Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE

JEE: Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE

The document Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE is a part of the JEE Course Mathematics (Maths) Class 12.
All you need of JEE at this link: JEE

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: What is the principal value branch of cosec–1 x ?
(a) (-1, 1)
(b) [-1,1]
(c) Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE
(d) Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE

Correct Answer is Option (c)

The cosec 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. For cosec function this interval is considered as Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE Thus when we take the inverse of the function the domain becomes range and the range becomes domain. Hence the principal value branch is the range of cosec–1 x, that is Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE


Q.2: Find the value of k if derivative of the function exists Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE
(a) k = 4/5
(b) k = 4/7
(c) k = 4/9
(d) k =4/11

Correct Answer is Option (c)

Differentiate and substitute the given value.


Q.3: The number of all possible matrices of order 3 × 3 with each entry 0 or 1 is: 
(a) 9 
(b) 28 
(c) 512 
(d) 64

Correct Answer is Option (c)

The given matrix of the order 3 × 3 has 9 elements and each of these elements can be either 0 or 1. Now, each of the 9 elements can be filled in two possible ways. Therefore, by the multiplication principle, the required number of possible matrices is 29 = 512.


Q.4: Calculate the determinant of the given matrix Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE
(a) 1/2
(b) -1/2
(c) 3/2
(d) None of the above

Correct Answer is Option (c)

Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE


Q.5: Which of the following is satisfied by the function, f (x)= 2 sin x−x+1 in the interval Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE

(a) Function has local minimum at x = π/3
(b) Function has local maximum at x = π/3
(c) Function has no critical points in the given interval
(d) Function is increasing in the given interval

Correct Answer is Option (b)

f'(x) > 0 for x < π/3 and f"(x) < 0 for x < π/3


Q.6: if Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE then the value of x is:

(a) –6
(b) –36
(c) 6
(d) 36

Correct Answer is Option (d)

Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE


Q.7: If the set A contains 3 elements and the set B contains 6 elements, then the number of bijective mappings from A to B is: 
(a) 520 
(b) 10 
(c) 0 

(d) None of these

Correct Answer is Option (c)

We know that, if A and B are two non-empty finite sets containing m and n elements, respectively, then the number of one-one and onto mapping (bijective mappings) from A to B is
n! if m = n 0,
if m ≠ n
Given that, m = 5 and n = 6 ⇒ m ≠ n
Number of one-one and onto mapping = 0


Q.8: If Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE
(a) Null Matrix 
(b) I 
(c) A 
(d) –A

Correct Answer is Option (b)

Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE

Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE
Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE


Q.9: The normal to curve y = 7x2 – x4 at x=2 passes through 
(a) (30,4) 
(b) (20,4) 
(c) (10,5) 
(d) (5,20)

Correct Answer is Option (b)

Tangent is perpendicular to the normal.


Q.10: What is the domain of the sin–1 x ? 
(A) [–∞,∞] 
(B) (∞,-∞) 
(C) (–1, 1) 
(D) [–1, 1]

Correct Answer is Option (d)

The sine 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 sine function, that is, [-1,1] becomes the domain of inverse function.


Q.11: Let f : R → R be defined as f (x) = 5x. Choose the correct answer. 
(a) f is one-one onto 
(b) f is many-one onto 
(c) f is one-one but not onto 
(d) f is neither one-one nor onto

Correct Answer is Option (a)

f : R R is defined as f(x) = 5x. Let x, y ∈ R such that
f(x) = f(y) ⇒ 5x = 5y
⇒ x = y
Therefore, f is one-one. Also, for any real number (y) in co-domain R, there exists y/5 in R such that
Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE
Therefore, f is onto. Hence, function f is one-one and onto.


Q.12: Find dy/dx where y = cosec x log x.

(a) Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE

(b) Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE

(c) Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE

(d) Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE

Correct Answer is Option (a)

y = cosecx logx
Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE


Q.13: The value of x for the given determinant Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE is

(a) ± 3 

(b) 3, 1/2

(c) 0

(d) -3, 1/2

Correct Answer is Option (d)

In the given determinant, to find the value of x,
Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE
Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE
Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE


Q.14: What is second derivative of the function, Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE
(a) Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE
(b) Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE
(c) Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE
(d) Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE

Correct Answer is Option (a)

Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE

Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE

Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE


Q.15: Skew symmetric matrix is also called: 
(a) symmetric 
(b) identical matrix 
(c) square matrix 
(d) anti symmetric

Correct Answer is Option (d)

In mathematics, particularly in linear algebra, a skew symmetric (or anti symmetric or antisymmetric) matrix is a square matrix whose transpose equals its negative; that is, it satisfies the condition A = – At.


