Welcome to your Entry Test Preparation (ECAT) Math Mock Test 2 If $\cos{2x} = 0.1$ then value of $\sin{x}$ is; $\frac{2}{5\sqrt{3}}$ $\frac{3}{2\sqrt{5}}$ Cannot be determine $\frac{1}{2\sqrt{5}}$ None If $\frac{dy}{dx}=\frac{x^2 - 1}{x}$ then $y = ?$ $x - \frac{1}{x}$ $\frac{x^2}{2} - \ln{x}$ $x + \frac{2}{x}$ $x + \frac{1}{x}$ None The equation $ax^2+by^2+2hxy+2gx+2fy+c=0$ may be a parabola if; $h^2 - ab < 0$ $h^2 - ab > 0$ $h^2 - ab = 1$ $h^2 - ab = 0$ None If m, n are the roots of the equation $x^2 + 5x + 6 = 0$, then value of $m^2 + n^2$ is; -13 13 36 14 None If $A$ is a square matrix of order $5$, and $\left|A\right|=3$ then $\left|2A\right|=?$ 27 125 40 96 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 $\lim_{n \to \infty} \frac{n^3 + 4n}{4 - 3n^2} =?$ $\infty$ $-\frac{1}{3}$ 0 $-3$ None The center and radius of circle $x^2 + y^2 -6x + 10y -15 = 0$; $(3, -5), 49$ $(-5, -3), 7$ $(3, -5), 7$ $(5, -3), 7$ None For $1 < n < 5$ , which is true? $n^2 > 5n$ None $n^2 = 5n$ $n^2 < 5n$ None If the vertices of a triangle are $A(0, 0)$ , $B(4, 3)$ , $C(3, 0)$ then centroid is; $(1.50, 3.50)$ $(3.50, 2.50)$ $(0, 0)$ $(2.33, 1)$ None None $\frac{1}{2} \sin({-\pi-2\theta})=?$ $\sin{2\theta}$ $-\sin{\theta}\cos{\theta}$ $-2\sin{\theta}\cos{\theta}$ $\sin{\theta}\cos{\theta}$ None The eccentricity of the hyperbola $x^2 - y^2 =1$ is; $e>1$ $e=\infty$ $e=\sqrt{2}$ $e=1$ None $\tan^{-1}(x) + \tan^{-1}(\frac{1}{x}) =?$ 1 None 0 $\frac{\pi}{2}$ None If one root of the equation $3x^2 + 13x + k = 0$ is reciprocal of the other then $k=?$ $\frac{1}{5}$ 3 5 $-5$ None $a + ar + ar^2 + … + ar^n =? r>1$ $a(r^{n+1}-1)$ $\frac{a(a^{n+1}-1)}{r-1}$ None $\frac{a(r-1)}{r-1}$ 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 $6, -5$ $1, -5$ $6, 5$ $-3, 2$ None The rank of the matrix $ \begin{bmatrix} 1 & -1 & 2 & -3 \\ 2 & 0 & 7 & -7 \\ 3 & 1 & 12 & -11 \\ \end{bmatrix} $ is; 1 5 4 2 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 $\cos{22 \frac{1}{2}^o} = ?$ $-\sqrt{1 + \frac{1}{2\sqrt{2}}}$ $\sqrt{\frac{\sqrt{2}+1}{2\sqrt{2}}}$ $\sqrt{\frac{\sqrt{2}-1}{2\sqrt{2}}}$ $\pm\sqrt{\frac{\sqrt{2}+1}{2\sqrt{2}}}$ None Term independent of $x$ in the expansion of $(2x+\frac{1}{x})^4$ is; 32 None such term exists 24 64 None The sides of a triangle are $7, 4\sqrt{3}, \sqrt{13}$ . Then smallest angle would be; $30^\circ$ $45^\circ$ $15^\circ$ $20^\circ$ None $\int_{0}^{8} \left|x-5\right| \, dx=$ 17 25 12 $-8$ None When $y=p$ where $p$ is the distance from origin, then slope of $y$ is; $\infty$ 0 1 None None 20 years ago my age was $\frac{1}{3}$ of what it is now, what is my present age? 30 36 33 66 None $\int x^3 e^{5x} \, dx = ?$ $e^{5x} (x^3 -\frac{3}{5}x^2 + \frac{6}{25} x - \frac{6}{125})$ none of these $\frac{1}{5} e^{5x} (x^3 -\frac{3}{5}x^2 + \frac{6}{25} x - \frac{6}{125})$ $5e^{5x} (x^3 -\frac{3}{5}x^2 + \frac{6}{25} x - \frac{6}{125})$ None $\sin({\cos^{-1}{\frac{5}{4}}})=?$ $\frac{3}{5}$ $\frac{5}{6}$ $-\frac{3}{5}$ Cannot be determine None The sum of squares of first 18 natural numbers is; 2109 2209 1509 1809 None The value of $\vec{i}\cdot[(\vec{k}\times\vec{j})\cdot(\vec{i}\times\vec{k})]$ is; 4 Not Possible 1 2 None If $\vec{u} = 2\vec{i} + 6 , \vec{v} = -9\vec{i}+ 8\vec{j} + 4\vec{k}$ then $\vec{u} \cdot \vec{v} = ?$ 4 6 10 8 None Bisma's Salary was reduced by $25\%$. Percentage increase to be effected to bring the salary to original level is; $30.3\%$ $33.3\%$ $32.3\%$ $31.3\%$ None The graph of $x=-16y^2$ opens towards; Left Up Down Right None Which one is greater? $2^x$ both are equal None of these $\log_{x}(2)$ None $\lim_{{x \to \infty}}\frac{3x^2 - 1}{4 - 2x^2} =\,?$ $1$ $\frac{3}{4}$ $-\frac{3}{2}$ $\infty$ None If $n$ is divisble by $5$ the remainder is 3. If $3n$ is divisible by $5$ then the remainder is; 3 4 5 2 None Which of the following is equation whose eccentricity is $1$? $2x^2+2y^2+1=0$ $2x^2+2xy+2y^2 =0$ $2x^2+2x+4y+1=0$ None None $x^2 -5xy + 4y^2$ is made from which of the following pairs? $(x + y)(x - 4y)$ $(x - y)(x - 4y)$ $(x + 5y)(x - 4y)$ None None The contra positive of $\neg B \to \neg A$ is; $B \to A$ $A \to B$ $A \to \neg B$ $\neg A \to B$ None If $A=\{a,b,c,d\}, B=\{0,1,2,3\}$ then $f=\{(0, a), (1, b), (2, c), (2, d)\}$ is; Not a function Bijective Onto One to one None The number of points of intersection of the circle $x^2 + y^2 =7$ and the hyperbola $x^2 - y^2 =1$ 4 2 5 1 None Time's up