Welcome to your Entry Test Preparation (ECAT) Math Mock Test 2 $\tan^{-1}(x) + \tan^{-1}(\frac{1}{x}) =?$ 0 $\frac{\pi}{2}$ None 1 None If $x-1$ is a factor of $x^3-x^2-ax+1$ then value of $a=?$ 0 2 1 -1 None $\int [x\ln{x} + x(\ln{x})^2] \, dx = ?$ None of these $\frac{x^2}{2} \ln(x) - \frac{x^2}{4} (\ln(x))^2 + x + c$ $\frac{x^2}{2} \ln(x) - \frac{x^2}{4} (\ln(x))^2 + c$ $\frac{(x\ln(x))^2}{2} + c$ None Which one is monoid? $(E, \cdot)$ $(N, +)$ $(N, \cdot)$ None of these None $\cos{22 \frac{1}{2}^o} = ?$ $\sqrt{\frac{\sqrt{2}-1}{2\sqrt{2}}}$ $\pm\sqrt{\frac{\sqrt{2}+1}{2\sqrt{2}}}$ $-\sqrt{1 + \frac{1}{2\sqrt{2}}}$ $\sqrt{\frac{\sqrt{2}+1}{2\sqrt{2}}}$ None Find the average of first 50 whole numbers. 25 24.5 None 23 None None $a + ar + ar^2 + … + ar^n =? r>1$ $\frac{a(a^{n+1}-1)}{r-1}$ None $\frac{a(r-1)}{r-1}$ $a(r^{n+1}-1)$ None If $\vec{u} = 2\vec{i} + 6 , \vec{v} = -9\vec{i}+ 8\vec{j} + 4\vec{k}$ then $\vec{u} \cdot \vec{v} = ?$ 8 4 10 6 None $\sum_{k=1}^{100} (-1)^k=$ 5050 50 56 0 None $\lim_{{x \to \infty}}\frac{3x^2 - 1}{4 - 2x^2} =\,?$ $1$ $\infty$ $\frac{3}{4}$ $-\frac{3}{2}$ None Direction of Qibla can be determined by; Spherical Trigonometry Solid Geometry none Plane Geometry None $x^2 -5xy + 4y^2$ is made from which of the following pairs? None $(x - y)(x - 4y)$ $(x + y)(x - 4y)$ $(x + 5y)(x - 4y)$ None The number of points of intersection of the circle $x^2 + y^2 =7$ and the hyperbola $x^2 - y^2 =1$ 2 4 5 1 None $\sin({\cos^{-1}{\frac{5}{4}}})=?$ $\frac{3}{5}$ $-\frac{3}{5}$ Cannot be determine $\frac{5}{6}$ None The middle term in the expansion of $(1+\frac{x}{2})^{20}$ is; $33th$ None $11th$ $22th$ None Bisma's Salary was reduced by $25\%$. Percentage increase to be effected to bring the salary to original level is; $32.3\%$ $33.3\%$ $30.3\%$ $31.3\%$ None For $1 < n < 5$ , which is true? $n^2 < 5n$ None $n^2 = 5n$ $n^2 > 5n$ None The value of $\vec{i}\cdot[(\vec{k}\times\vec{j})\cdot(\vec{i}\times\vec{k})]$ is; 4 2 Not Possible 1 None The line $y = mx + c ,$ tangent to parabola $y^2 =x $ if; $m = \frac{1}{4}$ $m = -\frac{1}{3}$ $m = \frac{1}{2}$ $ m = 2$ None Which one is in range of $f(x)=\frac{2}{3} \sin{x} ?$ $\pi$ 0 1 $\frac{\pi}{2}$ None When $y=p$ where $p$ is the distance from origin, then slope of $y$ is; 1 $\infty$ None 0 None $\lim_{n \to \infty} \frac{n^3 + 4n}{4 - 3n^2} =?$ $\infty$ 0 $-3$ $-\frac{1}{3}$ None The center and radius of circle $x^2 + y^2 -6x + 10y -15 = 0$; $(-5, -3), 7$ $(5, -3), 7$ $(3, -5), 49$ $(3, -5), 7$ None The equation $ax^2+by^2+2hxy+2gx+2fy+c=0$ may be a parabola if; $h^2 - ab = 0$ $h^2 - ab > 0$ $h^2 - ab < 0$ $h^2 - ab = 1$ None Term independent of $x$ in the expansion of $(2x+\frac{1}{x})^4$ is; 32 None such term exists 24 64 None If $x=a\cos{\theta} + ib\sin{\theta}$ and $y=a\cos{\theta} + ib\sin{\theta}$ then $\left| xy \right|=?$ $\sqrt{a^2 \cos^2 {\theta} + b^2 \sin^2 {\theta}}$ None of these $a^2 \cos^2 {\theta} + b^2 \sin^2 {\theta}$ $\sqrt{a^2 \cos^2 {\theta} - b^2 \sin^2 {\theta}}$ None Co-efficient of $x^n$ in the expansion of $(x^2 - \frac{1}{x})^n$ is; $(-1)^n \cdot32$ $(-1)^n \cdot64$ cannot be determine $-(-1)^n \cdot32$ None If $A=\{a,b,c,d\}, B=\{0,1,2,3\}$ then $f=\{(0, a), (1, b), (2, c), (2, d)\}$ is; Bijective Onto Not a function One to one None $\log_{10}(0.01)=?$ $-3$ None $-1$ $-2$ None Term independent of $x$ in the expansion of $(2x+\frac{1}{x})^3$ is; 2 No such term exists 1 6 None $\int x^3 e^{5x} \, dx = ?$ $5e^{5x} (x^3 -\frac{3}{5}x^2 + \frac{6}{25} x - \frac{6}{125})$ $e^{5x} (x^3 -\frac{3}{5}x^2 + \frac{6}{25} x - \frac{6}{125})$ $\frac{1}{5} e^{5x} (x^3 -\frac{3}{5}x^2 + \frac{6}{25} x - \frac{6}{125})$ none of these 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 Which of the following is not true? Range of $y=\cos{\theta}$ is $[-1, 1]$ $2\pi$ is not in domain of $\tan{x}$ Domain of $\sin{\theta}$ is $\mathbb{R} $ Period of $y=\sin{\theta}$ is $2\pi$ None The graph of $x=-16y^2$ opens towards; Right Down Up Left 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 $A$ is a square matrix of order $5$, and $\left|A\right|=3$ then $\left|2A\right|=?$ 125 40 96 27 None 20 years ago my age was $\frac{1}{3}$ of what it is now, what is my present age? 66 30 36 33 None Which of the following are the parametric questions of the ellipse $\frac{x^2}{a^2} +\frac{y^2}{b^2} = 1, a>b ?$ $x=a\cos{\theta} , y=b\sin{\theta}$ $x=a\cos{\theta} , y=a\sin{\theta}$ $x=a\cos{\theta} , y=b\sin{\theta}, \theta \in [0, 2\pi]$ $x=a\cos{\theta} , y=b\sin{\theta}, \theta \in [0, 2\pi)$ None If $A=\{1, 2, 3, 5, 7\}, U=\{1, 2, 3, …, 11, 12\} \,and\, B= \{4, 5, 7, 9, 3\} \,then\, P(A \cup B)=?$ $\frac{7}{12}$ $\frac{1}{2}$ $\frac{5}{12}$ $\frac{7}{10}$ None Time's up