Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 4 Notes | Study Mathematics (Maths) Class 12 - JEE

JEE: Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 4 Notes | Study Mathematics (Maths) Class 12 - JEE

The document Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 4 Notes | Study Mathematics (Maths) Class 12 - JEE is a part of the JEE Course Mathematics (Maths) Class 12.
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Class-XII
Time: 90 Minutes
Max. 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

Q.1: Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 4 Notes | Study Mathematics (Maths) Class 12 - JEEis equal to:
(a) 1/2
(b) 1/3
(c) –1

(d) 1

Correct Answer is Option (d)

Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 4 Notes | Study Mathematics (Maths) Class 12 - JEE
= 1


Q.2: The value of k (k < 0) for which the function f defined as
Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 4 Notes | Study Mathematics (Maths) Class 12 - JEE
is continuous at x = 0 is:
(a) ± 1
(b) –1              
(c) ±1/2
(d) 1/2

Correct Answer is Option (d)
Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 4 Notes | Study Mathematics (Maths) Class 12 - JEE
Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 4 Notes | Study Mathematics (Maths) Class 12 - JEE

Q.3: If A = [αij] is a square matrix of order 2 such that αij = Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 4 Notes | Study Mathematics (Maths) Class 12 - JEE then Ais:
(a)

Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 4 Notes | Study Mathematics (Maths) Class 12 - JEE
(b)
Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 4 Notes | Study Mathematics (Maths) Class 12 - JEE
(c)
Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 4 Notes | Study Mathematics (Maths) Class 12 - JEE
(d)
Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 4 Notes | Study Mathematics (Maths) Class 12 - JEE

Correct Answer is Option (d)
Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 4 Notes | Study Mathematics (Maths) Class 12 - JEE

Q.4: Value of k, for which A = Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 4 Notes | Study Mathematics (Maths) Class 12 - JEEis a singular matrix is:
(a) 4    
(b) –4                        
(c) ±4
(d) 0

Correct Answer is Option (c)

As A is singular matrix
⇒ |A| = 0

⇒ 2k2 – 32 = 0

⇒ k = ±4


Q.5: Find the intervals in which the function f given by f(x) = x2 – 4x + 6 is strictly increasing:
(a) (– ∞, 2) ∪ (2,  
)
(b) (2,  ∞)
(c) (− ∞, 2)
(d) (– ∞, 2] ∪ (2,  ∞)

Correct Answer is Option (b)

f(x) = x2 – 4x + 6
f'(x) = 2x – 4
Let f(x) = 0
⇒ x = 2
Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 4 Notes | Study Mathematics (Maths) Class 12 - JEE
⇒  f(x) is Strictly increasing in (2, ∞)


Q.6: Given that A is a square matrix of order 3 and | A | = - 4, then | adj A | is equal to:
(a) –4
(b) 4
(c) –16
(d) 16

Correct Answer is Option (d)
as |adj A| = |A|n – 1,
where n is order of matrix A
= (–4)2 = 16


Q.7: A  relation R in set A = {1, 2, 3} is defined as R = {(1, 1), (1, 2), (2, 2), (3, 3)}. Which of the following ordered pair in R shall be removed to make it an equivalence relation in A
(a) 
(1, 1)
(b) 
(1, 2)
(c) 
(2, 2)
(d) 
(3, 3)

Correct Answer is Option (b)


Q.8: If, Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 4 Notes | Study Mathematics (Maths) Class 12 - JEEthen value of a + b – c + 2d is:

(a) 8

(b) 10

(c) 4

(d) –8

Correct Answer is Option (a)
Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 4 Notes | Study Mathematics (Maths) Class 12 - JEE
∴ a + b – c + 2d = 8


Q.9: The point at which the normal to the curve y = x + 1/x, x > 0 x is perpendicular to the line 3x – 4y – 7 = 0 is:
(a) (2, 5/2)
(b) (±2, 5/2)
(c) (–1/2, 5/2)
(d) (1/2, 5/2)

Correct Answer is Option (d)

Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 4 Notes | Study Mathematics (Maths) Class 12 - JEE
As normal to f(x) is ⊥ to given line
Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 4 Notes | Study Mathematics (Maths) Class 12 - JEE


Q.10: sin (tan–1x), where |x| < 1, is equal to:
(a)Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 4 Notes | Study Mathematics (Maths) Class 12 - JEE
(b) Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 4 Notes | Study Mathematics (Maths) Class 12 - JEE
(c) Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 4 Notes | Study Mathematics (Maths) Class 12 - JEE
(d) Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 4 Notes | Study Mathematics (Maths) Class 12 - JEE

