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CBSE Class 12 Mathematics Previous Year Question Paper Term 1 2021 SSJ-1-Set-4

Your CBSE Class 12 syllabus for Maths consists of topics such as linear programming, vector quantities, determinants, etc. which lay the foundation for further education in science, engineering, management, etc. Studying differential equations will be useful for exploring subjects such as Physics, Biology, Chemistry, etc. where your knowledge can be applied for scientific investigations.

On TopperLearning, you can find study resources such as sample papers, mock tests, Class 12 Maths NCERT solutions and more. These learning materials can help you understand concepts such as differentiation of functions, direction cosines, integrals, and more. Also, you can practise the Maths problems by going through the solutions given by our experts.

Maths is considered as one of the most difficult subjects in CBSE Class 12 Science. Our Maths experts simplify complex Maths problems by assisting you with the right methods to solve problems and score full marks. You may still have doubts while referring to the Maths revision notes or Maths NCERT solutions. Solve those doubts by asking an expert through the “Undoubt” feature on the student dashboard.

SECTION A

In this section, attempt any 16 questions out of questions no. 1 to 20.

 

Question 1.

A relation R is defined on N. Which of the following is the reflexive relation?

  1. R = {(x, y): x > y; x, y ∊ N} 
  2. R = {(x, y): x + y = 10; x, y ∊ N)}
  3. R = {(x, y): xy is the square number; x, y ∊ N}
  4. R = {(x, y): x + 4y = 10; x, y ∊ N} 


Question 2.

The function f: R ⟶ R defined by f(x) = 4 + 3 cos x is:

  1. bijective
  2. one-one but not onto
  3. onto but not one-one
  4. neither one-one nor onto
 

Question 3.

If y = cot-1 x, x < 0, then:

  1. begin mathsize 11px style straight pi over 2 less than y less or equal than straight pi end style
  2. begin mathsize 11px style straight pi over 2 less than straight y less than straight pi end style
  3. begin mathsize 11px style negative straight pi over 2 less than straight y less than 0 end style
  4. begin mathsize 11px style negative straight pi over 2 less or equal than straight y less than 0 end style


Question 4.

The number of functions defined from {1, 2, 3, 4, 5} ⟶ {a, b} which are one-one is:

  1. 5
  2. 3
  3. 2
  4. 0
 

Question 5.

If A = begin mathsize 11px style open square brackets table row 4 2 row cell negative 1 end cell 1 end table close square brackets end style, then (A – 2I) (A – 3I) is equal to:

  1. A
  2. I
  3. 5I
  4. O


Question 6.

If P is a 3 x 3 matrix such that P’ = 2P + I, where P’ is the transpose of P, then:

  1. P = I
  2. P = –I
  3. P = 2I
  4. P = –2I

 

Question 7.

If order of matrix A is 2 x 3, of matrix B is 3 x 2, and of matrix C is 3 x 3, then which one of the following is not defined?

  1. C (A + B’)
  2. C (A + B’)’
  3. BAC
  4. CB + A'
 

Question 8.

If A = begin mathsize 11px style open square brackets table row alpha 2 row 2 alpha end table close square brackets end style  and |A3| = 27, then the value of α is:

  1. begin mathsize 11px style plus-or-minus 1 end style
  2. begin mathsize 11px style plus-or-minus 2 end style
  3. begin mathsize 11px style plus-or-minus square root of 5 end style
  4. begin mathsize 11px style plus-or-minus square root of 7 end style

Question 9.

begin mathsize 11px style 1 straight f space open vertical bar table row 5 3 cell negative 1 end cell row cell negative 7 end cell straight x cell negative 3 end cell row 9 6 cell negative 2 end cell end table close vertical bar end style = 0, then the value of x is:

  1. 3
  2. 5
  3. 7
  4. 9


Question 10.

The inverse of begin mathsize 11px style open square brackets table row cell negative 4 end cell 3 row 7 cell negative 5 end cell end table close square brackets end style is:

  1. begin mathsize 11px style open square brackets table row cell negative 5 end cell 3 row 7 cell negative 4 end cell end table close square brackets end style
  2. begin mathsize 11px style open square brackets table row 5 3 row 7 4 end table close square brackets end style
  3. begin mathsize 11px style open square brackets table row cell negative 5 end cell 7 row 3 cell negative 4 end cell end table close square brackets end style
  4. begin mathsize 11px style open square brackets table row cell negative 5 end cell cell negative 3 end cell row cell negative 7 end cell cell negative 4 end cell end table close square brackets end style
 

Question 11.

begin mathsize 11px style IF space straight A equals open square brackets table row 1 0 0 row 0 1 0 row 59 69 cell negative 1 end cell end table close square brackets end style, then A–1:

  1. is A
  2. is (-A)
  3. is A2
  4. does not exist


Question 12.

