Welcome to your Entry Test Preparation (ECAT) Math Mock Test 2 Which of the following is not true? $2\pi$ is not in domain of $\tan{x}$ Period of $y=\sin{\theta}$ is $2\pi$ Range of $y=\cos{\theta}$ is $[-1, 1]$ Domain of $\sin{\theta}$ is $\mathbb{R} $ None If $x=2at^2 , y=at^3$ then $\frac{dy}{dx}=?$ $-\frac{1}{2} t$ $\frac{3}{2} a$ $\frac{1}{2} t^2$ $\frac{3}{4} t$ None If $x=a\cos{\theta} + ib\sin{\theta}$ and $y=a\cos{\theta} + ib\sin{\theta}$ then $\left| xy \right|=?$ $\sqrt{a^2 \cos^2 {\theta} + b^2 \sin^2 {\theta}}$ $a^2 \cos^2 {\theta} + b^2 \sin^2 {\theta}$ None of these $\sqrt{a^2 \cos^2 {\theta} - b^2 \sin^2 {\theta}}$ None The fourth term in the expansion of $(1+x)^{-\frac{1}{2}}$ is; $-\frac{3}{16}$ $\frac{5}{16}x^3$ $-\frac{5}{16}x^3$ $\frac{1}{8}x^2$ None Which of the following are the parametric questions of the ellipse $\frac{x^2}{a^2} +\frac{y^2}{b^2} = 1, a>b ?$ $x=a\cos{\theta} , y=b\sin{\theta}, \theta \in [0, 2\pi)$ $x=a\cos{\theta} , y=b\sin{\theta}, \theta \in [0, 2\pi]$ $x=a\cos{\theta} , y=a\sin{\theta}$ $x=a\cos{\theta} , y=b\sin{\theta}$ None The minimum value of $y = 2x - x^2$ is -1 2 0 1 None If $\frac{dy}{dx}=\frac{x^2 - 1}{x}$ then $y = ?$ $x - \frac{1}{x}$ $x + \frac{1}{x}$ $x + \frac{2}{x}$ $\frac{x^2}{2} - \ln{x}$ None When $y=p$ where $p$ is the distance from origin, then slope of $y$ is; 1 0 None $\infty$ None If area of circle is $100\pi$, then radius of circle is; $\pm10$ None of these $\sqrt{10}$ $10$ None $\tan^{-1}(x) + \tan^{-1}(\frac{1}{x}) =?$ 1 0 None $\frac{\pi}{2}$ None None If $x-1$ is a factor of $x^3-x^2-ax+1$ then value of $a=?$ 2 0 -1 1 None If m, n are the roots of the equation $x^2 + 5x + 6 = 0$, then value of $m^2 + n^2$ is; 36 -13 14 13 None $\lim_{n \to \infty} \frac{n^3 + 4n}{4 - 3n^2} =?$ $\infty$ 0 $-3$ $-\frac{1}{3}$ None Which one is monoid? $(N, \cdot)$ $(N, +)$ $(E, \cdot)$ None of these None If $A=\{1, 2, 3, 5, 7\}, U=\{1, 2, 3, …, 11, 12\} \,and\, B= \{4, 5, 7, 9, 3\} \,then\, P(A \cup B)=?$ $\frac{1}{2}$ $\frac{7}{10}$ $\frac{7}{12}$ $\frac{5}{12}$ None If $\cos{2x} = 0.1$ then value of $\sin{x}$ is; $\frac{3}{2\sqrt{5}}$ $\frac{2}{5\sqrt{3}}$ $\frac{1}{2\sqrt{5}}$ Cannot be determine None Which of the following could be the equation of graph? $y=-x^6$ $y=x^3$ $y=x^4$ None $150^\circ$ equal to how many radians ? 2.615 2.715 2.45 2.515 None $\frac{1}{2} \sin({-\pi-2\theta})=?$ $\sin{\theta}\cos{\theta}$ $\sin{2\theta}$ $-2\sin{\theta}\cos{\theta}$ $-\sin{\theta}\cos{\theta}$ None Term independent of $x$ in the expansion of $(2x+\frac{1}{x})^4$ is; 32 None such term exists 24 64 None If $f(x)=(x+1)^2$ and $g(x)=x-1$ then value of $fg(4)=?$ 9 16 4 25 None The contra positive of $\neg B \to \neg A$ is; $A \to B$ $B \to A$ $A \to \neg B$ $\neg A \to B$ None Number of real roots $x^2 + 4x + 6 = 0$ are; 3 0 2 1 None The rank of the matrix $ \begin{bmatrix} 1 & -1 & 2 & -3 \\ 2 & 0 & 7 & -7 \\ 3 & 1 & 12 & -11 \\ \end{bmatrix} $ is; 5 2 4 1 None Find the average of first 50 whole numbers. None 24.5 25 23 None Maximum value of $f(x)=2\sin{x} + 1$ is; 3 2 1 4 None Which one is in range of $f(x)=\frac{2}{3} \sin{x} ?$ 1 $\frac{\pi}{2}$ $\pi$ 0 None If the width of rectangle is $4$ meters and its total area is $12$ meter square. What is its length? 2 meters 6 meters 4 meters None None The sum of Binomial coefficients in the expansion of $(1-3y)^7$ is; 128 32 64 256 None $\cos{22 \frac{1}{2}^o} = ?$ $-\sqrt{1 + \frac{1}{2\sqrt{2}}}$ $\sqrt{\frac{\sqrt{2}+1}{2\sqrt{2}}}$ $\sqrt{\frac{\sqrt{2}-1}{2\sqrt{2}}}$ $\pm\sqrt{\frac{\sqrt{2}+1}{2\sqrt{2}}}$ None The center and radius of circle $x^2 + y^2 -6x + 10y -15 = 0$; $(-5, -3), 7$ $(3, -5), 49$ $(5, -3), 7$ $(3, -5), 7$ None Which of the following is equation whose eccentricity is $1$? None $2x^2+2xy+2y^2 =0$ $2x^2+2x+4y+1=0$ $2x^2+2y^2+1=0$ None If $A$ is a square matrix of order $5$, and $\left|A\right|=3$ then $\left|2A\right|=?$ 27 96 40 125 None None Which of the following is right order? $2^{\frac{1}{4}}>3^{\frac{1}{3}}>4^{\frac{1}{5}}$ $2^{\frac{1}{4}}>3^{\frac{1}{2}}>4^{\frac{1}{2}}$ $2^{\frac{1}{4}}<4^{\frac{1}{5}}<3^{\frac{1}{3}}$ $4^{\frac{1}{3}}>3^{\frac{1}{4}}>2^{\frac{1}{5}}$ None If $A=\begin{bmatrix} 0 & 1 & b \\ -1 & 0 & -a \\ 5 & 6 & 0 \\ \end{bmatrix} $ is a skew symmetric matrix, then values of $a$ & $b$ respectively are $-3, 2$ $6, -5$ $1, -5$ $6, 5$ None The sides of a triangle are $7, 4\sqrt{3}, \sqrt{13}$ . Then smallest angle would be; $45^\circ$ $30^\circ$ $20^\circ$ $15^\circ$ None None The graph of $x=-16y^2$ opens towards; Left Right Up Down None Time's up