Mathematics – Class 12 Practice Test 6

1. Find \(\int_1^2 \frac{12 \,log⁡x}{x} \,dx\).

2. Which of the following functions is a solution for the differential equation xy'-y=0?

3. Find \(\int_{-2}^1 \,5x^4 \,dx\).

4. What is adding intervals property?

5. Find the order and degree of the differential equation (y''')²+7(y')²-(cos⁡x)²=0

6. Find the order of the differential equation \(\frac{9d^2 y}{dx^2}-\frac{7dy}{dx}+y^6=0\)

7. Find the degree of the differential equation y''-12cosec y=0.

8. Find the order of the differential equation y'-20y+2=0.

9. Evaluate the integral \(\int_1^{\sqrt{3}} \frac{3}{1+x^2}\).

10. Find \(\int_1^2 log⁡x.x^2 dx\)