≤ 1 -1 + 3 ≤ 2x – 3 + 3 ≤ 1 + 3 2 ≤ 2x ≤ 4 \(\frac{2}{2}\) ≤ \(\frac{2 x}{2}\) ≤ \(\frac{4}{2}\) ≤ 1 ≤ x ≤ 2; ∴ Domain x ∈ [1, 2]

Here, a ij = 2i + 3j, i < j a 12 = 2(1) + 3(2) = 2 + 6 = 8 > 5 ………. (i) a 13 = 2(1) + 3(3) = 2 + 9 = 11 > 5 ………… (ii) a 23 = 2(2) + 3(3) = 4 + 9 = 1 3 > 5 ……….. (iii) and a ij = 5, i = j a 11 = 5; a 22 = 5; a 33 = 5 then a ij = 3i – 2j, i > j a 21 = 3(2) – 2(1) = 6 – 2 = 4 a 31 = 3(3) – 2(1) = 9 – 2 = 7 > 5 ……… (iv) a 32 = 3(3) – 2(2) = 9 – 2 = 5 Number of elements in A which are more than 5 is 4 i.e., (a 12 , a 13 , a 23 , a 31 ).

Question 26. For the matrix X = \(\left[\begin{array}{lll} 0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 0 \end{array}\right]\), (X 2 — X) is (a) 21 (b) 31 (c) I (d) 5I Solution: (a) 21

Question 27. Let X = {x 2 : x ∈ N} and the function f : N → X is defined by f(x) = x 2 , x ∈ N. Then this function is (a) injective only (b) not bijective (c) surjective only (d) bijective Solution: (d) bijective

X = {x 2 : x ∈ N) Here x = 1, 2, 3, 4, 5,………… N → X Domain = N (natural numbers) Range = X = {1, 4, 9, 16, 25, ………} f(x) = x 2 , x ∈ N one-one, f(x 1 ) = f(x 2 ), x 1 , x 2 ∈ N \(x_1^2\) = \(x_2{ }^2\) x 1 = x 2 ∴ f is one-one For Onto, When x ∈ N, f(x) = x 2 Range = {1, 4, 9, 16, 25,……….} Co-domain = {1, 4, 9, 16, 25,……….} ∴ Range (f) = co-domain (f) ∴ f is onto. ∴ f is bijective.

Question 28. The corner points of the feasible region for a Linear Programming problem are P(0, 5), Q(1, 5), R(4, 2) and S(12, 0). The minimum value of objective function Z = 2x + 5y is at (a) P (b) Q (c) R (d) S Solution: (c) R

Question 29. A kite is flying at a height of 3 m and 5 m of string in out. If the kite in moving away horizontally at the rate of 200 cm/s, then the rate at which string is being released. (a) 5 m/s (b) 3 m/s (c) \(\frac{3}{5}\) m/s (d) \(\frac{8}{5}\) m/s Solution: (d) \(\frac{8}{5}\) m/s

Question 30. If A is a square matrix of order 3 and |A| = -5, then |adj A| is (a) 125 (b) -25 (c) 25 (d) ± 25 Solution: (c) 25

As we know, |adj A| = |A| n-1 = |A| 2 (∵ order n = 3) = (-5) 2 = 25

Question 31. The simplest form of tan -1 \(\left[\frac{\sqrt{1+x}-\sqrt{1-x}}{\sqrt{1+x}+\sqrt{1-x}}\right]\) is (a) \(\frac{\pi}{4}-\frac{x}{2}\) (b) \(\frac{\pi}{4}+\frac{x}{2}\) (c) \(\frac{\pi}{4}-\frac{1}{2} \cos ^{-1} x\) (d) \(\frac{\pi}{4}+\frac{1}{2} \cos ^{-1} x\) Solution: (c) \(\frac{\pi}{4}-\frac{1}{2} \cos ^{-1} x\)

Question 32. If for the matrix A = \(\left[\begin{array}{cc} \alpha & -2 \\ -2 & \alpha \end{array}\right]\), |A 3 | = 125, then the value of α is (a) ± 3 (b) -3 (c) ± 1 (d) 1 Solution: (a) ± 3

Question 34. The principal value of [tan -1 \(\sqrt{3}\) – cot -1 (-\(\sqrt{3}\))] is (a) π (b) \(-\frac{\pi}{2}\) (c) 0 (d) 2\(\sqrt{3}\) Solution: (b) \(-\frac{\pi}{2}\)

tan -1 \(\sqrt{3}\) – cot -1 \((-\sqrt{3})\) = \(\frac{\pi}{3}\)(π – cot -1 \(\sqrt{3}\)) [∵ cot -1 (-A) = π – cot -1 A = \(\frac{\pi}{3}-\pi+\frac{\pi}{6}\) = \(-\frac{\pi}{2}\)

