Mathematics – Class 12 Practice Test 7

1. Which of the given qualities is a vector?

2. What will be the value of the differential equation dy/dx = (x + y)²/(x + 2)(y – 2)?

3. Find the particular solution of the differential equation \(\frac{dy}{dx}=\frac{9y \,log⁡x}{5x \,log⁡y}\).

4. Find the particular solution of the differential equation \(\frac{dy}{dx}\)+2x=5 given that y=5, when x=1.

5. What will be the general solution of the differential equation d²y/dx² = e^2x(12 cos3x – 5 sin3x)? (here, A and B are integration constant)

6. What is the order of the differential equation of the family of circles with one diameter along the line y = x axis?

7. Which of the following is not a vector quantity?

8. If k is any scalar and \(\vec{a}\), \(\vec{b}\) be vectors then k \(\vec{a}\) + m\(\vec{a}\) can also be written as ________

9. Find the particular solution for the differential equation \(\frac{dy}{dx}=\frac{3x^2}{7y}\) given that, y=1 when x=1.

10. 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?