Class 12 Sample Paper 2022 Maths Term 1

DOE PRACTICE PAPER – 1 (TERM – 1) (SESSION 2021 – 22)
CLASS XII
MATHEMATICS (CODE: 041)

Time Allowed: 90 Minutes Maximum Marks: 40

General Instructions:
1. This question paper contains three sections – A, B and C. Each part is compulsory.
2. Section - A has 20 MCQs, attempt any 16 out of 20.
3. Section - B has 20 MCQs, attempt any 16 out of 20.
4. Section - C has 10 MCQs, attempt any 8 out of 10.
5. There is no negative marking.
6. All questions carry equal marks.

SECTION – A
In this section, attempt any 16 questions out of Questions 1 – 20.
Each question is of 1 mark weightage.

Each MCQ has four options with only one correct option, choose the correct option.
1. 1 1
The range of the function f(x) = tan x  cot x is
    1
(a) [ - , ] (b) [ 0,  ] (c) [0, ] (d) { }
2 2 2 2
2. 1 1 1 1
The value of the expression sec (2) + sin ( ) + tan (  3) is 1
2
5   
(a) (b) (c) (d)
6 3 3 6
3. The relation R in the set {a, b, c} given by R = {(a, a), (b, b), (a, b), (b, a)}
is 1
(a) symmetric and transitive, but not reflexive
(b) reflexive and symmetric, but not transitive
(c) symmetric, but neither reflexive nor transitive
(d) an equivalence relation
4. A = {1, 2, 3, 4}, A relation R in the set A is given by
R = { (1, 1), (2, 3), (3, 2), (4, 3), (3, 4) }, then relation R is 1

(a) Reflexive (b) symmetric (c) Transitive (d) Equivalence
5. If A is any square matrix of order 3 × 3 such that |adj A| = 256, then
the sum of all possible values of |A| is 1

(a) 256 (b) 16 (c) – 16 (d) 0

6. 0 1
If  x  2 5  y  O ,Then x + y =
1 0  1
(a) 0 (b) – 2 (c) – 1 (d) – 3
2
7. If A is a diagonal matrix of order 3 x 3 such that A = A, then number of
possible matrices A are 1
(a) 4 (b) 8 (c) 16 (d) 32
8.
1  1 3 4 a b
If    X   , w here X   ,Then a  c  b  d  1
2 3  5 6 c d 
(a) 13 (b) 5 (c) – 8 (d) – 3
9. If A is a symmetric matrix then which of the following is not
Symmetric matrix, 1
(a) A + AT (b) A.AT (c) A - AT (d) AT
10. If A is a non-singular square matrix of order 3 such that |A| = 3, then
value of |2AT| is 1
(a) 3 (b) 6 (c) 12 (d) 24
11. 1 1 1 dy
If y = ba ca
 c b a b
 a c bc , then = 1
1 x x 1 x x 1 x x dx
abc abc
1
(a) x (b) x (c) (d) 0
x  xb  x c
a

12. Suppose P, Q and R are different matrices of order 3 × 5, a × b and c x d
respectively, then value of ac + bd is, if matrix 2P + 3Q – 4R is defined 1

(a) 9 (b) 30 (c) 34 (d) 15
13. The function given below at x = 4 is
2 x  3, x  4 1
f ( x)   2
 x  5, x  4
(a) Continuous but not differentiable
(b) Differentiable but not continuous
(c) Continuous as well as differentiable
(d) Neither continuous nor differentiable
14. dy
If x  3 x y  y  2021  xy then
3 2 3

dx 1
3x 2  6 xy  y
(a)
3x 2  3 y 2  x
3x 2  6 xy  y
(b) 2
3 y  3x2  x
6 xy  y  3x 2
(c) 2
3 y  3x 2  x

3x 2  6 xy  y
(d) 2
3x  3 y 2  x

15. The slope of the tangent to the curve y = x3, at the point (2, 8) is
1
(a) 2 (b) 6 (c) 11 (d) 12
16. Corner points of the feasible region determined by the system of linear
constraints are (0, 3), (1, 1) and (3, 0). Let Z = px+qy, where p, q > 0. 1
Condition on p and q so that the minimum of Z occurs at (3, 0) and
(1, 1) is
(a) p = 2q (b) q = 2p (c) p = 3q (d) p = q
2 2
17. The points on the curve 4x + 9y = 36 at which tangent to the curve is
parallel to x-axis, is 1
(a) (±2, 0) (b) (0, ±2) (c) (0, ±3) (d) (±3, 0)
3 2
18. The interval in which y = - x + 3x + 2021 is increasing is
(a) (- ∞, ∞) (b) (0, 2) (c) (2, ∞) (d) ( - 2, 0) 1
19. 2
d y dy
If x = loge y, then 2
2  1
dx dx
(a) y (b) 2y (c) – 2y (d) – y
20. If x = sin3 t, y = cos3 t then
dy

dx 1
(a) tan t (b) cot t (c) - tant (d) – cot t
SECTION – B
In this section, attempt any 16 questions out of Questions 21 – 40.
Each question is of 1 mark weightage.