Correct Answer is Option (d)
Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 4 Notes | Study Mathematics (Maths) Class 12 - JEE


Q.11: Let the relation R in the set A = {x ∈ Z : 0 ≤ x ≤ 12}, given by R = {(a, b) : |a – b| is a multiple of 4}. Then [1], the equivalence class containing 1, is:
(a)
{1, 5, 9}
(b) 
{0, 1, 2, 5}

(c) ϕ

(d) A

Correct Answer is Option (a)


Q.12: If ex + ey = ex+y, then dy/dx is:
(a) ey – x
(b) ex + y
(c) –ey – x
(d) 2e
x – y

Correct Answer is Option (c)
 ex + ey = ex + y
⇒ e–y + e–x = 1
Differentiating w.r.t. x:
Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 4 Notes | Study Mathematics (Maths) Class 12 - JEE


Q.13: Given that matrices A and B are of order 3 × n and m × 5 respectively, then the order of matrix C = 5A + 3B is:
(a) 3 × 5 and m = n
(b) 3 × 5
(c) 3 × 3
(d) 5 × 5

Correct Answer is Option (b)


Q.14: If y  = 5 cos x – 3 sin x, then d2y/dx2 is equal to:
(a) –y
(b) y
(c) 25y
(d) 9y

Correct Answer is Option (a)
y = 5cos x – 3sin x
⇒ dy/dx = –5sin x – 3cos x

⇒ d2y/dx= –5cos x + 3sin x
= –y

Q.15: For matrix A = Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 4 Notes | Study Mathematics (Maths) Class 12 - JEE (αdj A)' is equal to:
(a) Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 4 Notes | Study Mathematics (Maths) Class 12 - JEE
(b) Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 4 Notes | Study Mathematics (Maths) Class 12 - JEE
(c) Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 4 Notes | Study Mathematics (Maths) Class 12 - JEE
(d) Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 4 Notes | Study Mathematics (Maths) Class 12 - JEE

Correct Answer is Option (c)
Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 4 Notes | Study Mathematics (Maths) Class 12 - JEE


Q.16: The points on the curve Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 4 Notes | Study Mathematics (Maths) Class 12 - JEE at which the tangents are parallel to y-axis are:
(a) (0, ±4)
(b) (±4, 0)
(c) (±3, 0)
(d) (0, ±3)

Correct Answer is Option (b)

Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 4 Notes | Study Mathematics (Maths) Class 12 - JEE
Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 4 Notes | Study Mathematics (Maths) Class 12 - JEE
⇒ Slope of normal = Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 4 Notes | Study Mathematics (Maths) Class 12 - JEE
As curve's tangent is parallel to y-axes

⇒ 9y/16x = 0
⇒ y = 0 and x = ±3
∴ points = (±3, 0)


Q.17: Given that A = [aij] is a square matrix of order 3 × 3 and |A| = −7, then the value of Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 4 Notes | Study Mathematics (Maths) Class 12 - JEEwhere Aij denotes the cofactor of element αij is:
(a) 7

(b) –7

(c) 0

(d) 49

Correct Answer is Option (b)
|A| = –7

Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 4 Notes | Study Mathematics (Maths) Class 12 - JEE 


Q.18: If y  = log(cos ex), then dy/dx is:
(a) cos ex−1
(b) e–x cos ex
(c) ex sin ex
(d) –ex tan e
x

Correct Answer is Option (b)
y = log(cos ex)
Differentiating w.r.t. x:
Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 4 Notes | Study Mathematics (Maths) Class 12 - JEE


Q.19: Based on the given shaded region as the feasible region in the graph, at which point(s) is the objective function Z = 3x + 9y maximum?
Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 4 Notes | Study Mathematics (Maths) Class 12 - JEE
(a) Point B
(b) Point C
(c) Point D
(d) every point on the line segment CD

Correct Answer is Option (d)
Z is maximum 180 at points C (15, 15) and D(0, 20).
⇒ Z is maximum at every point on the line segment CD.


Q.20: The least value of the function f(x) = 2cos x + x in the closed interval [0, π/2] is:
(a) 2  
(b) π/6 + √3
(c) π/2
(d) The least value does not exist

Correct Answer is Option (c)
f(x) = 2cos x + x,
Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 4 Notes | Study Mathematics (Maths) Class 12 - JEE


Section - B

Q.21: Which of the following functions from Z into Z are bijections?
(a) f(x) = x3
(b) f(x) = x + 8
(c) f(x) = 4x + 1
(d) f(x) = x2 + 7

Correct Answer is Option (b)
For bijection on Z, f(x) must be one-one and onto. Function f(x) = x2 + 7 is many-one as f(1) = f(–1) Range of f(x) = x3 is not Z for x ∈ Z. Also f(x) = 4x + 1 takes only values of type = 4k + 1 for x ∈ k ∈ Z But f(x) = x + 8 takes all integral values for x ∈ Z. Hence f(x) = x + 8 is a bijection of Z. 