Question 35. The maximum value of \(\left(\frac{1}{x}\right)^x\) is (a) e 1/e (b) e (c) \(\left(\frac{1}{e}\right)^{1 / e}\) (d) e e Solution: (a) e 1/e

Question 36. Let matrix X = [x ij ] is givne by X = \(\left[\begin{array}{ccc} 1 & -1 & 2 \\ 3 & 4 & -5 \\ 2 & -1 & 3 \end{array}\right]\). Then the matrix Y = [m<sub.ij], where m ij = Minor of x ij , is (a) \(\left[\begin{array}{ccc} 7 & -5 & -3 \\ 19 & 1 & -11 \\ -11 & 1 & 7 \end{array}\right]\) (b) \(\left[\begin{array}{ccc} 7 & -19 & -11 \\ 5 & -1 & -1 \\ 3 & 11 & 7 \end{array}\right]\) (c) \(\left[\begin{array}{ccc} 7 & 19 & -11 \\ -3 & 11 & 7 \\ -5 & -1 & -1 \end{array}\right]\) (d) \(\left[\begin{array}{ccc} 7 & 19 & -11 \\ -1 & -1 & 1 \\ -3 & -11 & 7 \end{array}\right]\) Solution: (d) \(\left[\begin{array}{ccc} 7 & 19 & -11 \\ -1 & -1 & 1 \\ -3 & -11 & 7 \end{array}\right]\)

M 11 = 12 – 5 = 7 M 12 = 9 + 10 = 19 M 13 = -3 – 8 = -11 M 21 = -3 + 2 = -1 M 22 = 3 – 4 = -1 M 23 = -1 + 2 = 1 M 31 = 5 – 8 = -3 M 32 = -5 – 6 = -11 M 33 = 4 + 3 = 7 ∴ Minor of X = \(\left[\begin{array}{rrr} 7 & 19 & -11 \\ -1 & -1 & 1 \\ -3 & -11 & 7 \end{array}\right]\)

Question 37. A function f : R → R defined by f(x) = 2 + x 2 is (a) not one-one (b) one-one (c) not onto (d) neither one-one nor onto Solution: (d) neither one-one nor onto

For one-one: f(x 1 ) = f(x 2 ) 2 + \(x_1^2\) = 2 + \(x_2^2\) \(x_1^2\) = ± x 2 ∴ f is not one-one. For onto: Let y = f(x) y = 2 + x 2 y – 2 = x 2 x = ±\(\sqrt{y-2}\) ∉ R for some y ∈ R. For y = 0 ∈ R, there is no x ∈ R such that f(x) = y. ∴ 0 ∈ R does not have pre-image in R. ∴ f is not onto. Hence f is neither one-one nor onto.

Question 38. A Linear Programming Problem is as follows: Maximise/Minimise objective function Z = 2x – y + 5 Subject to the constraints: 3x + 4y ≤ 60 x + 3y ≤ 30 x ≥ 0, y ≥ 0 If the corner points of the feasible region are A(0,10), B(12, 6), C(20, 0) and 0(0, 0), then which of the following is true? (a) Maximum value of Z is 40 (b) Minimum value of Z is -5 (c) Difference of maximum and minimum values of Z is 35 (d) At two corner points, value of Z are equal Solution: (b) Minimum value of Z is -5

Question 39. If x = -4 is a root of \(\left|\begin{array}{lll} x & 2 & 3 \\ 1 & x & 1 \\ 3 & 2 & x \end{array}\right|\) = 0, then the sum of the other two roots is (a) 4 (b) -3 (c) 2 (d) 5 Solution: (a) 4

We have, \(\left|\begin{array}{lll} x & 2 & 3 \\ 1 & x & 1 \\ 3 & 2 & x \end{array}\right|\) = 0 x(x 2 – 2) -2 (x – 3) + 3(2 – 3x) = 0 ⇒ x 3 – 2x – 2x + 6 + 6 – 9x = 0 x 3 – 13x + 12 = 0 Here a = 1, b = 0, c = -13, d = 12 Let roots are: α = -4, β, and δ Sum of roots, α + β + δ = \(\frac{-b}{a}\) -4 + β + δ = \(\frac{0}{1}\) ∴ β + δ = 4

Question 40. The absolute maximum value of the function f(x) = 4x – \(\frac{1}{2} x^2\) in the interval [-2, \(\frac{9}{2}\)] is (a) 8 (b) 9 (c) 6 (d) 10 Solution: (a) 8

Section – C

Attempt any 8 Questions out of the Questions 41-50. Each question is of one mark.