Q.16: What are the local maximum and minimum for the function 3x4 −54x2 −108x+4x3 in the interval [–5 5] 
(a) x =−1, 3,−3 
(b) x =−1, 3,−2 
(c) x =−1, 4,−4 
(d) x = 2, 3,−3

Correct Answer is Option (a)

Max and min points are the points at which derivative has value 0.


Q.17: Matrix Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE
(a) Skew-symmetric matrix 
(b) Symmetric matrix 
(c) Scalar matrix 
(d) None of these

Correct Answer is Option (d)

The given matrix is not a skew symmetric matrix as A’ ≠ -A. By Definition; we know, A matrix is a skew- symmetric matrix if A’ = -A.


Q.18: Find dy/dx where Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE
(a) Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE
(b) Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE
(c) Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE
(d) Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE

Correct Answer is Option (a)

Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE
Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE


Q.19: For the constraints of a LPP problem given by 
x1 + 2x2 ≤ 2000, x1 + x2 ≤ 1500, x2 ≤ 600 and x1, x2 ≥ 0, the points does not lie in the positive bounded region. 
(a) (1000,0) 
(b) (0, 500) 
(c) (2, 0) 
(d) (2000,0)

Correct Answer is Option (d)

Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE

From the graph, it is clear that the point (2000, 0) is outside.


Q.20: If y = f (x)= sin(log x), then dy/dx =
(a) Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE
(b) Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE
(c) Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE
(d) Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE

Correct Answer is Option (a)

y = f(x) = sin(log x)

Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE

Section - B

Q.21: The function f : R → R defined as f(x) = x3 is:
(a) One-one but not onto
(b) Not one-one but onto
(c) Neither one-one nor onto
(d) One-one and onto

Correct Answer is Option (d)

Let f(x1) = f(x2) ∀ x1, x2 ∈ R
Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE
⇒ f is one-one Let f(x) = x3 = y ∀ y ∈ R
⇒ x = y1/3 every image y ∈ R has a unique pre image in R
⇒ f is onto
∴ f is one-one and onto.


Q.22: If x = a sec θ, y = b tan θ, then Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE
(a) Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE

(b) Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE
(c) Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE
(d) Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE

Correct Answer is Option (a)

x = a secθ
Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE
Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE
Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE


Q.23: In the given graph, the feasible region for a LPP is shaded. The objective function Z = 2x – 3y, will be minimum at:
Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE

(a) (4, 10)
(b) (6, 8)

(c) (0, 8)
(d) (6, 5)

Correct Answer is Option (c)

Z is minimum –24 at (0, 8)


Q.24: The derivative of Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE w.r.t Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE is:
(a) 2
(b) π/2 - 2
(c) π/2
(d) -2

Correct Answer is Option (a)
Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE
and
Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE
⇒ sin v = x   ...(i)

Using (i), we get

⇒ sin–1(2sin v cos v)

⇒ u = 2v
Differentiating with respect to v, we get:
du/dv = 2


Q.25: if Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE, then:

(a) A–1 = B
(b) A–1 = 6B

(c) B–1 = B
(d) B–1 = 1/6A

Correct Answer is Option (d)

AB = 6I
B–1 = 1/6A


Q.26: The real function f(x) = 2x3 – 3x2 – 36x + 7 is:
(a) Strictly increasing in (− ∞,−2) and strictly decreasing in ( −2, ∞)

(b) Strictly decreasing in ( −2, 3)

(c) Strictly decreasing in (− ∞, 3) and strictly increasing in (3, ∞)

(d) Strictly decreasing in (− ∞, −2) ∪ (3, ∞)

Correct Answer is Option (b)

f'(x) = 6(x2 – x – 6)

= 6(x – 3)(x + 2)
Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE
As f'(x) < 0∀ x ∈ (–2, 3)

⇒ f(x) is strictly decreasing in (–2, 3)


Q.27: Simplest form of Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE
(a) π/2 - x/2
(b) 3π/2 - x/2
(c) -x/2
(d) π - x/2

Correct Answer is Option (a)
Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE
Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE


Q.28: Given that A is a non-singular matrix of order 3 such that A2 = 2A, then value of |2A| is:
(a) 6
(b) 8
(c) 64
(d) 16

Correct Answer is Option (c)

A2 = 2A

⇒ |A2| = |2A|

⇒ |A|2 = 23|A|
as |kA| = kn|A| for a matrix of order n.

