PYQ Vault

Day 139: CBSE Class 12 Maths

5 questions (9 parts). Try each one first, then open its answer.

  1. Question 1 (case study, 4 parts)

    Inverse Trigonometric Functions. Asked once: 2024 (same type asked 4 times)

    If a function f:X→Yf : X \to Y defined as f(x)=yf(x) = y is one-one and onto, then we can define a unique function g:Y→Xg : Y \to X such that g(y)=xg(y) = x, where x∈Xx \in X and y=f(x)y = f(x), y∈Yy \in Y. Function g is called the inverse of function f. The domain of sine function is R and function sine : R→RR \to R is neither one-one nor onto. The following graph shows the sine function. Let sine function be defined from set A to [−1,1][-1, 1] such that inverse of sine function exists, i.e., sin⁡−1x\sin^{-1} x is defined from [−1,1][-1, 1] to A. On the basis of the above information, answer the following questions :
    38 (i)
    If A is the interval other than principal value branch, give an example of one such interval.
    38 (ii)
    If sin⁡−1(x)\sin^{-1} (x) is defined from [−1,1][-1, 1] to its principal value branch, find the value of sin⁡−1(−12)−sin⁡−1(1)\sin^{-1} \left( -\dfrac{1}{2} \right) - \sin^{-1} (1).
    38 (iii) (a)
    Draw the graph of sin⁡−1x\sin^{-1} x from [−1,1][-1, 1] to its principal value branch.
    38 (iii) (b)
    Find the domain and range of f(x)=2sin⁡−1(1−x)f(x) = 2 \sin^{-1} (1 - x).

  2. Question 2

    Linear Programming. Asked once: 2026 (same type asked 4 times)

    30
    Solve the following linear programming problem graphically : Minimize Z=13x−15yZ = 13x - 15y Subject to constraints x+y≤7x + y \leq 7, 2x−3y+6≥02x - 3y + 6 \geq 0, x≥0x \geq 0, y≥0y \geq 0

  3. Question 3

    Linear Programming. Asked once: 2025 (same type asked 4 times)

    30
    In the Linear Programming Problem for objective function Z=18x+10yZ = 18x + 10y subject to constraints 4x+y≥204x + y \ge 20 2x+3y≥302x + 3y \ge 30 x, y≥0x,\ y \ge 0 find the minimum value of Z.

  4. Question 4 (case study, 2 parts)

    Linear Programming. Asked once: 2024 (same type asked 4 times)

    The month of September is celebrated as the Rashtriya Poshan Maah across the country. Following a healthy and well-balanced diet is crucial in order to supply the body with the proper nutrients it needs. A balanced diet also keeps us mentally fit and promotes improved level of energy. A dietician wishes to minimize the cost of a diet involving two types of foods, food X (x kg) and food Y (y kg) which are available at the rate of ₹ 16/kg and ₹ 20/kg respectively. The feasible region satisfying the constraints is shown in Figure-2. On the basis of the above information, answer the following questions :
    37 (i)
    Identify and write all the constraints which determine the given feasible region in Figure-2.
    37 (ii)
    If the objective is to minimize cost Z=16x+20yZ = 16x + 20y, find the values of x and y at which cost is minimum. Also, find minimum cost assuming that minimum cost is possible for the given unbounded region.

  5. Question 5

    Linear Programming. Asked once: 2025 (same type asked 4 times)

    14
    For a Linear Programming Problem (LPP), the given objective function is Z=x+2yZ = x + 2y. The feasible region PQRS determined by the set of constraints is shown as a shaded region in the graph. (Note : The figure is not to scale) P≡(313, 2413)P \equiv \left(\dfrac{3}{13},\ \dfrac{24}{13}\right), Q≡(32, 154)Q \equiv \left(\dfrac{3}{2},\ \dfrac{15}{4}\right), R≡(72, 34)R \equiv \left(\dfrac{7}{2},\ \dfrac{3}{4}\right), S≡(187, 27)S \equiv \left(\dfrac{18}{7},\ \dfrac{2}{7}\right) Which of the following statements is correct ?

    Tap an option to check your answer.