Question 41. In a sphere of radius r, a right circular cone of height h having maximum curved surface area is inscribed. The expression for the square of curved surface of cone is (a) 2π 2 rh(2rh + h 2 ) (b) π 2 hr(2rh + h 2 ) (c) 2π 2 r(2rh 2 – h 3 ) (d) 2π 2 r 2 (2rh – h 2 ) Solution: (c) 2π 2 r(2rh 2 – h 3 )

Question 42. The corner points of the feasible region determined by a set of constraints (linear inequalities) are P(0, 5), Q(3, 5), R(5, 0) and S(4,1) and the objective function is Z = ax + 2by where a, b > 0. The condition on a and b such that the maximum Z occurs at Q and S is (a) a – 5b = 0 (b) a – 3b – 0 (c) a – 2b = 0 (d) a – 8b = 0 Solution: (d) a – 8b = 0

Z = ax + 2by At Q(3, 5), At S(4, 1),

Z = a(3) + 2b(5) Z = a(4) + 2b(1) Maximum Z occurs at Q and S (Given) ∴ 3a + 10b = 4a + 2b ⇒ 0 = 4a + 2b – 3a – 10b ∴ a – 8b = 0

Question 43. The volume of metal of a hollow sphere is constant. If the inner radius is increasing at the rate of 1 cm/s, find the rate of increase of the outer radius, when the radii are 3 cm and 6 cm respectively. (a) 0.25 cm/sec (b) 0.5 cm/sec (c) 0.75 cm/sec (d) 2 cm/sec Solution: (a) 0.25 cm/sec

In a residential society comprising of 100 houses, there were 60 children between the ages of 10-15 years. They were inspired by their teachers to start composting to ensure that biodegradable waste is recycled. For this purpose, instead of each child doing it for only his/her house, children convinced the Residents welfare association to do it as a society initiative. For this they identified a square area in the local park. Local authorities charged amount of ₹50 per square metre for space so that there is association takes it seriously. Association charged ₹400 × (depth) 2 . Association will like to have minimum cost.

Based on this information, answer any four of the following questions.

Question 46. Let side of square plots is x m and its depth is h metres, then cost c for the pit is (a) \(\frac{50}{h}\) + 400 h 2 (b) \(\frac{12,500}{h}\) + 400h 2 (c) \(\frac{250}{h}\) + h 2 (d) \(\frac{250}{h}\) + 400h 2 Solution: (b) \(\frac{12,500}{h}\) + 400h 2

Question 47. Value of h (in m) for which \(\frac{d c}{d h}\) = 0 is (a) 1.5 (b) 2 (c) 2.5 (d) 3 Solution: (c) 2.5

Question 48. \(\frac{d^2 c}{d h^2}\) is given by (a) \(\frac{25,000}{h^3}\) + 800 (b) \(\frac{500}{h^3}\) + 800 (c) \(\frac{100}{h^3}\) + 800 (d) \(\frac{500}{h^3}\) + 2 Solution: (a) \(\frac{25,000}{h^3}\) + 800

\(\frac{d c}{d h}\) = -12,500 h 2 + 800h Differentiating w.r.t. h, we get \(\frac{d^2 c}{d h^2}\) = \(\frac{25,000}{h^3}\) + 800

Question 49. Value of x (in m) for minimum cost is (a) 5 (b) 10\(\sqrt{\frac{5}{3}}\) (c) 5\(\sqrt{5}\) (d) 10 Solution: (d) 10

Volume of cuboid = 250 m 2 x.x.h = 250 x 2 = \(\frac{250}{h}\) ⇒ x 2 = 250 × \(\frac{2}{5}\) …… [From Question 47 ⇒ x 2 = 100 ∴ x = 10

Question 50. Total minimum cost of digging the pit (in ₹) is (a) 4,100 (b) 7,500 (c) 7,850 (d) 3,220 Solution: (b) 7,500

\(\left(\frac{d^2 c}{d h^2}\right)_{h=\frac{5}{2}}\) = 25,000 × \(\frac{2}{5}\) × \(\frac{2}{5}\) × \(\frac{2}{5}\) + 800 > 0 Cost is minimum at h = \(\frac{5}{2}\) c = \(\frac{12,500}{h}\) + 400h 2 c = 12,500 × \(\frac{2}{5}\) + 400 × \(\frac{5}{2}\) × \(\frac{5}{2}\) = 5,000 + 2,500 = ₹7,500

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CBSE Sample Paper for Class 12 English (Core) Board Exam 2021 (with Answers & Marking Scheme)

Cbse english sample paper 2021: check the new cbse sample paper for class 12 english board exam 2021(based on rationalised cbse syllabus 2021) along with answers and cbse 12th english marking scheme 2021..