If the function Error converting from MathML to accessible text.is continuous, then the value of k is:

  1. begin mathsize 11px style 2 over 7 end style
  2. begin mathsize 11px style 7 over 2 end style
  3. begin mathsize 11px style 3 over 7 end style
  4. begin mathsize 11px style 4 over 7 end style


Question 13.

The function f(x) = [x], where lx] is the greatest integer function that is less than or equal to x, is continuous at:

  1. 4
  2. –2
  3. 1.5
  4. 1
 

Question 14.

If y = tan–1(e2x), then begin mathsize 11px style dy over dx end style  is equal to:

  1. begin mathsize 11px style fraction numerator 2 straight e to the power of 2 straight x end exponent over denominator 1 plus straight e to the power of 4 straight x end exponent end fraction end style
  2. begin mathsize 11px style fraction numerator 1 over denominator 1 plus straight e to the power of 4 x end exponent end fraction end style
  3. begin mathsize 11px style fraction numerator 2 over denominator straight e to the power of 2 straight x end exponent plus straight e to the power of negative 2 straight x end exponent end fraction end style
  4. begin mathsize 11px style fraction numerator 1 over denominator straight e to the power of 2 straight x end exponent minus straight e to the power of negative 2 straight x end exponent end fraction end style


Question 15.

If y2 (2 – x) = x3,  then begin mathsize 11px style open parentheses straight d subscript straight y over dx close parentheses subscript left parenthesis space 1 comma 1 right parenthesis end subscript end style is equal to:

  1. 2
  2. –2
  3. 3 
  4. begin mathsize 11px style negative 3 over 2 end style
 

Question 16.

The angle between the tangents to the curve y = x2 – 5x + 6 at the points (2, 0) and (3, 0) is:

  1. begin mathsize 11px style straight pi over 2 end style
  2. begin mathsize 11px style straight pi over 3 end style
  3. begin mathsize 11px style straight pi over 4 end style
  4. 0

Question 17.

The interval, in which function y = x3 + 6x2 + 6 is increasing is:

  1. (–∞, –4) U (0, ∞)
  2. (–∞, 4)
  3. (–4, 0)
  4. (–∞, 0) U (4, ∞)
 

Question 18.

The value of x for which (x – x2) is maximum, is:

  1. begin mathsize 11px style 3 over 4 end style
  2. begin mathsize 11px style 1 half end style
  3. begin mathsize 11px style 1 third end style
  4. begin mathsize 11px style 1 fourth end style

Question 19.

If the corner points of the feasible region of an LPP are (0, 3), (3, 2) and (0, 5), then the minimum value of Z = 11x + 7y is:

  1. 21
  2. 33
  3. 14
  4. 35
 

Question 20.

The number of solutions of the system of inequations x + 2y ≤ 3, 3x + 4y ≥ 12, x ≥ 0, y ≥ 1 is:

  1. 0
  2. 2
  3. finite
  4. infinite

 

SECTION B

In this section, attempt any 16 questions out of questions no. 21 to 40.

 

Question 21.

The number of equivalence relations in the set {1, 2, 3} containing the elements (1, 2) and (2, 1) is:

  1. 0
  2. 1
  3. 2
  4. 3
 

Question 22.

Let f: R ⟶ R be defined by f(x) = begin mathsize 11px style 1 over straight x end style, for all x ∊ R. Then, f is:

  1. one-one
  2. onto
  3. bijective
  4. not defined
 

Question 23.

The function f: N ⟶ N is defined by f(n) = begin mathsize 11px style open curly brackets table attributes columnalign left end attributes row cell fraction numerator straight n plus 1 over denominator 2 end fraction comma space if space straight n space is space odd end cell row cell straight n over 2 comma space if space straight n space is space even end cell end table close end style  

The function f is:

  1. bijective
  2. one-one but not onto
  3. onto but not one-one
  4. neither one-one nor onto


Question 24.

The value of sin–1 begin mathsize 11px style open parentheses cos fraction numerator 13 straight pi over denominator 5 end fraction close parentheses end style is:

  1. begin mathsize 11px style negative fraction numerator 3 straight pi over denominator 5 end fraction end style 
  2. begin mathsize 11px style negative straight pi over 10 end style
  3. begin mathsize 11px style fraction numerator 3 straight pi over denominator 5 end fraction end style
  4. begin mathsize 11px style straight pi over 10 end style


Question 25.

If sin–1 x > cos–1 x, then x should lie in the interval:

  1. begin mathsize 11px style open parentheses negative 1 comma negative fraction numerator 1 over denominator square root of 2 end fraction close parentheses end style
  2. begin mathsize 11px style open parentheses 0 comma fraction numerator 1 over denominator square root of 2 end fraction close parentheses end style
  3. begin mathsize 11px style open parentheses fraction numerator 1 over denominator square root of 2 end fraction comma 1 close parentheses end style
  4. begin mathsize 11px style open parentheses negative fraction numerator 1 over denominator square root of 2 end fraction comma 0 close parentheses end style


Question 26.