Q.22: If Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 4 Notes | Study Mathematics (Maths) Class 12 - JEEthen dy/dx is equal to
(a) Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 4 Notes | Study Mathematics (Maths) Class 12 - JEE
(b) Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 4 Notes | Study Mathematics (Maths) Class 12 - JEE
(c) Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 4 Notes | Study Mathematics (Maths) Class 12 - JEE
(d) Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 4 Notes | Study Mathematics (Maths) Class 12 - JEE

Correct Answer is Option (b)
Given that,
Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 4 Notes | Study Mathematics (Maths) Class 12 - JEE
Differentiate with respect to x, we have
Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 4 Notes | Study Mathematics (Maths) Class 12 - JEE


Q.23: The feasible region for an LPP is always a _______ polygon.
(a) Concave
(b) Convex
(c) Both A and B
(d) None

Correct Answer is Option (b)
The feasible region for an LPP is always a convex polygon.


Q.24: Local maximum of the function 3x 4 −20x3+36x 2 + 322 in (−10, 10) ?
(a) 2

(b) 3

(c) 0

(d) 5
Correct Answer is Option (a)
Let f(x)
= 3x4 – 20x3 +36 x2 + 322
f '(x) = 12x3 – 60x2 + 72x
Put f '(x) = 0
12x3 – 60x2 + 72x = 0
12x (x2 – 5x + 6) = 0
12x (x – 2) (x – 3) = 0
x = 0, 2, 3
f ''(x) = 36x2 – 120x + 72
f ''(0) = 72 > 0
f ''(2) = 36 × 22 – 120 × 2 + 72 = –24 < 0
f ''(3) = 36 × 32 – 120 × 3 + 72 = 36 > 0
∴ We get local maxima at x = 2.


Q.25: If the matrix A is both symmetric and skew symmetric, then
(a) A is a diagonal matrix
(b) A is a zero matrix
(c) A is a square matrix
(d) None of these

Correct Answer is Option (b)
If A is both symmetric and skew-symmetric then we have, A' = A and A' = –A
⇒ A = –A
⇒  A + A = 0
⇒ 2A = 0
⇒ A = 0
Therefore, A is a zero matrix.


Q.26: f(x) = [x] The function is:
(a) Not Continuous
(b) continuous
(c) Differentiable
(d) None of these

Correct Answer is Option (a)
L.H.L and R.H.L. are not equal at integer points.


Q.27: What is the domain of the sec–1 x ?
(a) [−∞, ∞]
(b) (−∞, ∞)
(c) (–1, 1)
(d) (−∞, −1] ∪ [1,∞)

Correct Answer is Option (d)
The sec function is periodic so to calculate its inverse function we need to make the function bijective. For that we have to consider an interval in which all values of the function exist and do not repeat. Now for the inverse of a function the domain becomes range and the range becomes domain. Thus the range of secant function, that is, (−∞,−1]∪[1,∞) becomes the domain of inverse function.


Q.28: If Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 4 Notes | Study Mathematics (Maths) Class 12 - JEEthen det (adj A) equals

(a) a27

(b) a9

(c) a6

(d) a2

Correct Answer is Option (c)
Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 4 Notes | Study Mathematics (Maths) Class 12 - JEE


Q.29: The tangent to the curve y = e2x at the point (0, 1) meets x-axis at :
(a) (0, 1)
(b) (-1/2, 0)
(c) (2, 0)
(d) (0, 2)

Correct Answer is Option (b)
The equation of the curve is given by  y = e2x Since, it passes through the point (0, 1).
Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 4 Notes | Study Mathematics (Maths) Class 12 - JEE
= Slope of tangent to the curve.
∴ Equation of tangent is
y - 1 = 2(x -0)
⇒ y = 2x + 1
Since, tangent to the curve y = e2x at the point (0, 1) meets x-axis, i.e., y = 0.
∴ 0 = 2x + 1
x = -1/2
So, the required point is (-1/2, 0).