CBSE English Sample Paper 2021: Check the new CBSE Sample Paper for Class 12 English board exam 2021(based on rationalised CBSE Syllabus 2021) along with answers and CBSE 12th English Marking Scheme 2021. This CBSE 12th English Sample Paper 2021 and CBSE 12th English Marking Scheme 2021 is important for the preparation of upcoming CBSE 12th English board exam 2021. Links to download CBSE Class 12th English (Core) Sample Paper is given at the end of this article.

Also Check:   CBSE Sample Paper for Class 12 - All Subjects 

CBSE Sample Paper for Class 12 English (Core) Board Exam 2021:

General Instructions:

1. This paper is divided into two parts: A and B.  All questions are compulsory.

2. Separate instructions are given with each section and question, wherever necessary. Read these instructions very carefully and follow them.

3. Do not exceed the prescribed word limit while answering the questions.

Part A (40 Marks)

READING (20 marks)

1. Read the passage given below. (1x10 = 10)

1. “Who doesn't know how to cook rice? Cooking rice hardly takes time.” said my father. So, I challenged myself. I switched from news to YouTube and typed, “How to cook rice?” I took one and a half cups of rice. Since I didn't have access to a rice cooker, I put the rice in a big pot. Firstly, the rice has to be washed to get rid of dust and starch. I thought I won't be able to drain the rice and that it will fall out of the pot. I observed the chef as I swirled the rice around and used my dexterous hands to drain it, not once, not twice, but three times. I looked down at the sink and saw less than 50 grains that made their way out of the pot. Suffice to say, I was up to the mark.

2. The video stated that the key to perfect rice is equal amounts of rice and water. I have heard that professionals don't need to measure everything; they just know what the right amount is. But as this was my first time in the kitchen, I decided to experiment by not measuring the water needed for boiling the rice. I wanted the rice to be firm when bitten, just like pasta. I don’t enjoy the texture of mushy rice. It has to have that chutzpah; it has to resist my biting power just for a bit before disinte- grating. 

3. After what seemed like 10 minutes, all the water disappeared. I went in to give it a good stir. To my surprise, some of the rice got stuck to the pot. I tried to scrape it off but to no avail. At the same time, there was a burning smell coming from it. I quickly turned the stove off. “What have you done to the kitchen?” shouted Mother, while coming towards the kitchen. I managed to ward her off.

4. Finally, when the time came to taste my creation, I was surprised! It wasn’t bad at all. The rice had the desired consistency. Sure, a little more salt would've been better, but I just added that while eating. The experience was fairly rewarding and memorable. It taught me a new sense of respect for those who cook food on a regular basis at home or engage in gourmet creations professionally.

On the basis of your understanding of the above passage, answer ANY TEN questions from the eleven given below.  (1x10 = 10)

i.  Father’s question to the narrator, about knowing how to cook rice, was intended to

a.  criticize the narrator’s lack of abilities. 

b.  make the process sound simple.

c.  encourage the narrator to take up cooking.

d.  showcase his own expertise in cooking rice.

 ii.  “I switched from news to YouTube …” Pick the option in which the meaning of ‘switch(ed)’ is NOT the same as it is in the passage.

a. He switched on the radio to listen to the news while having dinner.

b. “Forget these diet supplements and switch to yoga, if you want a true sense of well-being.”

c. Mom switched to reading fiction recently because she was bored with cook-books.

d. The company will switch the trucks to other routes to bring down city pollution.

iii. Based on your understanding of the passage, choose the option that lists the correct sequence of the process.

1. Use water to wash the rice.

2. Repeat the process three times.

3. Drain the water off.

4. Put rice in a utensil.

5. Swirl the water in and around the rice.

a.    4,2,1,3,5 

b.    1,3,2,5,4 

c.    4,1,5,3,2 

d.   5,1,2,4,3

iv.  The narrator says that he has dexterous hands. He would have had a problem had it been the opposite. NOT BEING dexterous means, being

a.  uncomfortable.

b . clumsy. 

c.  unclear. 

d.  clueless.

v a.  Which option represents the correct ratio of water to rice for cooking ‘perfect rice’?

a.    Image 1 

b.    Image 2 

c.    Image 3 

d.   Image 4

FOR VISUALLY IMPAIRED CANDIDATES IN LIEU OF Q  v a

v b.Which option represents the correct ratio of water to rice for cooking ‘perfect rice’?

a. 50% water: 50% rice b. 70% water: 30%rice c.  25% water: 75% rice d. 45% water: 55% rice

vi. How did mother react to the burning smell?