If A =  begin mathsize 11px style open square brackets table row cos straight alpha cell negative sin end cell straight alpha row sin alpha cos straight alpha end table close square brackets end style and A + A’ = I, then the value of α is:

  1. begin mathsize 11px style straight pi over 6 end style
  2. begin mathsize 11px style straight pi over 3 end style
  3. begin mathsize 11px style pi end style
  4. begin mathsize 11px style fraction numerator 3 straight pi over denominator 2 end fraction end style

Question 27.

The determinant  begin mathsize 11px style open vertical bar table row cell straight Y plus straight k end cell straight y straight y row straight y cell straight y plus straight k end cell straight y row straight y straight y cell straight y plus straight k end cell end table close vertical bar end style is equal to:

  1. k(3y + k2)
  2. 3y + k3
  3. 3y + k2
  4. k2(3y + k)

 

Question 28.

If A =  begin mathsize 11px style open vertical bar table row 1 cell negative 2 end cell 4 row 2 cell negative 1 end cell 3 row 4 2 0 end table close vertical bar end style is the adjoint of a square matrix B, then B-1 is equal to:

  1. ±A
  2. ±√2A
  3. begin mathsize 11px style plus-or-minus fraction numerator 1 over denominator square root of 2 end fraction straight B end style
  4. begin mathsize 11px style plus-or-minus fraction numerator 1 over denominator square root of 2 end fraction straight A end style


Question 29.

If A = begin mathsize 11px style open square brackets table row 1 cell negative 1 end cell 1 row 1 cell negative 1 end cell 1 row 1 cell negative 1 end cell 1 end table close square brackets end style , then A5 – A4 – A3+ A2 is equal to

  1. 2A
  2. 2A
  3. 4A
  4. O


Question 30.

If y = e-x, then begin mathsize 11px style fraction numerator straight d squared straight y over denominator dx squared end fraction end style  is equal to:

  1. –y
  2. y
  3. x
  4. –x


Question 31.

If x = t2 + 1, y = 2at, then begin mathsize 11px style fraction numerator straight d squared straight y over denominator dx squared end fraction end style  at t = a is:

  1.  begin mathsize 11px style negative 1 over straight a end style
  2. begin mathsize 11px style negative fraction numerator 1 over denominator 2 straight a squared end fraction end style
  3. begin mathsize 11px style fraction numerator 1 over denominator 2 straight a squared end fraction end style
  4. 0

 

Question 32.

The function begin mathsize 11px style straight f left parenthesis straight x right parenthesis equals open curly brackets table attributes columnalign left end attributes row cell straight x squared comma space for space straight x space less than space 1 end cell row cell 2 minus straight x comma space for space straight x space greater or equal than 1 end cell end table close end style is: 

  1. not differentiable at x = 1
  2. differentiable at x = 1
  3. not continuous at x = 1
  4. neither continuous nor differentiable at x = 1


Question 33.

The curve x2 – xy + y2 = 27 has tangents parallel to x-axis at:

  1. (3, 6) and (–3, –6)
  2. (3, –6) and (–3, 6)
  3. (–3, –6) and (3, –6)
  4. (–3, 6) and (–3, –6)

 

Question 34.

A wire of length 20 cm is bent in the form of a sector of a circle. The maximum area that can be enclosed by the wire is:

  1. 20 sq cm
  2. 25 sq cm
  3. 10 sq cm
  4. 30 sq cm


Question 35.

The function (x – sin x) decreases for:

  1. all x
  2.  begin mathsize 11px style straight x less than straight pi over 2 end style
  3.  begin mathsize 11px style 0 less than straight x less than straight pi over 4 end style
  4. no value of x


Question 36.

If θ is the angle of intersection between the curves y2 = 4ax and ay = 2x2 at (a, 2a),  then the value of tan θ is: 

  1. begin mathsize 11px style 3 over 5 end style
  2. begin mathsize 11px style 2 over 3 end style
  3. begin mathsize 11px style 3 over 4 end style
  4. begin mathsize 11px style 2 over 5 end style


Question 37.

The maximum value of Z = 3x + 4y subject to the constraints x ≥ 0, y ≥ 0 and x + y ≤ 1 is:

  1. 7
  2. 4
  3. 3
  4. 10
 

Question 38.

The feasible region of an LPP is given in the following figure:

 

Then, the constraints of the LPP are x ≥ 0, y ≥ 0 and

  1. 2x + y ≤ 52 and x + 2y ≤ 76
  2. 2x + y ≤ 104 and x + 2y ≤ 76
  3. x + 2y ≤ 104 and 2x + y ≤ 76
  4. x + 2y ≤ 104 and 2x + y ≤ 38
 

Question 39.

