TN Maths, 12th Chapter 10 Important Questions

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Class : XII

Subject : Maths

Chapter : 10

Chapter : Ordinary Differential Equations

IMPORTANT QUESTIONS

      

2 & 3 Marks Questions

1. Determine the order and degree (of exists) of the following differential equations: 

i) dy+(xy–cosx)dx = 0

ii) x = e^[xy ( dx / dy)]

2. Show that each of the following expressions is a solutions if the corresponding given differential equation  y =2x², xy¹ = 2y.

3. Find the value of m so that the function y = emx is a solution of the given differential equation

i) y¹+2y = 0

ii) y¹¹– 5y¹ + 6y = 0

4. Show that x²+y²=r², where r is a constant , is a solution of the differential equation (dy/dx) = (-x/y).

5. Show that y= ax+b/x , x≠ 0 is a solution of the differential equation x²y¹¹ + xy¹ – y =0.

6. Solve (1 + x²)dy/dx = 1 + y².

7. Solve the following differential equation ydx+(1+x²)tan-¹ xdy = 0.

5 Mark Questions

1. Solve ( x² – 3y²)dx + 2xy dy = 0

2. Solve y² + x²(dy/dx) = xy (dy/dx)

3. Solve [1 + 2 e^(x/y)] dx + [2e^(x/y)] [(1–x)/y]dy

4. The equation of electromotive force for an electric circuit containing resistance and self inductance is E = Ri + L (di/dt), where E is the electromotive force is given to the circuit, R the resistance and L, the coefficient of induction. Find the current i at time t when E=0.

5. Water at temperature 1000c cools in 10 minutes to 800c in a room temperature of 250c Find,

i) The temperature of water after 20 minutes

ii) The time when the temperature is 400c .

 [ loge 11 = -0.3101; loge 5 = 1.6094]

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