a.   She commented on it. 

b.   She brushed it aside.

c.   She enquired about it . 

d.   She handled it .

vii. According to the passage, the fact that the narrator risked experimentation, on his maiden attempt in the kitchen, shows that he was

a.   conscientious.

b.    nervous. 

c.    presumptuous.

d.   courteous.

viii. Pick the option showing the CORRECT use of the word ‘chutzpah’.

a. It is the court’s duty to dispense chutzpah to everyone irrespective of caste or creed.

b. The speaker may not have much of a stage presence, but you've got to admit she's got chutzpah. 

c. I could crack the code easily which proved me to be a chutzpah and I was the only one who could do so.

d. After his father’s demise, the daughter took over the family’s chutzpah to save it from disaster.

ix. Pick the option that correctly states what DID NOT happen after the writer checked on the rice.

a.   Turning the stove off.

b.    Being taken aback at the condition of rice.

c.    Forgetting to scrape the stuck rice.

d.   Smelling the delicious aroma of cooked rice.

x. The narrator’s creation was

a.    almost perfect to taste.

b.    way off from what he wanted.

c.    overly seasoned.

d.   quite distasteful.

xi. Pick the option that correctly lists the final feelings of the writer with reference to the cooking experience.

1.   frustrating

2.   amusing

3.   satisfying

4.   disillusioning

5.   exacting

6.   enlightening

a.    1 and 4 

b.    2 and 5 

c.    3 and 6 

d.   1 and 3

For rest of the questions, download the complete CBSE Class 12 English Sample Paper 2021 & for answers download CBSE Class 12 Marking Scheme 2021

- Download CBSE Class 12 English Sample Paper 2021

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• CBSE Class 12

CBSE Board Class 12th

After the Class 10 board exam, the Class 12th board exam is the next milestone in the journey of education. Compared to the Class 10 board exams, the degree of complexity for Class 12 is higher. CBSE Class 12 results decide the career of the students and what they want to pursue in the future. Scoring a good percentile in the Class 12 Board exam will boost students’ confidence.

Note : As per the latest notification dated 6th April 2023 , there are a few changes in the CBSE Class 12 Examination and Assessment practices for the academic session 2023-24 to align assessment to Competency Focused Education. The changes are as mentioned below,

CBSE Class 12 Study Material for Board Exam

CBSE Class 12 Exams are near to its conduct. Students must have completed their term 1 syllabus and started with the revision. Here, we have provided the CBSE Study Plan for the Term 1 Exam to help students with CBSE Term 1 Board Exams preparation. They will find the study resource extremely beneficial as it contains everything from practice multiple choice questions, study notes, day-wise planners, and mock tests. Referring to this meticulously curated revision planner will boost students’ exam preparation. We have created a day-wise study plan for each subject. Students can easily access it by clicking on the link below. They can also download the study material in pdf for each subject.

• CBSE Class 12 Study Plan for Physics
• CBSE Class 12 Study Plan for Chemistry
• CBSE Class 12 Study Plan for Biology
• CBSE Class 12 Study Plan for Maths

CBSE Class 12 Study Plan for Physics Exam

CBSE Class 12 Study Plan for Chemistry Exam

CBSE Class 12 Study Plan for Biology Exam

CBSE Class 12 Study Plan for Maths Exam

CBSE Class 12 Subjects

In CBSE Class 12, five subjects are compulsory. The subjects mentioned below are for the students who opted Science and Commerce stream. 

• Accountancy
• Business Studies

CBSE Syllabus for Class 12

CBSE Class 12 syllabus is not only important for students to pass the Board exam, but it is also necessary for competitive exams. The Class 12 syllabus is prepared by the CBSE board, so it is important for students to study according to the syllabus mentioned below.

• CBSE class 12 Syllabus All Subjects
• CBSE Class 12 Physics Syllabus
• CBSE Class 12 Chemistry Syllabus
• CBSE Class 12 Biology Syllabus
• CBSE Class 12 Maths Syllabus
• CBSE Class 12 Accountancy Syllabus
• CBSE Class 12 Business Studies Syllabus
• CBSE Class 12 Economics Syllabus

CBSE Study Materials for Class 12

CBSE study materials for Class 12 are being designed in such a way that it gives the complete idea of the CBSE Class 12 syllabus. The study materials mentioned below will help students to prepare for all the subjects equivalently. Notes

• CBSE class 12 Notes All Subjects
• CBSE Class 12 Physics Detailed Notes
• CBSE Class 12 Biology Detailed Notes
• CBSE Class 12 Chemistry Detailed Notes
• CBSE Class 12 Maths Detailed Notes