⇒ either |A| = 0 or |A| = 8

But A is non-singular matrix

∴ |2A| = 82 = 64


Q.29: The value of b for which the function f(x) = x + cosx + b is strictly decreasing over R is: 
(a) b < 1 
(b) No value of b exists 
(c) b ≤ 1 
(d) b ≥ 1

Correct Answer is Option (b)

f'(x) = 1 – sin x

⇒ f'(x) > 0 ∀ x ∈ R

⇒ no value of b exists


Q.30: Let R be the relation in the set N given by R = {(a, b) : a = b – 2, b > 6}, then:
(a) (2, 4) ∈ R 
(b) (3, 8) ∈ R 
(c) (6, 8) ∈ R 
(d) (8, 7) ∈ R

Correct Answer is Option (c)

a = b – 2 and b > 6

⇒ (6, 8) ∈ R


Q.31: The point(s), at which the function f given by Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE is continuous, is/are:

(a) −6, −12, −18
(b) −6, −4, −9

(c) −6, 4, 9
(d) −6, 12, 18

Correct Answer is Option (a)
Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE

⇒ f(x) = –1∀ x ∈ R

⇒ f(x) is continuous ∀ x ∈ R as it is a constant function


Q.32: If Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE then the values of k, a and b respectively are:
(a) −6, −12, −18 
(b) −6, −4, −9 
(c) −6, 4, 9 
(d) −6, 12, 18

Correct Answer is Option (b)

Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE
⇒ k = –6, a = –4
and b = –9


Q.33: A linear programming problem is as follows: Minimize Z = 30x + 50y subject to the constraints, 
3x + 5y ≥15 
2x + 3y ≤ 18 
x ≥ 0, y ≥ 0 
In the feasible region, the minimum value of Z occurs at 
(a) a unique point 
(b) no point 
(c) infinitely many points 
(d) two points only

Correct Answer is Option (d)
Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE

Minimum value of Z occurs at two points


Q.34: The area of a trapezium is defined by function f and given by Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE then the area when it is maximised is:
(a) 75 cm2
(b) 7√3 cm2
(c) 75√3 cm2
(d) 5cm2

Correct Answer is Option (c)
Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE
But x > 0

⇒ x = 5
Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE

Maximum area of trapezium is 75√3 cm2 when x = 5


Q.35: If A is square matrix such that A2 = A, then (I + A)³ – 7 A is equal to: 

(a) A 

(b) I + A 

(c) I − A 

(d) I

Correct Answer is Option (d)

(I + A)3 – 7A

= I + A + 3A + 3A – 7A = I


Q.36: If tan–1 x = y, then:
(a) −1< y <1
(b) Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE
(c) Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE
(d) Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE

Correct Answer is Option (c)


Q.37: Let A = {1, 2, 3}, B = {4, 5, 6, 7} and let f = {(1, 4), (2, 5), (3, 6)} be a function from A to B. Based on the given information, f is best defined as: 
(a) Surjective function 
(b) Injective function 
(c) Bijective function 
(d) function

Correct Answer is Option (b)

As every per-image x ∈A has a unique image y ∈ B
⇒ f is injective function


Q.38: For Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE then 14A–1 is given by:
(a) Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE
(b) Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE
(c) Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE
(d) Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE

Correct Answer is Option (b)

Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE
Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE


Q.39: The point(s) on the curve y = x3 – 11x + 5 at which the tangent is y = x – 11 is/are: 
(a) (–2, 19) 
(b) (2, – 9) 
(c) (±2, 19) 
(d) (–2, 19) and (2, – 9)

Correct Answer is Option (b)
y = x3 – 11x + 5
Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE
Slope of line y = x – 11 is 1

⇒ 3x2 – 11 = 1

⇒ x = ± 2

∴ point is (2, –9) as (–2, 19) does not satisfy given line


Q.40: Given that Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE and A2 = 3I, then:

(a) 1 + α2 + βg = 0
(b) 1 – α2 – βg = 0

(c) 3 – α2 – βg = 0
(d) 3 + α2 + βg = 0

Correct Answer is Option (c)

A2 = 3I
Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE

Section - C

Q.41: The feasible region for an LPP is shown in the given Figure. Let F = 3x – 4y be the objective function. Maximum value of F is
Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE

(a) 0 
(b) 8
(c) 12 
(d) –18

Correct Answer is Option (c)

The feasible region as shown in the figure, has objective function F = 3x – 4y.
Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE
Hence, the maximum value of F is 12.


