Board Paper of Class 12 2022 Mathematics Term-1 Set-4 CODE 065/2/4
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.
- The question paper consists of 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. Attempt any 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 (MCQ). Marks will not be awarded for answering more than one option.
- There is no negative marking.
Question 1
Differential of is
Ans. (a)
![](/landing/images/cbse/y21/mathematics-1.png)
Question 2
The number of all possible matrices of order 2 × 3 with each entry 1 or 2 is
- 16
- 6
- 64
- 24
Ans. (c)
Sol: Number of elements in matrix of order 2 × 3 = 6
Number of all possible matrices = = 64
Question 3
A function is defined as Then the function has
- no minimum value
- no maximum value
- both maximum and minimum values
- neither maximum value nor minimum value
Ans. (d)
![](/landing/images/cbse/y21/mathematics-3.png)
Question 4
If then is
Ans.(a)
![](/landing/images/cbse/y21/mathematics-4.png)
Question 5
The points on the curve where tangent is parallel to x-axis are
- (±5, 0)
- (0, ±5)
- (0, ±3)
- (±3, 0)
Ans. (b)
![](/landing/images/cbse/y21/mathematics-5.png)
Question 6
Three points are collinear, then x is equal to
- 0
- 2
- 3
- 1
Ans. (d)
![](/landing/images/cbse/y21/mathematics-6.png)
Question 7
The principal value of is
Ans: (a)
![](/landing/images/cbse/y21/mathematics-7.png)
Question 8
If
Ans. (c)
![](/landing/images/cbse/y21/mathematics-8.png)
Question 9
If a matrix A is both symmetric and skew symmetric, then A is necessarily a
- Diagonal matrix
- Zero square matrix
- Square matrix
- Identity matrix
Ans. (b)
![](/landing/images/cbse/y21/mathematics-9.png)
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
- {(1, 1), (2, 3), (1, 2)}
- {(3, 3), (3, 1), (1, 2)}
- {(1, 1), (3, 3), (3, 1), (2, 3)}
- {(1, 1), (3, 3), (3, 1), (1, 2)}
Ans. (c)
Sol. To make R reflexive: Add (3, 1), (2, 3) in the relation R.
To make R symmetric: Add (1, 1), (3, 3) in the relation R.
The ordered pairs should be added in Relation ‘R’ are {(1, 1) (3, 3) (3, 1), (2, 3)}.
Question 11
Ans. (b)
![](/landing/images/cbse/y21/mathematics-11-2.png)
Question 12
The function is continuous at x = 0 for the value of k, as
- 3
- 5
- 2
- 8
Ans.(d)
![](/landing/images/cbse/y21/mathematics-12.png)
Question 13
If denotes the cofactor of element of the matrix P = then the value of .
- 5
- 24
Ans.(a)
Sol. Given, matrix is
P
Then,
Question 14
The function is decreasing in the interval is decreasing in the interval
Ans. (d)
![](/landing/images/cbse/y21/mathematics-14.png)
Question 15
If R is a relation in set Z, then domain of R is
- {0, 1, 2}
- {–2, –1, 0, 1, 2}
- {0, –1, –2}
- {–1, 0, 1}
Ans. (b)
![](/landing/images/cbse/y21/mathematics-15.png)
Question 16
The system of linear equations 5x + ky = 5, 3x + 3y = 5; will be consistent if
- k – 3
- k = – 5
- k = 5
- k 5
Ans. (d)
Sol.
The system of linear equation will be consistent if
Now,
Question 17
The equation of the tangent to the curve where it crosses the x-axis is
- x – 5y = 2
- 5x – y = 2
- x + 5y = 2
- 5x + y = 2
Ans. (c)
![](/landing/images/cbse/y21/mathematics-17.png)
Question 18
If are equal, then value of abcd is
- 4
- 16
- 6
- 16
Ans. (a)
![](/landing/images/cbse/y21/mathematics-18.png)
Question 19
The principal value of is
Ans. (a)
![](/landing/images/cbse/y21/mathematics-19.png)
Question 20
For two matrices P = and , PQ is
Ans. (b)
![](/landing/images/cbse/y21/mathematics-20.png)
Question 21
The function is increasing in the interval
![](images/Math-C10-Y21-Q25-Sol.png)
Ans: (c);
![](/landing/images/cbse/y21/mathematics-21.png)
Question 22
If
Ans. (b)
![](/landing/images/cbse/y21/mathematics-22.png)
Question 23
What is the domain of the function
Ans: (d);
![](/landing/images/cbse/y21/mathematics-23.png)
Question 24
Ans: (b);
![](/landing/images/cbse/y21/mathematics-24-2.png)
Question 25
If a function f defined by , then the value of k is
- 2
- 3
- 6
- 6
Ans. (c)
![](/landing/images/cbse/y21/mathematics-25.png)
Question 26
For the matrix is
- 2I
- 3I
- I
- 5I
Ans. (a)
![](/landing/images/cbse/y21/mathematics-26.png)
Question 27
Let and the function is defined by Then this function is
- injective only
- not bijective
- surjective only
- bijective
Ans.(d)
![](/landing/images/cbse/y21/mathematics-27.png)
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 the objective function Z = 2x + 5y is at the point
- P
- Q
- R
- S
Sol. (c);
Given, points of the feasible region: P (0, 5), Q (1, 5), R (4, 2) and S (12, 0) and objective function Z = 2x + 5y
Here,
Hence, the minimum value of Z is at the point R.