Revision Notes

• CBSE Class 12 Revision Notes
• CBSE Class 12 Physics Revision Notes
• CBSE Class 12 Biology Revision Notes
• CBSE Class 12 Chemistry Revision Notes
• CBSE Class 12 Maths Revision Notes
• CBSE Class 12 Business Studies Revision Notes
• CBSE Class 12 Economics Revision Notes

NCERT Notes

• NCERT Notes for Class 12 Chemistry
• NCERT Notes for Class 12 Mathematics
• NCERT Notes for Class 12 Biology
• NCERT Notes for Class 12 Physics

CBSE Class 12 Books

CBSE Class 12 books are very helpful in understanding all the complex topics as every topic is explained in a very easy language along with examples and diagrams. The chapters in the books have illustrative examples and practice problems for getting a hold of any kind of concept.

• CBSE Class 12 Physics Book
• CBSE Class 12 Chemistry Book
• CBSE Class 12 Biology Book
• CBSE Class 12 Maths Book

CBSE Class 12 Textbooks Solutions

CBSE Class 12 textbook solutions act as a vital tool for students in their exam preparation and home assignments. These solutions provide answers to all the problems, in-depth with concepts covered in the syllabus.

• NCERT Solutions for class 12
• NCERT Solutions for Class 12 Maths
• NCERT Solutions for Class 12 Physics
• NCERT Solutions for Class 12 Chemistry
• NCERT Solutions for Class 12 Biology
• NCERT Solutions for Class 12 Accountancy
• NCERT Solutions for Class 12 Business Studies
• NCERT Solutions for Class 12 Economics
• TS Grewal Class 12 Accountancy Solutions
• HC Verma Class 12 Physics Solutions
• RD Sharma Class 12 Solutions

CBSE Sample Papers for Class 12

CBSE sample papers for Class 12 are very useful for students preparing for the Board examination. Sample question papers help students to get a better understanding of the concepts by practising them on a regular basis. It also boosts students’ confidence.

• CBSE Class 12 Sample Paper for Physics
• CBSE Class 12 Sample Paper for Chemistry
• CBSE Class 12 Sample Paper for Biology
• CBSE Class 12 Sample Paper for Maths

Previous Year Question Papers for CBSE Class 12

Class 12 CBSE previous year question papers available on BYJU’S website are prepared as per the latest CBSE Class 12 syllabus and marking scheme. By solving these previous years’ question papers, students will get to know the exact idea about the final question paper.

• CBSE Previous Year Question Papers for Class 12 Maths
• CBSE Previous Year Question Papers for Class 12 Physics
• CBSE Previous Year Question Papers for Class 12 Chemistry
• CBSE Previous Year Question Papers for Class 12 Biology

CBSE Class 12 Marks-Wise Important Questions

The marks-wise important questions for Class 12 Science given here are from varied CBSE Class 12 chapters and might be included in the exam. There is a high chance that similar questions might be included in the exam.

• Important 2 Marks Questions for CBSE 12th Maths
• Important 4 Marks Questions for CBSE 12th Maths
• Important 6 Marks Questions for CBSE 12th Math
• Important 2 marks Question Physics Class 12th
• Important 3 marks Question Physics Class 12th
• Important 5 marks Question Physics Class 12th
• Important 2 Marks Questions for CBSE 12th Chemistry
• Important 3 Marks Questions for CBSE 12th Chemistry
• Important 5 Marks Questions for CBSE 12th Chemistry
• Important 2 Marks Questions For CBSE Class 12 Biology Exam
• Important 3 Marks Questions For CBSE Class 12 Biology Exam
• Important 5 Marks Questions For CBSE Class 12 Biology Exam

CBSE Class 12 Chapter-Wise Important Questions

CBSE Class 12 chapter-wise important questions help students by providing a strategy to prepare for board examinations. All the questions present in these materials are framed under the guidance of the NCERT textbook from every chapter.

• Chapter wise important Questions for CBSE Class 12 Maths
• Chapter wise important Questions for CBSE Class 12 Physics
• Chapter wise important Questions for CBSE Class 12 Chemistry
• Chapter wise important Questions for CBSE Class 12 Biology

CBSE Class 12 Videos

CBSE Class 12 videos make learning more easier and simpler. Learning through videos makes the concept flow into your mind and gets established there in a way that it becomes impossible for the student to forget it.

How to Study in CBSE Class 12 (Preparation Tips )

• Students should have a clear understanding of the topics and concepts included in the syllabus.
• Class 12 students should strictly follow the NCERT textbook syllabus to prepare for their Class 12 board exams.
• Students should pay attention to key features like diagrams, graphs, and numerical problems to score good marks in the final exam.
• Students should solve previous years’ question papers and sample papers on a regular basis. It will also boost the student’s confidence.
• Once a chapter is completed, it is better to revise that chapter first before moving on to the next chapter.