Q.30: Consider the set A = {1, 3, 5, 7}. The number of reflexive relations on set A is :
(a) 212
(b) 122
(c) 24
(d) 4
2

Correct Answer is Option (a)
By definition, a relation in A is said to be reflexive if xRx, ∀x ∈ A.
So R is true.
The number of reflexive relations on a set containing n elements is 2 n2 -n
Here n = 4.
The number of reflexive relations on a set A = 212


Q.31: The interval on which the function f (x) = 2x+ 9x2 + 12x- 1 is decreasing is:
(a) [–1, ∞)
(b) (–2, –1)
(c) (–∞, –2]
(d) [–1, 1]

Correct Answer is Option (c)
Given that,
f(x) = 2x3 + 9x+ 12x - 1
f'(x) = 6x2 + 18x + 12
= 6(x2 + 3x + 2)
6(x + 2)(x + 1)

So, f'(x) ≤ 0 for decreasing.
On drawing number lines as below:
Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 4 Notes | Study Mathematics (Maths) Class 12 - JEE
We see that f '(x) is decreasing in (−2, −1).


Q.32: If A Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 4 Notes | Study Mathematics (Maths) Class 12 - JEEFind A2

(a) Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 4 Notes | Study Mathematics (Maths) Class 12 - JEE
(b) Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 4 Notes | Study Mathematics (Maths) Class 12 - JEE
(c) Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 4 Notes | Study Mathematics (Maths) Class 12 - JEE
(d) None of these

Correct Answer is Option (b)
We need to find A2 and we know that A2 = A.A
Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 4 Notes | Study Mathematics (Maths) Class 12 - JEE


Q.33: A corner point of a feasible region is a point in the region which is the __________ of two boundary lines.
(a) Intersection
(b) Disjoint
(c) Middle point
(d) None

Correct Answer is Option (a)
A corner point of a feasible region is a point in the region which is the intersection of two boundary lines.


Q.34: The function f(x) = 2x3 – 3x2 – 12x + 4, has
(a) two points of local maximum
(b) two points of local minimum
(c) one maxima and one minima
(d) no maxima or minima

Correct Answer is Option (c)
We have,
f(x) = 2x3 + 3x2 + 12x + 4
f'(x) = 6 x2 + 6x - 12
Now, f'(x) = 0
⇒ 6(x2 - x - 2) = 0
⇒ 6 (x + 1)(x - 2) = 0
⇒ x = -1 and x = +2
On number line for f’(x), we get
Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 4 Notes | Study Mathematics (Maths) Class 12 - JEE
Hence, x = −1 is point of local maxima and x = 2 is point of local minima.
So, f(x) has one maxima and one minima.


Q.35: If A Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 4 Notes | Study Mathematics (Maths) Class 12 - JEEthen A2 – 5A + 7I2 is equal to
(a) 0
(b) 1
(c) –1
(d) 2

Correct Answer is Option (a)
Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 4 Notes | Study Mathematics (Maths) Class 12 - JEE
Value of A2 – 5A + 7I2
Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 4 Notes | Study Mathematics (Maths) Class 12 - JEE
Since, all the elements of matrix are zero. So, given matrix is null/zero matrix.


Q.36: The principal value of tan−1 (−√3) is:
(a) π/3
(b) - π/3
(c) 2π/3
(d) π/6

Correct Answer is Option (b)
The principal value of tan−1 (−√3) means that we need to find an angle in the principal branch of the function where the tangent function is equal to -√3 . Hence the required value is - π/3.

Q.37: The principal value of Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 4 Notes | Study Mathematics (Maths) Class 12 - JEE is:
(a) π/3
(b) π/2
(c) π/6
(d) π/4

Correct Answer is Option (c)
The principal value of means that we need to find an angle in the principal branch of the function where the secant function is equal to 2/√3. Hence the required value is π/6.

Q.38. Evaluate the determinant Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 4 Notes | Study Mathematics (Maths) Class 12 - JEE
(a) –17
(b) log3 18
(c) log28
(d) 15/2

Correct Answer is Option (d)
For simplification usage of the properties of logarithm are required
Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 4 Notes | Study Mathematics (Maths) Class 12 - JEE


Q.39: The points at which the tangents to the curve y = x3 – 12x + 18  are parallel to x-axis are:
(a) (2, 2), (–2, –34)
(b) (2, 34), (–2, 0)
(c) (0, 34), (–2, 0)
(d) (2, 2), (–2, 34)

Correct Answer is Option (d)
The equation of the curve is given by
y = x3 – 12x + 18
On differentiating with respect to x, we get
Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 4 Notes | Study Mathematics (Maths) Class 12 - JEE
So, the slope of line parallel to the x-axis,
Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 4 Notes | Study Mathematics (Maths) Class 12 - JEE
So, the points are (2, 2) and (−2, 34).


