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Class 12 Maths Practice Test - Linear First Order Differential Equations
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Class 12 Maths Practice Test - Linear First Order Differential Equations
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20 Questions

1. What will be the value of dy/dx = (x + 2y + 3)/(2x + 3y + 4)?
2. A particle starts from the origin with a velocity 5cm/sec and moves in a straight line, its acceleration at time t seconds being (3t2 – 5t)cm/sec2. What will be the velocity of the particle?
3. What is the solution of dy/dx = (6x + 9y – 7)/(2x + 3y – 6)?
4. What will be the value of the differential equation dy/dx = (x + y)2/(x + 2)(y – 2)?
5. What will be the differential equation form of √(a2 + x2)dy/dx + y = √(a2 + x2) – x?
6. A particle starts from the origin with a velocity 5cm/sec and moves in a straight line, its acceleration at time t seconds being (3t2 – 5t)cm/sec2. What will be the distance from the origin at the end of 4 seconds?
7. What is the solution of (y(dy/dx) + 2x)2 = (y2 + 2x2)[1 + (dy/dx)2]?
8. What is the differential equation whose solution represents the family c(y + c)2 = x3?
9. What will be the general solution of differential equation for 2x – y dx + 2y – x dy = 0?
10. If, A normal is drawn at a point P(x, y) of a curve. It meets the x-axis at Q. If PQ is of constant length k. What kind of curve is passing through (0, k)?
11. What will be the value of dy/dx – a/x * y = (x + 1)/x?
12. A curve passes through (1, 1) such that the triangle formed by the coordinate axes and the tangent at any point of the curve is in the first quadrant and has its area equal to 2. What is the differential equation?
13. What is the equation of the curve passing through (1, 0) of (y(dy/dx) + 2x)2 = (y2 + 2x2)[1 + (dy/dx)2]?
14. A normal is drawn at a point P(x, y) of a curve. It meets the x-axis at Q. If PQ is of constant
length k. Then what is the differential equation describing such curve?
15. A normal is drawn at a point P(x, y) of a curve. It meets the x-axis at Q. If PQ is of constant
length k. What is the equation of such curve passing through (0, k)?
16. What is the solution of the equation(y + x(√xy)(x + y))dx – (y + y(√xy)(x + y))dy = 0?
17. What is the order of the differential equation of the family of circles with one diameter along the line y = x axis?
18. What is the value of the solution of dy/dx = (6x + 9y – 7)/(2x + 3y – 6)?
19. What will be the value of x(x – 1)dy/dx – y = x2(x – 1)2?
20. A curve passes through (1, 1) such that the triangle formed by the coordinate axes and the tangent at any point of the curve is in the first quadrant and has its area equal to 2. What will be the equation of the curve?

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