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CBSE NCERT Solutions

NCERT and CBSE Solutions for free

Class 12 Physics Assignments

We have provided below free printable Class 12 Physics Assignments for Download in PDF. The Assignments have been designed based on the latest NCERT Book for Class 12 Physics . These Assignments for Grade 12 Physics cover all important topics which can come in your standard 12 tests and examinations. Free printable Assignments for CBSE Class 12 Physics , school and class assignments, and practice test papers have been designed by our highly experienced class 12 faculty. You can free download CBSE NCERT printable Assignments for Physics Class 12 with solutions and answers. All Assignments and test sheets have been prepared by expert teachers as per the latest Syllabus in Physics Class 12. Students can click on the links below and download all Pdf Assignments for Physics class 12 for free. All latest Kendriya Vidyalaya Class 12 Physics Assignments with Answers and test papers are given below.

Physics Class 12 Assignments Pdf Download

We have provided below the biggest collection of free CBSE NCERT KVS Assignments for Class 12 Physics . Students and teachers can download and save all free Physics assignments in Pdf for grade 12th. Our expert faculty have covered Class 12 important questions and answers for Physics as per the latest syllabus for the current academic year. All test papers and question banks for Class 12 Physics and CBSE Assignments for Physics Class 12 will be really helpful for standard 12th students to prepare for the class tests and school examinations. Class 12th students can easily free download in Pdf all printable practice worksheets given below.

Topicwise Assignments for Class 12 Physics Download in Pdf

Advantages of Class 12 Physics Assignments

• As we have the best and largest collection of Physics assignments for Grade 12, you will be able to easily get full list of solved important questions which can come in your examinations.
• Students will be able to go through all important and critical topics given in your CBSE Physics textbooks for Class 12 .
• All Physics assignments for Class 12 have been designed with answers. Students should solve them yourself and then compare with the solutions provided by us.
• Class 12 Students studying in per CBSE, NCERT and KVS schools will be able to free download all Physics chapter wise worksheets and assignments for free in Pdf
• Class 12 Physics question bank will help to improve subject understanding which will help to get better rank in exams

Frequently Asked Questions by Class 12 Physics students

At https://www.cbsencertsolutions.com, we have provided the biggest database of free assignments for Physics Class 12 which you can download in Pdf

We provide here Standard 12 Physics chapter-wise assignments which can be easily downloaded in Pdf format for free.

You can click on the links above and get assignments for Physics in Grade 12, all topic-wise question banks with solutions have been provided here. You can click on the links to download in Pdf.

We have provided here topic-wise Physics Grade 12 question banks, revision notes and questions for all difficult topics, and other study material.

We have provided the best collection of question bank and practice tests for Class 12 for all subjects. You can download them all and use them offline without the internet.

Related Posts

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CBSE Term 1 Answer Key 2022 Class 12: Download CBSE Board Exam 2021 Answer Key PDFs For All Subjects

• Hindi Result

Latest Updates

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Collegedunia Team

Content Curator | Updated On - Jun 27, 2024

CBSE Class 12 official Answer Key 2021 is expected to be released by Central Board of Secondary Education for all subjects on its official website soon. CBSE Class 12 Answer Key 2021 by subject experts is provided further in this article. Students can download PDFs to calculate their probable scores. Answer keys mention correct answers for all questions included in their respective examinations. CBSE Class 12 Term 1 exam paper has all questions in MCQ format. Exam duration is 1 hour 30 minutes and timings are from 11:30 am to 1:00 pm. 

Students can follow below steps for downloading the official answer key as soon as CBSE releases it. Meanwhile, links provided below can be used to check Class 12 CBSE 2021 Answer Key shared by subject experts.

December 15: CBSE Class 12 Economics Answer Key and Exam Analysis 2021-22 released. Read more

December 14: CBSE Class 12 Chemistry Answer Key, Exam Analysis, and Marking Scheme 2021-22 released. Check here

December 10: Class 12 Physics Paper Analysis 2021 released by CBSE. Click here

How to Download CBSE Class 12 Answer Key 2021-22

CBSE Class 12 Official Answer Key 2021-22 is yet to be released by Central Board of Secondary Education. Here’s how you can download CBSE 12th Answer Key 2021:

• Visit official website at cbse.gov.in
• Click on CBSE Class 12 Answer Keys
• Select the subject for which you wish to download keys
• New PDF will popup on your screen
• You can now download the PDF.

Candidates can compare their answers with answer keys to calculate a probable score. Please note that there are no negative markings by CBSE in Term 1 Examinations.

