Mathematics Mock Test

\[ \int \left(2x + \dfrac{1}{x}\right) dx = ? \] ||| \(x^2 + \ln|x| + C\) ||| \(x^2 - \ln x + C\) ||| \(x^2 + \dfrac{1}{x} + C\) ||| \(x^2 + x + C\) ||| 1 ||| 2 Find \[ \frac{d}{dx}(\ln (e^x)) \] ||| \(x\) ||| \(\ln x\) ||| 1 ||| \(e^x\) ||| 3 ||| 2 If \[ \log_2(x^2 - 5x + 6) = 1 \], then what is the sum of all real roots of \(x\)? ||| 5 ||| 3 ||| 6 ||| 2 ||| 2 ||| 2 \[ \lim_{x \to \infty} \frac{2x^2 + 3x + 1}{x^2 + x + 5} = ? \] ||| 2 ||| 1 ||| \(\infty\) ||| 0 ||| 1 ||| 1 If \[ z = 3 + 4i \], then the value of \(|z|^2\) is: ||| 25 ||| 5 ||| 7 ||| 9 ||| 1 ||| 1 The expression \(\sum_{k=1}^{n} 2k = 110\). What is the value of \(n\)? ||| 10 ||| 11 ||| 12 ||| 13 ||| 2 ||| 2 The slope of the line \[ 3x + 2y = 6 \] is ||| \(-\frac{3}{2}\) ||| \(\frac{2}{3}\) ||| \(\frac{3}{2}\) ||| \(-\frac{2}{3}\) ||| 4 ||| 2 The function \[ f(x) = \frac{1}{x} \] is: ||| Even ||| Odd ||| Neither ||| Constant ||| 2 ||| 1 \[ \int \left(3x^2 + 4x + 1\right) \, dx = ? \] ||| \(x^3 + 2x^2 + x + C\) ||| \(x^3 + x^2 + x + C\) ||| \(3x^3 + 4x^2 + x + C\) ||| \(x^3 + 4x^2 + x + C\) ||| 3 ||| 2 The length of the diagonal from origin to point \((1,2,2)\) is ||| \(\sqrt{6}\) ||| 3 ||| \(2\sqrt{2}\) ||| \(\sqrt{9}\) ||| 1 ||| 2 The minimum value of \(\sin x + \cos x\) is: ||| -1 ||| \(-\sqrt{2}\) ||| \(\sqrt{2}\) ||| 0 ||| 2 ||| 2 \[ \lim_{x \to 0} \frac{e^x - 1}{x} \] equals: ||| 0 ||| 1 ||| \(\infty\) ||| \(e\) ||| 2 ||| 2 If a circle has center at (0,0) and radius 5, then area is: ||| \(25\pi\) ||| \(10\pi\) ||| \(5\pi\) ||| \(20\pi\) ||| 1 ||| 1 \[ \int_{0}^{1} \left( e^x + \ln(1 + x) \right) dx = ? \] ||| \(e - 1 + \ln 2\) ||| \(e + \ln 2\) ||| \(e^1 + \ln 2 - 1\) ||| \(e + \ln(1)\) ||| 3 ||| 2 A die is rolled. Probability of getting a prime number is: ||| \(\frac{1}{2}\) ||| \(\frac{1}{3}\) ||| \(\frac{2}{3}\) ||| \(\frac{1}{6}\) ||| 1 ||| 1 What is the distance between the points \((1,2)\) and \((4,6)\)? ||| 5 ||| \(\sqrt{25}\) ||| \(\sqrt{20}\) ||| 6 ||| 1 ||| 2 Derivative of \(\ln(x^2 + 1)\) is: ||| \(\frac{2x}{x^2 + 1}\) ||| \(\ln(x^2 + 1)\) ||| \(\frac{1}{x^2 + 1}\) ||| \(2x \ln(x^2 + 1)\) ||| 1 ||| 2 If a point moves along the line \(x = y = z\), then it lies on: ||| x-axis ||| y-axis ||| A diagonal line in 3D ||| xy-plane ||| 3 ||| 1 Find the angle between vectors \(\vec{a} = \hat{i} + \hat{j}\) and \(\vec{b} = \hat{i} - \hat{j}\) ||| \(45^\circ\) ||| \(60^\circ\) ||| \(90^\circ\) ||| \(180^\circ\) ||| 3 ||| 2 If \(\vec{r} = 2\hat{i} + 3\hat{j} + 6\hat{k}\), then magnitude of \(\vec{r}\) is: ||| 11 ||| 7 ||| \(\sqrt{49}\) ||| 6 ||| 3 ||| 1