Mathematical Induction PYQs Set 1 (PDF)

Set 1 of 1 · Questions 1-8 of 8

In the print window choose “Save as PDF”. The file prints without a web address or date line.

Mere Teacher · Previous Year Questions JEE Main Mathematics · Mathematical Induction · Set 1 (Q1-8)
Scan or visit mereteacher.com for free PYQ practice, timed CBT tests, step-by-step solutions and BroBot AI. Answers and solutions are free with a sign-up.
1. $The shaded region in the figure given is the solution of which of the inequations?$ (1) $x+y\geq7,2x-3y+6\geq0,x\geq0,y\geq0$ (2) $x+y\leq7,2x-3y+6\geq0,x\geq0,y\geq0$ (3) $x+y\leq7,2x-3y+6\leq0,x\geq0,y\geq0$ (4) $x+y\geq7,2x-3y+6\leq0,x\geq0,y\geq0$ 2. $The solution set of the inequalities 4 x + 3 y \leq 60, y \geq 2 x, x \geq 3, x, y \geq 0 is represented by region$ (1) $S_{2} region$ (2) $S_{1} region$ (3) $S_{3} region$ (4) $S_{4} region$ 3. $The maximum value of the objective function z = 4 x + 5 y subject to constraints 2 x + 3 y \leq 12, 2 x + y \leq 8 and x \geq 0, y \geq 0 is$ (1) $24$ (2) $23$ (3) $22$ (4) $21$ 4. $The shaded region is the solution set of the inequalities.$ (1) $5x+4y\geq20,x\leq6,y\geq3,x\geq0,y\geq0$ (2) $5x+4y\leq20,x\leq6,y\leq3,x\geq0,y\geq0$ (3) $5x+4y\geq20,x\leq6,y\leq3,x\geq0,y\geq0$ (4) $5x+4y\geq20,x\geq6,y\leq3,x\geq0,y\geq0$ 5. $The graphical solution set of the system of inequations x + y \leq 70, x + 2 y \leq 100, 2 x + y \leq 120, x \geq 0, y \geq 0 is given by$ (1) $Fig. 4$ (2) $Fig. 2$ (3) $Fig. 1$ (4) $Fig. 3$ 6. $If feasible region is as shown in the figure, then the related inequalities are$ (1) $3x+4y\geq12,y-x\geq0,y\leq3,x,y\geq0$ (2) $3x+4y\leq12,y-x\leq0,y\geq3,x,y\geq0$ (3) $3x+4y\leq12,y-x\geq0,y\leq3,x,y\geq0$ (4) $3x+4y\geq12,y-x\leq0,y\geq3,x,y\geq0$ 7. $The shaded region in the following figure represents the solution set for a certain linear programming problem. Then, linear constraints for this region are given by$ (1) $2x+3y\geq6,-x+2y\geq2,3x+6y\leq18,5-3y\geq 3,x\geq0,y\geq0$ (2) $2x+3y\geq6,-x+2y\leq2,x-3y\leq3,2y\geq18, x\geq0,y\geq0$ (3) $2x+3y\leq6,-x+2y\geq2,3x+6y\leq18,x-3y\leq 3,x\geq0,y\geq0$ (4) $2x+3y\geq6,3x+6y\leq18,x-3y\leq3,-x+2y\leq2, x\geq0,y\geq0$ 8. $A dietician has to develop a special diet using two foods X and Y . Each packet (containing 30 g) of food. X contains 12 units of calcium, 4 units of iron, 6 units of cholesterol and 6 units of vitamin A. Each packet of the same quantity of food Y contains 3 units of calcium, 20 units of iron, 4 units of cholesterol and 3 units of vitamin A . The diet requires atleast 240 units of calcium, atleast 460 units of iron and atmost 300 units of cholesterol. The corner points of the feasible region are$ (1) $(2, 72), (40, 15), (15, 20)$ (2) $(0, 23), (40, 15), (2, 72)$ (3) $(2, 72), (15, 20), (0, 23)$ (4) $(2, 72), (40, 15), (115, 0)$