Welcome to your Entry Test Preparation (ECAT) Math Mock Test 2 If $\cos{2x} = 0.1$ then value of $\sin{x}$ is; $\frac{1}{2\sqrt{5}}$ $\frac{2}{5\sqrt{3}}$ Cannot be determine $\frac{3}{2\sqrt{5}}$ None Co-efficient of $x^n$ in the expansion of $(x^2 - \frac{1}{x})^n$ is; $(-1)^n \cdot32$ $(-1)^n \cdot64$ $-(-1)^n \cdot32$ cannot be determine None $\log_{10}(0.01)=?$ $-2$ $-1$ None $-3$ None Which one is greater? $\log_{x}(2)$ $2^x$ both are equal None of these None The contra positive of $\neg B \to \neg A$ is; $B \to A$ $\neg A \to B$ $A \to \neg B$ $A \to B$ None The equation $\frac{x^2}{16} + \frac{y^2}{81}=1$ is symmetric about; $x-$axis not $y-$axis $x-$axis $y-$axis not $x-$axis Origin, $x-$axis and $y-$axis None H. M between $\frac{1}{2} and \frac{1}{3} $ is; $\frac{5}{4}$ $\frac{2}{5}$ $\frac{1}{5}$ $\frac{7}{5}$ None Which one is monoid? $(N, \cdot)$ $(E, \cdot)$ $(N, +)$ None of these None $\int_{0}^{8} \left|x-5\right| \, dx=$ 25 $-8$ 12 17 None If $\sin{x} + \cos{x} = 0$ then $x=?$ $\{\frac{5\pi}{4} + 2n\pi \}$ $\{\frac{\pi}{4} + 2n\pi \}$ $\{\frac{3\pi}{4} + n\pi \}$ $\{\frac{\pi}{4} + n\pi \}$ None If m, n are the roots of the equation $x^2 + 5x + 6 = 0$, then value of $m^2 + n^2$ is; 14 13 -13 36 None For $1 < n < 5$ , which is true? None $n^2 < 5n$ $n^2 > 5n$ $n^2 = 5n$ 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 minimum value of $y = 2x - x^2$ is -1 0 2 1 None The line $y = mx + c ,$ tangent to parabola $y^2 =x $ if; $m = -\frac{1}{3}$ $ m = 2$ $m = \frac{1}{4}$ $m = \frac{1}{2}$ None The eccentricity of the hyperbola $x^2 - y^2 =1$ is; $e=\sqrt{2}$ $e=\infty$ $e>1$ $e=1$ None When $y=p$ where $p$ is the distance from origin, then slope of $y$ is; None 1 0 $\infty$ None If area of circle is $100\pi$, then radius of circle is; None of these $\sqrt{10}$ $\pm10$ $10$ None Which of the following is right order? $2^{\frac{1}{4}}>3^{\frac{1}{2}}>4^{\frac{1}{2}}$ $2^{\frac{1}{4}}>3^{\frac{1}{3}}>4^{\frac{1}{5}}$ $4^{\frac{1}{3}}>3^{\frac{1}{4}}>2^{\frac{1}{5}}$ $2^{\frac{1}{4}}<4^{\frac{1}{5}}<3^{\frac{1}{3}}$ None If $A$ is a square matrix of order $5$, and $\left|A\right|=3$ then $\left|2A\right|=?$ 125 27 96 40 None Term independent of $x$ in the expansion of $(2x+\frac{1}{x})^4$ is; 32 64 None such term exists 24 None The number of points of intersection of the circle $x^2 + y^2 =7$ and the hyperbola $x^2 - y^2 =1$ 2 1 4 5 None $\sum_{k=1}^{100} (-1)^k=$ 56 0 50 5050 None From a deck of 52 playing cards, two cards are drawn at random. What is the probability of getting both aces? (where first card is replaced before drawing other) $\frac{2}{169}$ $\frac{1}{169}$ $\frac{1}{221}$ $\frac{1}{220}$ 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 the vertices of a triangle are $A(0, 0)$ , $B(4, 3)$ , $C(3, 0)$ then centroid is; $(1.50, 3.50)$ $(3.50, 2.50)$ $(2.33, 1)$ $(0, 0)$ None $\lim_{n \to \infty} \frac{n^3 + 4n}{4 - 3n^2} =?$ $\infty$ $-3$ 0 $-\frac{1}{3}$ None The fourth term in the expansion of $(1+x)^{-\frac{1}{2}}$ is; $-\frac{5}{16}x^3$ $-\frac{3}{16}$ $\frac{1}{8}x^2$ $\frac{5}{16}x^3$ None If $x=2at^2 , y=at^3$ then $\frac{dy}{dx}=?$ $\frac{3}{2} a$ $\frac{3}{4} t$ $-\frac{1}{2} t$ $\frac{1}{2} t^2$ None None Find the average of first 50 whole numbers. 25 24.5 None 23 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 $\int \sin{x}\cos{x} \, dx = ?$ All of these $\frac{1-\cos2x}{4} + c$ $-\frac{\cos2x}{4} + k$ $\frac{\sin^2(x)}{2} + \lambda$ None $\tan^{-1}(x) + \tan^{-1}(\frac{1}{x}) =?$ 0 1 $\frac{\pi}{2}$ None None The sum of squares of first 18 natural numbers is; 2209 1509 1809 2109 None If one root of the equation $3x^2 + 13x + k = 0$ is reciprocal of the other then $k=?$ $-5$ $\frac{1}{5}$ 5 3 None Which of the following is equation whose eccentricity is $1$? $2x^2+2xy+2y^2 =0$ $2x^2+2x+4y+1=0$ $2x^2+2y^2+1=0$ None None $\int x^3 e^{5x} \, dx = ?$ $e^{5x} (x^3 -\frac{3}{5}x^2 + \frac{6}{25} x - \frac{6}{125})$ $5e^{5x} (x^3 -\frac{3}{5}x^2 + \frac{6}{25} x - \frac{6}{125})$ $\frac{1}{5} e^{5x} (x^3 -\frac{3}{5}x^2 + \frac{6}{25} x - \frac{6}{125})$ none of these None If $(3,7)$ and $(8,9)$ belong to complex numbers then $(3,7)\div (8,9)=?$ $(\frac{37}{145}, \frac{29}{145})$ $(\frac{21}{192}, \frac{17}{193})$ $(\frac{87}{145}, \frac{29}{145})$ $(\frac{16}{43}, \frac{21}{43})$ None $\frac{1}{2} \sin({-\pi-2\theta})=?$ $-2\sin{\theta}\cos{\theta}$ $-\sin{\theta}\cos{\theta}$ $\sin{\theta}\cos{\theta}$ $\sin{2\theta}$ None Time's up
