Welcome to your Entry Test Preparation (ECAT) Math Mock Test 2 The fourth term in the expansion of $(1+x)^{-\frac{1}{2}}$ is; $-\frac{5}{16}x^3$ $-\frac{3}{16}$ $\frac{5}{16}x^3$ $\frac{1}{8}x^2$ None The eccentricity of the hyperbola $x^2 - y^2 =1$ is; $e=1$ $e=\infty$ $e>1$ $e=\sqrt{2}$ 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 $\cos{22 \frac{1}{2}^o} = ?$ $\sqrt{\frac{\sqrt{2}+1}{2\sqrt{2}}}$ $\pm\sqrt{\frac{\sqrt{2}+1}{2\sqrt{2}}}$ $\sqrt{\frac{\sqrt{2}-1}{2\sqrt{2}}}$ $-\sqrt{1 + \frac{1}{2\sqrt{2}}}$ None The middle term in the expansion of $(1+\frac{x}{2})^{20}$ is; $11th$ None $33th$ $22th$ 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 $6, -5$ $-3, 2$ $6, 5$ $1, -5$ 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 Number of real roots $x^2 + 4x + 6 = 0$ are; 0 3 2 1 None If $A=\{a,b,c,d\}, B=\{0,1,2,3\}$ then $f=\{(0, a), (1, b), (2, c), (2, d)\}$ is; One to one Bijective Not a function Onto None If $\frac{dy}{dx}=\frac{x^2 - 1}{x}$ then $y = ?$ $\frac{x^2}{2} - \ln{x}$ $x - \frac{1}{x}$ $x + \frac{2}{x}$ $x + \frac{1}{x}$ None $\int [x\ln{x} + x(\ln{x})^2] \, dx = ?$ $\frac{x^2}{2} \ln(x) - \frac{x^2}{4} (\ln(x))^2 + x + c$ $\frac{x^2}{2} \ln(x) - \frac{x^2}{4} (\ln(x))^2 + c$ None of these $\frac{(x\ln(x))^2}{2} + c$ None Which one is monoid? None of these $(N, \cdot)$ $(E, \cdot)$ $(N, +)$ None The rank of the matrix $ \begin{bmatrix} 1 & -1 & 2 & -3 \\ 2 & 0 & 7 & -7 \\ 3 & 1 & 12 & -11 \\ \end{bmatrix} $ is; 4 2 1 5 None Co-efficient of $x^n$ in the expansion of $(x^2 - \frac{1}{x})^n$ is; $(-1)^n \cdot64$ $-(-1)^n \cdot32$ $(-1)^n \cdot32$ cannot be determine None $\sum_{k=1}^{100} (-1)^k=$ 50 0 56 5050 None If $\sin{x} + \cos{x} = 0$ then $x=?$ $\{\frac{\pi}{4} + n\pi \}$ $\{\frac{\pi}{4} + 2n\pi \}$ $\{\frac{5\pi}{4} + 2n\pi \}$ $\{\frac{3\pi}{4} + n\pi \}$ None Which of the following is not true? Period of $y=\sin{\theta}$ is $2\pi$ Range of $y=\cos{\theta}$ is $[-1, 1]$ Domain of $\sin{\theta}$ is $\mathbb{R} $ $2\pi$ is not in domain of $\tan{x}$ None Which one is greater? $2^x$ both are equal $\log_{x}(2)$ None of these None If $n$ is divisble by $5$ the remainder is 3. If $3n$ is divisible by $5$ then the remainder is; 2 5 3 4 None For $1 < n < 5$ , which is true? None $n^2 > 5n$ $n^2 < 5n$ $n^2 = 5n$ None If area of circle is $100\pi$, then radius of circle is; $\pm10$ None of these $10$ $\sqrt{10}$ None If $x=a\cos{\theta} + ib\sin{\theta}$ and $y=a\cos{\theta} + ib\sin{\theta}$ then $\left| xy \right|=?$ $\sqrt{a^2 \cos^2 {\theta} - b^2 \sin^2 {\theta}}$ $\sqrt{a^2 \cos^2 {\theta} + b^2 \sin^2 {\theta}}$ None of these $a^2 \cos^2 {\theta} + b^2 \sin^2 {\theta}$ None $\log_{10}(0.01)=?$ $-2$ None $-3$ $-1$ None The value of $(1 + i)^4 (1 + \frac{1}{i})^4$ equals to: $-16$ $2$ $15$ $16$ None If the width of rectangle is $4$ meters and its total area is $12$ meter square. What is its length? 4 meters 2 meters None 6 meters None $x^2 -5xy + 4y^2$ is made from which of the following pairs? $(x + y)(x - 4y)$ $(x - y)(x - 4y)$ None $(x + 5y)(x - 4y)$ None If m, n are the roots of the equation $x^2 + 5x + 6 = 0$, then value of $m^2 + n^2$ is; 13 36 14 -13 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 Which one is in range of $f(x)=\frac{2}{3} \sin{x} ?$ 0 $\frac{\pi}{2}$ $\pi$ 1 None 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 The sum of Binomial coefficients in the expansion of $(1-3y)^7$ is; 32 128 64 256 None $\lim_{{x \to \infty}}\frac{3x^2 - 1}{4 - 2x^2} =\,?$ $1$ $-\frac{3}{2}$ $\infty$ $\frac{3}{4}$ None The equation $ax^2+by^2+2hxy+2gx+2fy+c=0$ may be a parabola if; $h^2 - ab < 0$ $h^2 - ab = 1$ $h^2 - ab = 0$ $h^2 - ab > 0$ None The contra positive of $\neg B \to \neg A$ is; $B \to A$ $A \to \neg B$ $\neg A \to B$ $A \to B$ None If $(3,7)$ and $(8,9)$ belong to complex numbers then $(3,7)\div (8,9)=?$ $(\frac{87}{145}, \frac{29}{145})$ $(\frac{37}{145}, \frac{29}{145})$ $(\frac{16}{43}, \frac{21}{43})$ $(\frac{21}{192}, \frac{17}{193})$ None If $\vec{u} = 2\vec{i} + 6 , \vec{v} = -9\vec{i}+ 8\vec{j} + 4\vec{k}$ then $\vec{u} \cdot \vec{v} = ?$ 6 8 10 4 None $\sum_{k=1}^{98} (\omega^k) =\,?$ $\omega$ 0 $\omega^2$ -1 None The value of $\vec{i}\cdot[(\vec{k}\times\vec{j})\cdot(\vec{i}\times\vec{k})]$ is; 2 Not Possible 4 1 None $\int \sin{x}\cos{x} \, dx = ?$ $\frac{\sin^2(x)}{2} + \lambda$ $-\frac{\cos2x}{4} + k$ $\frac{1-\cos2x}{4} + c$ All of these None Time's up
