# Sample Paper Class 12 Mathematics Term 1 Set A

**SECTION-A**

**In this section, attempt any 16 questions out of Questions 1 –20.****Each Question is of 1 mark weightage.**

**1. What is the principal value of tan–1(1) ? **

(A) π/8

(B) π/6

(C) π/3

(D) π/4

**Answer**

D

**2. Which of the function is decreasing in the interval (π/2 ,π) ? **

(A) sin x

(B) e^{x}

(C) log x

(D) none of these

**Answer**

A

**3. The inverse of the matrices **

**Answer**

C

**4. Consider matrix A =**

(A) column matrix

(B) Row matrix

(C) scalar matrix

(D) Null matrix

**Answer**

A

**5. The function f(x) = 4-X ^{2}/4x – x^{3} **

(A) discontinuous at only one point

(B) discontinuous at exactly two points

(C) discontinuous at exactly three points

(D) none of these

**Answer**

C

**6. Given that a matrix A = **

**satisfies the equation x ^{2} – 6x + 17 = 0. Then the inverse of the matrix by using the equation is:**

(A) -1/17(A – 6I2)

(B) 1/17 (A – 6I2)

(C) 1/17 (A + 6I2)

(D) -1/17 (A + 6I2)

**Answer**

A

**7. The relation R is defined on the set of natural numbers as {(a, b): 2a = b}. which of the following can be an element of the given relation? **

(A) (2, 1), (4, 2), (6, 3)

(B) (1, 2), (2, 4), (3, 6)

(C) All of the above

(D) None of these

**Answer**

B

**8. Given the equations x – 2y – 4 = 0 and –3x + 5y + 7 = 0 are consistent and has the solution as **

(A) x = –6, y = –5

(B) x = 6, y = 5

(C) x = –6, y = 5

(D) x = 6, y = –5

**Answer**

A

**9. Find slope of the normal to the curve y = 5x ^{3} at x = 1/3 ? **

(A) -3/5

(B) -2/5

(C) -6/5

(D) -9/5

**Answer**

A

**10. What is the principal value of cosec–1(2)? **

(A) π/8

(B) π/6

(C) π/3

(D) π/12

**Answer**

B

**11. If f(x _{1}) = f(x_{2}) ⇒ x_{1} = x_{2} ∀ x_{1}.x_{2} ∈ A then the function f : A → B is **

(A) one-one

(B) one-one onto

(C) onto

(D) many one

**Answer**

A

**12. If y = asec ^{2}q and x = acosec^{2}q then (dy/dx)_{θ = π/4} will be **

(A) 0

(B) –1

(C) 2

(D) 4

**Answer**

B

**13. If A _{2} – A + I = 0 then the inverse of A is **

(A) A – I

(B) I – A

(C) A + I

(D) A

**Answer**

B

**14. If y = 5t ^{3}/tan t then dy/dt will be **

**Answer**

C

**15. The determinant of matrix A = **

**is given as |A| = –37, then calculate the determinant of **

(A) –37

(B) –74

(C) 74

(D) –296

**Answer**

D

**16. If y = 2x – log x then the slope of tangent at x = 1 is **

(A) 2

(B) 3

(C) –2

(D) 1

**Answer**

D

**17. If matrix A is inverse of matrix B, then (AB) will be equal to: **

(A) A + B

(B) (BA)

(C) B/A

(D) A – B

**Answer**

B

**18. If y = cos ^{2}θ/sin^{2} θ – cos^{2}θ then dy/dx will be **

(A) y = 2 cos θ/sin θ – cos

^{2}θ

(B) y = sin θ/sin

^{2}θ – tan θ

(C) 0

(D) y = cos tan θ/sin

^{2 }θ – cos

^{2}θ

**Answer**

C

**19. Minimize Z = 14x – 15y subject to the constraints: x + y ≤ 7, 3x + 2y – 6 ≥ 0, x ≥ 0, y ≥ 0 **

(A) (0, 3)

(B) (3, 2)

(C) (0, 7)

(D) (3, 4)

**Answer**

C

**20. In the interval (0,π/2) local maximum of the function f (x) = 2sinx – x + 1 is at **

(A) x = π/32

(B) x = π/4

(C) x = π/12

(D) x = π/3

**Answer**

D

**SECTION-B**

**In this section, attempt any 16 questions out of the Questions 21 -40.****Each Question is of 1 mark weightage.**

**21. Given a function, f(x) = x ^{3} + x then the function is **

(A) Bijective

(B) Injective

(C) Surjective

(D) None of these

**Answer**

B

**22. If xy5 + 2y + 5x = 0 then dy/dx = y1 will be **

**Answer**

A

**23. Neha goes to the market with Rs 500 to buy salt which is available in packets of 1kg. The price of one packet of salt is ₹30. If y denotes the number of the packets of salts which she buys, then the constraints are_______ and________ **

(A) y ≥ 0 and 30y > 500

(B) y ≤ 0 and y < 500

(C) y > 0 and 30y ≤ 500

(D) y ≥ 0 and 30y ≤ 500

**Answer**

D

**24. If y = 1/√x ^{2} + y then dy/dx will be **

(A) xy

^{3}/2 – y

^{3}

(B) y

^{3}x/2+y

^{3}

(C) -2y

^{3}x/2+y

^{3}

(D) 2y

^{3}x/2+y

^{3}

**Answer**

C

**25. Let AX = B be a system of n-linear equations in n unknowns and |A| = 0 and (adj A)B ≠ 0, then the system of linear equations is **