If the minimum value of an objective function Z =  ax + by occurs at two points (3, 4) and (4, 3), then:

  1. a + b = 0
  2. a = b
  3. 3a = b
  4. a = 3b


Question 40.

For the following LPP
Maximise Z = 3x + 4y
Subject to constraints
x – y ≥ -1, x ≤ 3
x ≥ 0, y ≥ 0
The maximum value is:

  1. 0
  2. 4
  3. 25
  4. 30

 

SECTION C


In this section, attempt any 8 questions out of questions no. 41 – 50.8 × 1 = 8

 

Question 41.

A relation R is defined on Z as:
aRb if and only if a2 – 7ab + 6b2 = 0.
Then, R is:

  1. reflexive and symmetric
  2. symmetric but not reflexive
  3. transitive but not reflexive
  4. reflexive but not symmetric
 

Question 42.

The value of begin mathsize 11px style open vertical bar table row cell vertical line 1 end cell cell vertical line 2 end cell cell vertical line 3 end cell row cell 2 vertical line 2 end cell cell 3 vertical line 3 end cell cell 4 vertical line 4 end cell row cell vertical line 3 end cell cell vertical line 4 end cell cell vertical line 5 end cell end table close vertical bar end style is:

  1. 12
  2. –12
  3. 24
  4. –24

 

Question 43.

begin mathsize 11px style If space open square brackets table row 1 cell negative tan space straight theta end cell row cell tan space straight theta end cell 1 end table close square brackets open square brackets table row 1 cell tan space straight theta end cell row cell negative tan space straight theta end cell 1 end table close square brackets to the power of negative 1 end exponent equals open square brackets table row straight a cell negative straight b end cell row straight b straight a end table close square brackets comma space than colon end style

  1. a = 1 = b
  2. a = cos 2θ, b = sin 2θ
  3. a = sin 2θ, b = cos 2θ
  4. a = cos θ, b = sin θ

 

Question 44.

The normal to the curve 3y = 6x – 5x3 at the  point  begin mathsize 11px style open parentheses 1 comma 1 third close parentheses end style passes through the point:

  1. (3, 1)
  2. (3, 2)
  3. (2, 3)
  4. (1, 1)

 

Question 45.

If y = sin(2 sin-1x), then (1 – x2)y2 is equal to:

  1. –xy1 + 4y
  2. –xy1 – 4y
  3. xy1 – 4y
  4. xy1 + 4y

 

Case Study

Some young entrepreneurs started an industry “young achievers” for casting metal into various shapes. They put up an advertisement online stating the same and expecting order to cast metal for toys sculptures, decorative pieces and more.
A group of friends wanted to make innovative toys and hence contacted the “young achievers” to order them to cast metal into solid half cylinders with a rectangular base and semi-circular ends.

 

Based on the above information, answer the following questions:

 

Question 46.

The volume (V) of the casted half cylinder will be:

  1. πr2h
  2.  begin mathsize 11px style table attributes columnalign left end attributes row 1 row cell 3 with bar on top end cell end table πr squared straight h end style
  3.  begin mathsize 11px style table attributes columnalign left end attributes row 1 row cell 2 with bar on top end cell end table πr squared straight h end style
  4.  πr2(r + h)
 

Question 47.

The total surface area (S) of the casted half cylinder will be:

  1. πrh + 2πr2 + rh
  2. πrh + πr2 + 2rh
  3. 2πrh + πr2 + 2rh
  4. πrh + πr2 + rh
 

Question 48.

The total surface area S can be expressed in terms of V and r as:

  1. begin mathsize 11px style 2 πr plus fraction numerator 2 straight V left parenthesis straight pi plus 2 right parenthesis over denominator πr end fraction end style
  2. begin mathsize 11px style πr plus fraction numerator 2 V over denominator pi r end fraction end style
  3. begin mathsize 11px style πr squared plus fraction numerator 2 straight V left parenthesis straight pi plus 2 right parenthesis over denominator πr end fraction end style
  4. begin mathsize 11px style 2 πr squared plus fraction numerator 2 straight V left parenthesis straight pi plus 2 right parenthesis over denominator πr end fraction end style


Question 49.

For the given half-cylinder of volume V, the total surface area S is minimum, when:

  1. (π + 2)V = π2r3
  2. (π + 2)V = π2r2
  3. 2(π + 2)V = π2r3
  4. (π + 2)V =π2r
 

Question 50.

The ratio h : 2r for S to be minimum will be equal to:

  1. 2π : π + 2
  2. 2π : π + 1
  3. π : π + 1
  4. π : π + 2


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