Each MCQ has four options with only one correct option, choose the correct option.
21. 1 1 2
If sin x  sin y  , cos 1 x  cos 1 y 
3 1
  
(a) (b) (c)  (d)
3 3 2
22. Let f : R → R be defined as f(x) = 7x – 5, then
(a) f is one-one onto 1
(b) f is many-one onto
(c) f is one-one but not onto
(d) f is neither one-one nor onto
23. A relation R in the set of real numbers R is given by
R = {(a, b) : a >b, a , b ∈ R}, The relation R is 1

(a) Reflexive (b) symmetric (c) Transitive (d) Equivalence
24. If a  2 s in x  c os x  b, then
1 1

 1
 
(a) a  0, b   (b) a   , b  2 (c) a  , b  (d) a  0, b 

2 2 2

25. 3 1 2 
1   1
If A   0 1 2  , then | adjA |
 0 2 1 
1 1
(a) (b) (c) – 9 (d) - 81
9 81
26. If A and B are two square matrices of same order such that,
AB = A and BA = B, then (A + B)(A – B) = 1
(a) A2 – B2 (b) 2A – 2B (c) 2A + 2B (d) O
27. dy
If 5x + 5y = 5x+y, then 
dx 1

(a) 5x – y (b) 5y – x (c) - 5x – y (d) - 5y – x
28. The interval on which the function f (x) = 2x3 – 3x2 – 36x + 10 is
decreasing is 1
(a) (- ∞, - 2) (b) (- 2, 3) (c) (2, 3) (d) (3, ∞)
2 3
29. If the curve ay + x = 7 and x = y, cut orthogonally at (1, 1), then
the value of a is: 1
(a) 1 (b) 3 (c) – 6 (d) 6
x2  y2
30. If log( 2 )  a , then dy  1
x y 2
dx
y y x x
(a) (b) (c) (d)
x x y y
31. The area of a triangle with vertices (–3, 0), (3, 0) & (0, k) is 9 sq.
units. The value of k is (k > 0) 1
(a) 3 (b) 6 (c) 9 (d) 12
32. 1 1 1  x   6 
     1
If  0 1 1  y    3  , then 2 x  y  z 
 0 0 1  z   2 
(a) 2 (b) 1 (c) 3 (d) 5
33. d y 2

If tan y  x, , then when x  1, value of 4 is 1
dx 2
(a) 2 (b) – 2 (c) 1 (d) – 1

34. If a non-singular Matrix A satisfy 2A2 + A – I = O, then A – 1 =
1
(a) 2A – I (b) 2A + I (c) 4A + 2I (d) 2A – 4I

35. The maximum value of the function f(x) = 4.sin x. cos x is
(a) 2 (b) 4 (c) 1 (d) 8 1

36. If the objective function z = ax + y is minimum at (1, 4) and its
minimum value is 13, then value of a is 1

(a) 1 (b) 4 (c) 9 (d) 13
37. Let L be the set of all lines in a plane. A relation R in L is given by
R = {(L1,L2):L1 and L2 intersect at exactly one point, L1,L2∈L}, then 1
the relation R is

(a) Reflexive (b) Symmetric (c) Transitive (d) Equivalence
38. If f : X → Y is defined, then f is
1

(a) Bijective function
(b) Many-oneone and onto
(c) Many-one
one and Into function
(d) One-one
one but not onto
39. The feasible region for an LPP is always a _____________ polygon
1
(a) Convex
(b) Concave
(c) either (a) or (b)
(d) neither (a) nor (b)
40. The tangent to the curve y = ex at the point (0, 1) meets x-axis
axis at
1
(a) (1, 0) (b)) ( - 1, 0) (c) (0, 0) (d) (2, 0)
SECTION – C

In this section, attempt any 8 questions out of Questions 41 – 50.
Each question is of 1 mark weightage.

Each MCQ has four options with only one correct option, choose the correct
option.

Questions 46-50
46 are based on a Case-Study

41. The feasible region, for the inequalities 𝑥 + 2𝑦 ≤ 6, 𝑦 ≥ 0, 0 ≤ 𝑥 lies
in 1
(a) First Quadrant
(b) Second Quadrant
(c) Third Quadrant
(d) Fourth Quadrant
42. 
Which of the following function is decreasing on (0, )
2 1
(a) sin x (b) cos x (c) tan x (d) sin 2x
43. If the function f(x) = sin x – ax + b, is decreasing on x ɛ R, then a
belongs to 1
(a) (1, ∞) (b) [0, ∞) (c) (0, ∞) (d) [1, ∞)
44. In a linear programming problem, If the feasible region is
bounded then objective function Z = px + qy has 1
(a) Maximum value only
(b) Minimum value only
(c) Maximum and minimum value both
(d) Neither maximum nor minimum value
45. 6 x 8 
If A   3 2  is singular matrix, then the value of x is 1
 
(a) 3 (b) – 2 (c) 0 (d) 2
CASE STUDY

The fuel cost per hour for running a train is proportional to the square of the
speed it generates in km per hour. If the fuel costs ₹ 48 per hour at speed 16 km
per hour and the fixed charges to run the train amount to ₹ 1200 per hour.
Assume the speed of the train as 𝑣 km/h.

Based on the given information, answer the following questions.

46. Given that the fuel cost per hour is 𝑘 times the square of the
speed the train generates in km/h, the value of 16𝑘 is: 1
(a) 1 (b) 2 (c) 3 (d) 4
47. If the train has travelled a distance of 1000 km, then the total cost
of running the train is given by function: 1
375 60000
(a) v
4 v
375 60000
(b) v
8 v
375 60000
(c ) v
2 v
375 1200000
(d ) v
2 v
48. The most economical speed to run the train (in Km/hr) is:
(a) 50 (b) 80 (c) 400 (d) 800 1
49. The fuel cost (In Rs.)for the train to travel 1000km at the most
economical speed is: 1
(a) 15000 (b) 75000 (c) 100000 (d) 150000
50. The total cost of the train to travel 1000km at the most
economical speed is: 1
(a) 15000 (b) 30000 (c) 100000 (d) 150000