Q.40: If matrix A = [1   2   3]. Write A.A' where A' is the transpose of matrix A.
(a) 4
(b) 21
(c) 14
(d) 28

Correct Answer is Option (c)
Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 4 Notes | Study Mathematics (Maths) Class 12 - JEE

Section - C

Q.41: The optimal value of the objective function is attained at the points.
(a) X-axis only
(b) Y-axis only
(c) Corner points of feasible region
(d) Origin only

Correct Answer is Option (c)
The optimal value of the objective function is attained at the corner points of feasible region.


Q.42: For the curve y = 5x – 2x3, if x increases at the rate of 2 units/sec, then at x = 3 the slope of curve is changing at ________ units/sec.
(a) –72
(b) –36
(c) 24
(d) 48

Correct Answer is Option (a)
Given
Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 4 Notes | Study Mathematics (Maths) Class 12 - JEE


Q.43: y = x(x – 3)2 decreases for the values of x given by:
(a) 1 < x < 3
(b) x < 0
(c) x > 0
(d) 0 < x < 3/2

Correct Answer is Option (a)
Given that, y = x(x – 3)2
Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 4 Notes | Study Mathematics (Maths) Class 12 - JEE
So, y = x(x – 3)2 decreases for (1, 3).
[Since, y' < 0  for all x ∈ (1, 3), hence y is decreasing on (1, 3)].


Q.44: For the constraints of linear optimizing function Z = x1 + x2 given by x1 + x2 ≤ 1, 3x1 + x2 ≥1, there is feasible region
(a) Yes
(b) No
(c) Can't be determined
(d) None of these

Correct Answer is Option (b)
Clearly from the graph below that there is no feasible region.
Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 4 Notes | Study Mathematics (Maths) Class 12 - JEE


Q.45: Let A = Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 4 Notes | Study Mathematics (Maths) Class 12 - JEEthen |AB| is equal to
(a) 460
(b) 2000
(c) 3000
(d) – 7000

Correct Answer is Option (d)
Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 4 Notes | Study Mathematics (Maths) Class 12 - JEE


CASE-STUDY

A manufacture produces three stationery products Pencil, Eraser and Sharpener which he sells in two markets. Annual sales are indicated below
Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 4 Notes | Study Mathematics (Maths) Class 12 - JEEClass 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 4 Notes | Study Mathematics (Maths) Class 12 - JEEIf the unit Sale price of Pencil, Eraser and Sharpener are Rs 2.50, Rs 1.50 and Rs 1.00 respectively, and unit cost of the above three commodities are Rs 2.00, Rs 1.00 and Rs 0.50 respectively, then,
Based on the given information, answer the following questions.

Q.46: Total revenue of market A
(a) Rs 64,000
(b) Rs 60,400
(c) Rs 46,000
(d) Rs 40600

Correct Answer is Option (c)
Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 4 Notes | Study Mathematics (Maths) Class 12 - JEE


Q.47: Total revenue of market B
(a) Rs 35,000
(b) Rs 53,000
(c) Rs 50,300
(d) Rs 30,500

Correct Answer is Option (b)
Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 4 Notes | Study Mathematics (Maths) Class 12 - JEE
= [2.50 × 6,000 + 1.50 × 20,000 + 1.00 × 8,000]
= [53,000]


Q.48: Cost incurred in market A
(a) Rs 13,000
(b) Rs 30,100
(c) Rs 10,300
(d) Rs 31,000

Correct Answer is Option (d)
Cost incurred in marker A
Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 4 Notes | Study Mathematics (Maths) Class 12 - JEE


Q.49: Profits in market A and B respectively are
(a) (Rs 15,000, Rs 17,000)
(b) (Rs  17,000, Rs 15,000)
(c) (Rs  51,000, Rs 71,000)
(d) (Rs 10,000, Rs 20,000)

Correct Answer is Option (a)
Cost incurred in market B
Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 4 Notes | Study Mathematics (Maths) Class 12 - JEE
Profit of market A & B = total revenue of A and B – Cost increased in market A and B
Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 4 Notes | Study Mathematics (Maths) Class 12 - JEE


Q.50: Gross profit in both markets
(a) Rs 23,000
(b) Rs 20,300
(c) Rs 32,000
(d) Rs 30,200

Correct Answer is Option (c)
Gross profit in both markets = Profit in A + Profit in B
= 15,000 + 17,000
= Rs 32,000

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