2nd Year Mathematics Chapter 4 TestUNIT 4: DIFFERENTIAL EQUATIONS

Q1. Multiple choice questions (Attempt all · 10 × 1 = 10)

1. If y=cx-1. then its corresponding differential equation is:

   1. x=1+y

   2. =x+y

   3. x=y-1

   4. =cy

2. Inflation in economics means that the price of goods is:

   1. Decreasing over time

   2. Increasing over time

   3. Remaining constant

   4. Becoming zero

3. The differential equation =e^x-y is:

   1. Homogeneous but not separable

   2. Separable but not homogeneous

   3. Both separable and homogeneous

   4. Neither separable nor homogeneous

4. A differential equation of degree 1 is specifically called a:

   1. First-order differential equation

   2.  First-degree differential equation

   3. Linear differential equation

   4. Homogeneous differential equation

5. Which law states that the sum of voltages across the resistor and capacitor is equal to the total battery voltage?

   1. Ohm's Law

   2. Newton's Law

   3. Kirchhoff's Voltage Law

   4. Faraday's Law

6. If a differential equation cannot be written as a polynomial in derivatives, its degree is:

   1. Zero

   2. One

   3. Undefined

   4. Infinite

7. The degree of a differential equation is the greatest exponent of the:

   1. Lowest-order derivative

   2. Highest-order derivative

   3. Independent variable

   4. Dependent variable

8. The term "differential equation" was introduced by Leibniz in which year?

   1. 1686

   2. 1676

   3. 1776

   4. 1576

9. Which of the following is a homogeneous differential equation?

   1. x=1+y

   2. x²(2y+1)dy-dx=0

   3. (2xy+x²)dy-y²dx

   4. None

10. The general solution of the differential equation y dx + x dy=0 represents a family of:

    1. Straight lines passing through the origin

    2. Circles centered at the origin

    3. Rectangular hyperbolas

    4. Parabolas