Q.42: If the curve ay + x2 = 7 and x3 = y, cut orthogonally at (1, 1), then the value of a is: 
(a) 1 
(b) 0 
(c) –6 
(d) 6

Correct Answer is Option (d)

Given that, ay + x2 = 7 and x3 = y

On differentiating both equations with respect to x, we get
Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE
Since, the curve cuts orthogonally at (1, 1).
Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE


Q.43: If x is real, the minimum value of x2 – 8x + 17 is 
(a) -1 
(b) 0 
(c) 1 
(d) 2

Correct Answer is Option (c)

Let,

f (x) = x2 - 8x + 17

On differentiating with respect to x, we get
Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE

Now, Again on differentiating with respect to x, we get
f"(x) = 2 > 0,∀x

So, x = 4 is the point of local minima. Minimum value of f(x) at x = 4
f(4) = 4.4 − 8.4 + 17 = 1



Q.44: 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. Condition on p and q so that the minimum of Z occurs at (3, 0) and (1, 1) is 
(a) p = 2q 
(b) p = q/2 
(c) p = 3q 
(d) p = q

Correct Answer is Option (b)
Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE

So, condition of p and q, so that the minimum of Z occurs at (3, 0) and (1, 1) is

Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE


Q.45: if Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE Then A-1 exist if

(a) λ = 2
(b) λ ≠ 2

(c) λ ≠ –2
(d) None of these

Correct Answer is Option (a)

Given that,
Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE
Expanding along R1,
|A| = 2(6-5) - λ(-5) -3(-2)
= 2 + 5λ + 6

We know that A-1 exists, if A is nonsingular matrix, i.e., |A|≠0
Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE
So, A−1 exists if and only if Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE


Questions 46-50 are based on a Case-Study


Case- Study

Manjit wants to donate a rectangular plot of land for a school in his village. When he was asked to give dimensions of the plot, he told that if its length is decreased by 50 m and breadth is increased by 50 m, then its area will remain same, but if length is decreased by 10 m and breadth is decreased by 20 m, then its area will decrease by 5300 m2. Based on the given information, answer the following questions.

Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE


Q.46: The equations in terms of x and y are
(a) x – y = 50, 2x – y = 550
(b) x – y = 50, 2x + y = 550
(c) x + y = 50, 2x + y = 550
(d) x + y = 50, 2x + y = 550

Correct Answer is Option (b)
Let length of the plot be x and breadth be y.
According to question,
xy = (x – 50)(y + 50)
xy = xy + 50x – 50y – 2500
x – y = 50

And
(xy – 5300) = (x – 10)(y – 20)
xy – 5300 = xy – 20x – 10y + 200

2x + y = 550 ...(ii)


Q.47: Which of the following matrix equation is represented by the given information
(a) Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE
(b) Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE
(c) Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE
(d) Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE

Correct Answer is Option (a)


Q.48: The value of x (length of rectangular field) is 
(a) 150 m 
(b) 400 m 
(c) 200 m 
(d) 320 m

Correct Answer is Option (c)
We have,
Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE
Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE
Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE
Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE


Q.49: The value of y (breadth of rectangular field) is

(a) 150 m 
(b) 200 m
(c) 430 m 
(d) 350 m

Correct Answer is Option (a)


Q.50: How much is the area of rectangular field? 
(a) 60000 sq.m. 
(b) 30000 sq.m. 
(c) 30000 m 
(d) 3000 m

Correct Answer is Option (b)

Area of rectangular field
= xy
= 200 × 150
= 30000 sq.m

The document Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 2 Notes | Study Mathematics (Maths) Class 12 - JEE is a part of the JEE Course Mathematics (Maths) Class 12.
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