Class 12 · CBSE
Class 12 Mathematics questions
34 questions. Open one to try it and read its answer with a full explanation.
1. Relations and Functions
Chapter page →- R = {(T₁, T₂) : T₁ is similar to T₂} on triangles. Triangles P (sides 3, 4, 5), Q (6, 8, 10) and S (5, 12, 13): which pair is related?
- R = {(a, b) : a = b − 3, b > 5} on N. Which pair belongs to R?
- f : R → R is given by f(x) = 5x. Then f is
- A = {1, 2, 3}, B = {5, 6, 7, 8} and f = {(1, 5), (2, 6), (3, 7)}. Then f : A → B is
- A relation R on A = {1, 2, …, 12} is R = {(x, y) : 2x − y = 0}. Which statement is true?
- R = {(a, b) : b = a + 2} on the set {1, 2, 3, 4, 5}. Is R transitive?
- The relation R = {(a, b) : a ≥ b} on the set of real numbers is
- On the set {1, 2, 3}, the relation R = {(2, 3), (3, 2)} is
- R = {(a, b) : |a − b| is even} is an equivalence relation on {1, 2, 3, 4, 5, 6}. The set of all elements related to 2 is
- On A = {0, 1, 2, …, 10}, R = {(a, b) : |a − b| is a multiple of 3}. The elements related to 1 are
- R = {(L₁, L₂) : L₁ ∥ L₂} on the lines of the XY-plane. The lines related to y = 3x + 1 are
- On {1, 2, 3}, R = {(1, 1), (2, 2), (3, 3), (1, 2)}. Choose the correct option.
- f : R → R is given by f(x) = x². Then f is
- f : N → N is given by f(x) = x³. Then f is
- The greatest integer function f(x) = [x], f : R → R, is not one-one because
- On A = {−1, 0, 1}, let f(x) = x² and g(x) = |x|. Then
- Is f : R → R, f(x) = x³ one-one?
- How many onto functions are there from {1, 2, 3, 4} to itself?
- How many equivalence relations can be defined on the set {1, 2, 3}?
Appendix 2: Mathematical Modelling
Chapter page →- In mathematical modelling, which step comes right after turning the real situation into a mathematical model?
- A model's result does not agree with what is actually observed. What is the right next step?
- Which of these is a real limitation of mathematical modelling?
- An observer whose eye is 1.5 m above the ground stands 40 m from the foot of a tower. The angle of elevation of the top of the tower is 45°. How tall is the tower?
- Matrix A shows the orders of 2 clients for 3 products (order 2 × 3). Matrix B shows the units of 4 raw materials needed for each product (order 3 × 4). Which matrix gives the raw material each client's order needs?
- A client orders 2 units of P1 and 1 unit of P2, so A = [2 1]. Each unit of P1 needs 3 units of R1 and 1 unit of R2; each unit of P2 needs 2 units of R1 and 4 units of R2. How much raw material does the order need?
- To meet its orders a firm needs 120 units of R1 and 90 units of R2, but it has only 110 units of R1 and 100 units of R2. What follows?
- Profit Z = 5x + 4y is to be maximised. The corner points of the feasible region are (0, 0), (8, 0), (6, 4) and (0, 6). What is the maximum profit and where does it occur?
- Making 100 packets of A takes 2 machine hours and making 100 packets of B takes 1 machine hour; 40 machine hours are available. If x and y are the numbers of packets of A and B in hundreds, which constraint describes the machine time?
- A product has a fixed cost of ₹12,000, a variable cost of ₹30 per unit and sells for ₹50 per unit. How many units must be sold to break even?
- In the model P = (s − b)x − a, where s is the selling price and b the variable cost per unit, profit rises as more units are sold only when
- From a window 2 m above the ground, the angle of depression of the foot of a tower is 30° and the angle of elevation of its top is 45°. What is the height of the tower?
- Each unit of product X uses 2 units of R1 and 1 unit of R2; each unit of Y uses 1 unit of R1 and 3 units of R2. The firm has 50 units of R1 and 60 units of R2. How many of each should it make to use all of both materials?
- A tank holds 500 L of water with 20 kg of salt dissolved in it. Pure water flows in at 10 L/min and the well-stirred mixture flows out at the same rate. If y kg is the salt in the tank after t minutes, then dy/dt equals
- In a mixing model, the salt in a tank after t minutes is y(t) = 300 + 60e^(−t/20) kg. How much salt is there in the long run?