Mathematics - Class 12 Mock Test 5

10%

Question 1 of 10

1. \(\int \frac{dx}{x(x^2+1)}\) equals ______

\(log|x| - \frac{1}{2} log(x^2+1)\) + C

\(log|x| + \frac{1}{2} log(x^2+1)\) + C

-\(log|x| + \frac{1}{2} log(x^2+1)\) + C

\(\frac{1}{2} log|x| + log(x^2+1)\) + C

Question 1 of 10

Question 2 of 10

2. Find \(\int \frac{cos^{-1}x}{\sqrt{1-x^2}} dx\).

\(\frac{(sin^{-1}⁡x)^2}{2}+C\)

-\(\frac{(cos^{-1}⁡x)^2}{2}+C\)

\(\frac{(cos^{-1}⁡x)^2}{2}+C\)

\(\frac{(cos^{-1}⁡x)^2}{7}+C\)

Question 2 of 10

Question 3 of 10

3. Integrate ∫ log⁡x² dx

x log⁡x² + x+C

x log⁡x² - 2x+C

x log⁡x² - 1+C

log⁡x² + x+C

Question 3 of 10

Question 4 of 10

4. Find \(\int sin^2⁡(8x+5) dx\)

\(\frac{x}{2}+\frac{cos⁡(16x+5)}{32}+C\)

\(\frac{x}{2}-\frac{cos⁡(16x+10)}{32}+C\)

\(\frac{x}{4}+\frac{sin⁡(16x+10)}{32}+C\)

\(\frac{x}{2}-\frac{sin⁡(16x+10)}{32}+C\)

Question 4 of 10

Question 5 of 10

5. Find \(\int \frac{20x^3}{1+x^4} dx\).

-5 log⁡(1+x⁴)+C

5 log⁡(1+x⁴)+C

5 log⁡(x⁴)+C

log⁡(1+x⁴)+C

Question 5 of 10

Question 6 of 10

6. Find the approximate value of (127)^1/3.

5.04

2.0267

5.0267

8.0267

Question 6 of 10

Question 7 of 10

7. Monotonically increasing functions are usually referred to as decreasing functions.

False

True

Question 7 of 10

Question 8 of 10

8. Find the approximate value of f(5.03), where f(x)=4x²-7x+2.

78.09

67.66

67.99

56.99

Question 8 of 10

Question 9 of 10

9. Find ∫ 7x²-x³+2x dx.

\(\frac{7x^5}{9}-\frac{x^4}{4}+\frac{2x^2}{2}+C\)

\(\frac{7x^3}{3}+\frac{x^4}{4}+\frac{2x^2}{2}+C\)

\(\frac{7x^3}{3}+\frac{x^4}{5}-\frac{2x^2}{2}+C\)

\(\frac{7x^3}{3}-\frac{x^4}{4}+x^2+C\)

Question 9 of 10

Question 10 of 10

10. Find the integral of 2 sin⁡2x+3.

cos⁡2x-3x+12+C

sin⁡2x+3x+C

-cos⁡2x-3x³+C

-cos⁡2x+3x+C

Question 10 of 10