Welcome to your Entry Test Preparation (ECAT) Math Mock Test 2Which of the following is equation whose eccentricity is $1$? $2x^2+2xy+2y^2 =0$ $2x^2+2x+4y+1=0$ None $2x^2+2y^2+1=0$ None None $\sin({\cos^{-1}{\frac{5}{4}}})=?$ Cannot be determine $\frac{5}{6}$ $-\frac{3}{5}$ $\frac{3}{5}$ None If $x=a\cos{\theta} + ib\sin{\theta}$ and $y=a\cos{\theta} + ib\sin{\theta}$ then $\left| xy \right|=?$ $\sqrt{a^2 \cos^2 {\theta} - b^2 \sin^2 {\theta}}$ $a^2 \cos^2 {\theta} + b^2 \sin^2 {\theta}$ $\sqrt{a^2 \cos^2 {\theta} + b^2 \sin^2 {\theta}}$ None of these None The sides of a triangle are $7, 4\sqrt{3}, \sqrt{13}$ . Then smallest angle would be; $15^\circ$ $30^\circ$ $45^\circ$ $20^\circ$ None For $1 < n < 5$ , which is true? None $n^2 > 5n$ $n^2 < 5n$ $n^2 = 5n$ None The eccentricity of the hyperbola $x^2 - y^2 =1$ is; $e>1$ $e=\sqrt{2}$ $e=\infty$ $e=1$ None Value of A and B in equation $\frac{x}{(x+3)(x+2)} = \frac{A}{(x+3)} + \frac{B}{(x+2)}$ respectively; $-2, 3$ $-3, 2$ $-3, -2$ $3, -2$ None Which one is greater? None of these both are equal $2^x$ $\log_{x}(2)$ 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 $6, 5$ $6, -5$ $1, -5$ $-3, 2$ None Term independent of $x$ in the expansion of $(2x+\frac{1}{x})^3$ is; 6 1 2 No such term exists None Distance between lines $3x+4y-4=0$ and $6x+8y+2=0$ is; cannot be determine 1 5 $\frac{1}{\sqrt{5}}$ None The value of $\vec{i}\cdot[(\vec{k}\times\vec{j})\cdot(\vec{i}\times\vec{k})]$ is; 1 4 2 Not Possible None The sum of 3 A.Ms between 5 and 11; 12 34 25 24 None $\cos{22 \frac{1}{2}^o} = ?$ $-\sqrt{1 + \frac{1}{2\sqrt{2}}}$ $\sqrt{\frac{\sqrt{2}+1}{2\sqrt{2}}}$ $\pm\sqrt{\frac{\sqrt{2}+1}{2\sqrt{2}}}$ $\sqrt{\frac{\sqrt{2}-1}{2\sqrt{2}}}$ None 20 years ago my age was $\frac{1}{3}$ of what it is now, what is my present age? 66 33 36 30 None The fourth term in the expansion of $(1+x)^{-\frac{1}{2}}$ is; $\frac{5}{16}x^3$ $-\frac{5}{16}x^3$ $-\frac{3}{16}$ $\frac{1}{8}x^2$ None $\frac{1}{2} \sin({-\pi-2\theta})=?$ $\sin{\theta}\cos{\theta}$ $-\sin{\theta}\cos{\theta}$ $\sin{2\theta}$ $-2\sin{\theta}\cos{\theta}$ None The equation $\frac{x^2}{16} + \frac{y^2}{81}=1$ is symmetric about; $y-$axis not $x-$axis $x-$axis not $y-$axis Origin, $x-$axis and $y-$axis $x-$axis None $150^\circ$ equal to how many radians ? 2.715 2.45 2.615 2.515 None $\lim_{{x \to \infty}}\frac{3x^2 - 1}{4 - 2x^2} =\,?$ $1$ $-\frac{3}{2}$ $\infty$ $\frac{3}{4}$ None $\int_{0}^{8} \left|x-5\right| \, dx=$ 12 17 $-8$ 25 None If $f(x)=(x+1)^2$ and $g(x)=x-1$ then value of $fg(4)=?$ 25 4 16 9 None Term independent of $x$ in the expansion of $(2x+\frac{1}{x})^4$ is; 32 None such term exists 24 64 None H. M between $\frac{1}{2} and \frac{1}{3} $ is; $\frac{5}{4}$ $\frac{1}{5}$ $\frac{2}{5}$ $\frac{7}{5}$ None If $\frac{dy}{dx}=\frac{x^2 - 1}{x}$ then $y = ?$ $x + \frac{2}{x}$ $x - \frac{1}{x}$ $x + \frac{1}{x}$ $\frac{x^2}{2} - \ln{x}$ None $\log_{10}(0.01)=?$ $-1$ None $-3$ $-2$ None If the vertices of a triangle are $A(0, 0)$ , $B(4, 3)$ , $C(3, 0)$ then centroid is; $(2.33, 1)$ $(3.50, 2.50)$ $(0, 0)$ $(1.50, 3.50)$ None Bisma's Salary was reduced by $25\%$. Percentage increase to be effected to bring the salary to original level is; $30.3\%$ $33.3\%$ $31.3\%$ $32.3\%$ None If $x-1$ is a factor of $x^3-x^2-ax+1$ then value of $a=?$ 2 -1 1 0 None If $A=\{a,b,c,d\}, B=\{0,1,2,3\}$ then $f=\{(0, a), (1, b), (2, c), (2, d)\}$ is; Onto One to one Bijective Not a function None If $\sin{x} + \cos{x} = 0$ then $x=?$ $\{\frac{5\pi}{4} + 2n\pi \}$ $\{\frac{\pi}{4} + n\pi \}$ $\{\frac{\pi}{4} + 2n\pi \}$ $\{\frac{3\pi}{4} + n\pi \}$ None The minimum value of $y = 2x - x^2$ is 2 0 1 -1 None Which one is in range of $f(x)=\frac{2}{3} \sin{x} ?$ 0 $\pi$ 1 $\frac{\pi}{2}$ None If m, n are the roots of the equation $x^2 + 5x + 6 = 0$, then value of $m^2 + n^2$ is; 14 36 13 -13 None If the width of rectangle is $4$ meters and its total area is $12$ meter square. What is its length? None 4 meters 6 meters 2 meters None The center and radius of circle $x^2 + y^2 -6x + 10y -15 = 0$; $(5, -3), 7$ $(3, -5), 49$ $(3, -5), 7$ $(-5, -3), 7$ None Find the average of first 50 whole numbers. 23 24.5 None 25 None The rank of the matrix $ \begin{bmatrix} 1 & -1 & 2 & -3 \\ 2 & 0 & 7 & -7 \\ 3 & 1 & 12 & -11 \\ \end{bmatrix} $ is; 5 4 2 1 None $\tan^{-1}(x) + \tan^{-1}(\frac{1}{x}) =?$ 1 None 0 $\frac{\pi}{2}$ None Time's up