(A) Consistent

(B) Inconsistent

(C) Can’t determined

(D) None of these

**Answer**

B

**26. Angle between two curves y = x ^{2} – 5, y = x^{4} at x = 1 ? **

(A) 2/9

(B) 2/6

(C) 4/3

(D) 2/3

**Answer**

A

**27. The principal value of sin-1 (-1/2) + sin -1 (1/2) is **

(A) π/3

(B) -π/6

(C) π/6

(D) 0

**Answer**

D

**28. The area of a triangle with vertices (–3, 0), (3, 0) and (0, k) is 9 sq. units. Then, the value of k will be **

(A) 9

(B) 3

(C) –9

(D) 6

**Answer**

B

**29. The smallest value of the polynomial x ^{3} – 18x^{2} + 96x in [0, 9] is **

(A) 126

(B) 0

(C) 135

(D) 160

**Answer**

B

**30. Let R be the set of real numbers then A = {(x, y) ∈ R × R : y – x is an integer} is a **

(A) only reflexive

(B) only symmetric

(C) transitive relation

(D) empty relation

**Answer**

C

**31. The function f(x) = cot x is discontinuous on the set **

(A) {x = np; n∈Z}

(B) {x = 2np; n∈Z}

(C) {x = (2n+1)π/2 ; n∈Z}

(D) {x =nπ/2 ; n∈Z}

**Answer**

A

**32. Given a matrix A = **

(A) 0

(B) 5

(C) 3

(D) 1

**Answer**

A

**33. Which of the following term is not a part of a linear programming problem? **

(A) Concave region

(B) Slack variables

(C) Objective function

(D) Feasible solution

**Answer**

A

**34. Consider the function y = f(x) defined over [a, b], function has absolute maximum at b and local maximum at c where **

(A) c ≠ a, c ≠ b

(B) c = a, c ≠ b

(C) c ≠ a, c = b

(D) c = a = b

**Answer**

A

**35. Assume X, Y, Z, W and P are matrices of order 2 × n, 3 × k, 2 × p, n × 3 and p × k, respectively. If n = p, then the order of the matrix 7X – 5Z is: **

(A) p × 2

(B) 2 × n

(C) n × 3

(D) p × n

**Answer**

B

**36. If sin(sin–1x) = x, then **

(A) –p/2 < x < p/2

(B) –1 ≤ x ≤ 1

(C) –1 < x < 1

(D) –p/2 ≤ x ≤ p/2

**Answer**

B

**37. Consider the non-empty set consisting of children in a family and a relation R defined as aRb if a is brother of b. Then R is **

(A) symmetric but not transitive

(B) transitive but not symmetric

(C) neither symmetric nor transitive

(D) both symmetric and transitive

**Answer**

B

**38. If A and B are invertible matrices, then which of the following is not correct? **

(A) adj A = A .A^{-1}

(B) det(A- ) = [det(A)] ^{-1 }

(C) (AB) ^{-1} = B ^{-1} A ^{-1 }

(D) (A + B)^{-1} = B^{-1} + A^{-1}

**Answer**

D

**39. Let R be the relation in the set {1, 2, 3, 4} given by R = {(1, 2), (2, 2), (1, 1), (4, 4), (1, 3), (3, 3), (3, 2)}. ****Choose the correct answer.**

(A) R is reflexive and symmetric but not transitive

(B) R is reflexive and transitive but not symmetric

(C) R is symmetric and transitive but not reflexive

(D) R is an equivalence relation.

**Answer**

B

**40. If A =**

**and A + A’ = I, then the value of α is:**

(A) π/6

(B) π/3

(C) π

(D) 3π/2

**Answer**

B

**SECTION-C**

**In this section, attempt any 8 questions. Each question is of 1-Questions 46-50 are based on a Case-Study.**

**41. Non-negative restriction of decision variables satisfy_________ **

(A) Feasible solution

(B) Infeasible solution

(C) Graphical solution

(D) All of the above

**Answer**

A

**42. If y = 3cos ^{2}x + 4sin^{2}x then, **

(A) d

^{2}y/dx

^{2}+ 4 = 0

(B) d

^{2}y/dx – 3y = 0

(C) d

^{2}y/dx

^{2}– 4y = 0

(D) d

^{2}y/dx

^{2}+ 2y = 0

**Answer**

A

**43. The equation of normal to the curve 3x ^{2} – y^{2} = 8 which is parallel to the line x + 3y = 8 is **

(A) 3x – y = 8

(B) 3x + y + 8 = 0

(C) x + 3y ± 8 = 0

(D) x + 3y = 0

**Answer**

C

**44. The feasible region for a LPP is shown in fig. **

**The minimum value of z = 3x + 3 – 5y is**

(A) –595

(B) 550

(C) 0

(D) 470

**Answer**

D

**45. If **

(A) 6

(B) ±6

(C) –6

(D) 0

**Answer**

B

**CASE-STUDY**

**P(x) = –5x ^{2} + 125x + 37500 is the total profit function of a company, where x is the production of the company. **

**Based on the given information, answer the following questions.**

**46. What will be the production when the profit is maximum? **(A) 37,500

(B) 12.5

(C) – 12.5

(D) – 37,500

**Answer**

B

**47. What will be the maximum profit? **(A) ₹ 38,28,125

(B) ₹ 38,281.25

(C) ₹ 39,000

(D) None of these

**Answer**

B

**48. Check in which interval the profit is strictly increasing . **(A) (12.5, ∞)

(B) for all real numbers

(C) for all positive real numbers

(D) (0, 12.5)

**Answer**

D

**49. When the production is 2 units, what will be the profit of the company? **(A) 37,500

(B) 37,730

(C) 37,770

(D) None of these

**Answer**

B

**50. What will be production of the company when the profit is ₹ 38,250? **(A) 15

(B) 30

(C) 10

(D) data is not sufficient to find

**Answer**

C