CBSE Answer Key 2021 Class 12 2021

CBSE Answer Key 2021 Class 12 (Stream wise) has been shared below for your reference:

CBSE Class 12 Science Term-1 Answer Key

As per subject experts, in CBSE Class 12 Physics Term-1, number of numericals were more in comparison to direct answer questions. Also, candidates appearing for Mathematics exam shared that the question paper was lengthy and moderately difficult. Subject experts for CBSE Class 12 Biology Term 1 Exam 2021 stated that difficulty level of the paper was difficult and questions were directly picked from NCERT books. 

CBSE Answer Key 2021 for Science Class 12 has been shared below. 

CBSE Class 12 Arts Term-1 Answer Key

CBSE Class 12 Term-1 Exam 2021 for Geography was majorly focussed on Map-based practical comprehension questions. Students were able to finish the question paper on time. As per candidates of CBSE Class 12 Term-1 Political Science Exam 2022, difficulty level of the paper was between easy to moderate. Similarly, experts and subject teachers said that difficulty level of CBSE Class 12 History Exam was balanced and easy. 

CBSE Answer Key 2021 Class 12 for Arts stream has been shared below. 

CBSE Class 12 Commerce Term-1 Answer Key

CBSE Class 12 Business Studies paper difficulty level was moderate, as stated by students. Students who sat for CBSE Class 12 Economics Exam 2021 found economics paper easy and effortless. Students were of the view that few questions in CBSE Class 12 Accountancy Exam 2021 were on the tougher side. Overall it was tough and instructions were also not clear.

CBSE Answer Key 2021 Class 12 for Commerce by CBSE subject experts has been shared below. 

CBSE Class 12 Optional Subjects Term-1 Answer Key

CBSE Class 12 Psychology Exam 2021 question paper included well-balanced questions. Difficulty level of exam was set at an average level. CBSE Answer Key 2021 Class 12 for optional subjects has been shared below. 

Disclaimer: CBSE answer keys shared above have been generated by subject experts and are only for reference. Students can confirm the correct options with their teachers. They can also compare them with official answer keys as they get released.

Frequently Asked Questions

Ques. What are the total marks of CBSE Class 12 Term 1?

Ans:  CBSE Class 12 Term 1 question paper included MCQs and Application Based Questions. Total marks are 100, including theory and practical.

Ques: Will CBSE release the official Computer Science Class 12 Answer Key 2021-22?

Ans:  CBSE is yet to release official Computer Science Class 12 Answer Key 2021-22. Meanwhile, you can check Computer Science and IP Term 1 Answer Key and paper analysis by subject experts here .

Ques: When will CBSE announce CBSE 12th Board Result Term 1 examination?

Ans:  After completion of Class 12th Term 1 examination, CBSE will announce the result. Check latest updates here .

Ques: Where can I find Home Science Class 12 Answer Key Term 1?

Ans: We have shared Class 12 Home Science Answer Key 2021 for Term 1 on this page. You can check CBSE Class 12 Arts Term-1 Answer Key to calculate probable marks.

* The article might have information for the previous academic years, which will be updated soon subject to the notification issued by the University/College.

Exam Pattern

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Computer Science Syllabus

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Political Sci. Syllabus

History Syllabus

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Physics Practical

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Chapter Wise Weightage

Paper Analysis

CBSE CLASS XII Psychology

CBSE CLASS XII Computer Science

CBSE CLASS XII Music

CBSE CLASS XII Biotechnology

CBSE CLASS XII Home Science

CBSE CLASS XII Sociology

CBSE CLASS XII Applied Arts

CBSE CLASS XII Overview

CBSE CLASS XII Exam Pattern

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CBSE CLASS XII Question Paper 2024

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CBSE CLASS XII News

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Cbse class xii papers of 2021, cbse class xii papers of 2019, cbse-class-xii news.

CBSE Class 12 Geography Question Paper 2024 Set 3 64 5 3...

CBSE Class 12 Geography Question Paper 2024 Set 2 64 5 2...

CBSE Class 12 Geography Question Paper 2024 Set 1 64 5 1...

CBSE Class 12 Physics Question Paper 2024 Set 3 55 5 3...

As per the availiable details, there is no information regarding the challenge of the answer key for CBSE Class 12. For class X you can object to the answer key, but for class 12 th  CBSE has not revealed anything to object. 

For more information, refer to this link:  CBSE Class 12 official Answer Key 

As per the availiable information, CBSE has not released the information regarding the dates of the answer key for CBSE Class 12. Currently, for some courses, the exams are still going on. These exams are conducted from April 26, 2022, to June 15, 2022. 

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