Question 29
The equation of the normal to the curve at the point
Ans. (d)
![](/landing/images/cbse/y21/mathematics-29.png)
Question 30
If A is a square matrix of order 3 and ,then is
- 125
- –25
- 25
- ±25
Ans. (c)
![](/landing/images/cbse/y21/mathematics-30.png)
Question 31
The simplest form of
Ans.(c)
![](/landing/images/cbse/y21/mathematics-31.png)
Question 32
If for the matrix then the value of is
Ans : (a);
![](/landing/images/cbse/y21/mathematics-32.png)
Question 33
If then which one of the following equations is true?
Ans. (b)
![](/landing/images/cbse/y21/mathematics-33.png)
Question 34
The principal value of is
- 0
Ans. (b)
![](/landing/images/cbse/y21/mathematics-34.png)
Question 35
The maximum value of is
Ans. (a)
![](/landing/images/cbse/y21/mathematics-35.png)
Question 36
Let matrix is given by Then the matrix where = Minor of ,is
Ans. (d)
![](/landing/images/cbse/y21/mathematics-36.png)
Question 37
A function defined by
- not one-one
- one-one
- not onto
- neither one-one nor onto
Ans. (d)
![](/landing/images/cbse/y21/mathematics-37.png)
Question 38
Ans. (b)
Sol: Objective function Z = 2x – y + 5
Points of the feasible region are
A(0, 10), B(12, 6), C(20, 0) and O(0, 0)
Question 39
If x = – 4 is a root of then the sum of the other two roots is
- 4
- -3
- 2
- 5
Ans. (a)
![](/landing/images/cbse/y21/mathematics-39.png)
Question 40
The absolute maximum value of the function in the interval is
- 8
- 9
- 6
- 10
Ans. (a)
![](/landing/images/cbse/y21/mathematics-40.png)
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
Ans. (c)
![](/landing/images/cbse/y21/mathematics-41.png)
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 – 5b = 0
- a – 3b = 0
- a – 2b = 0
- a – 8b = 0
Ans. (d)
![](/landing/images/cbse/y21/mathematics-42.png)
Question 43
If curves and xy = c cut at right angles, then the value of c is
Ans. (a)
![](/landing/images/cbse/y21/mathematics-43.png)
Question 44
The inverse of the matrix is
Ans. (d)
![](/landing/images/cbse/y21/mathematics-44.png)
Question 45
For an L.P.P. the objective function is Z = 4x + 3y, and the feasible region determined by a set of constraints (linear inequations) is shown in the graph.
![](/landing/images/cbse/y21/mathematics-45.png)
Ans. (b)
Sol. Z = 4x + 3y
Corner points of feasible region are P(0, 40), O(0, 0), R(40, 0), and Q(30, 20)
![](/landing/images/cbse/y21/mathematics-46-1.png)
Question 46
Let side of square plot is x m and its depth is h metres, then cost c for the pit is
Ans. (b)
![](/landing/images/cbse/y21/mathematics-46-2.png)
Question 47
Value of h (in m) for which is
- 1.5
- 2
- 2.5
- 3
Ans. (c)
![](/landing/images/cbse/y21/mathematics-47.png)
Question 48
is given by
Ans. (a)
![](/landing/images/cbse/y21/mathematics-48.png)
Question 49
Value of x (in m) for minimum cost is
- 5
Ans. (d)
![](/landing/images/cbse/y21/mathematics-49.png)
Question 50
Total minimum cost of digging the pit (in ₹) is
- 4,100
- 7,500
- 7,850
- 3,220
Ans. (b)
![](/landing/images/cbse/y21/mathematics-50.png)