Welcome to your Entry Test Preparation (ECAT) Math Mock Test 2 Which of the following could be the equation of graph? $y=-x^6$ $y=x^3$ $y=x^4$ 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 $n$ is divisble by $5$ the remainder is 3. If $3n$ is divisible by $5$ then the remainder is; 2 3 4 5 None The sum of Binomial coefficients in the expansion of $(1-3y)^7$ is; 256 32 128 64 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 $-3, 2$ $6, 5$ $1, -5$ $6, -5$ 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 None Which of the following is right order? $4^{\frac{1}{3}}>3^{\frac{1}{4}}>2^{\frac{1}{5}}$ $2^{\frac{1}{4}}<4^{\frac{1}{5}}<3^{\frac{1}{3}}$ $2^{\frac{1}{4}}>3^{\frac{1}{3}}>4^{\frac{1}{5}}$ $2^{\frac{1}{4}}>3^{\frac{1}{2}}>4^{\frac{1}{2}}$ None 20 years ago my age was $\frac{1}{3}$ of what it is now, what is my present age? 30 66 36 33 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 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 If $f(x)=(x+1)^2$ and $g(x)=x-1$ then value of $fg(4)=?$ 9 16 25 4 None 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 Find the average of first 50 whole numbers. 25 23 None 24.5 None If $A=\{a,b,c,d\}, B=\{0,1,2,3\}$ then $f=\{(0, a), (1, b), (2, c), (2, d)\}$ is; Bijective One to one Not a function Onto None If $\vec{u} = 2\vec{i} + 6 , \vec{v} = -9\vec{i}+ 8\vec{j} + 4\vec{k}$ then $\vec{u} \cdot \vec{v} = ?$ 10 4 6 8 None $\sum_{k=1}^{98} (\omega^k) =\,?$ $\omega^2$ 0 -1 $\omega$ None The sum of 3 A.Ms between 5 and 11; 25 34 24 12 None The contra positive of $\neg B \to \neg A$ is; $B \to A$ $\neg A \to B$ $A \to B$ $A \to \neg B$ 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 If area of circle is $100\pi$, then radius of circle is; $\sqrt{10}$ $\pm10$ None of these $10$ None If $\frac{dy}{dx}=\frac{x^2 - 1}{x}$ then $y = ?$ $x - \frac{1}{x}$ $\frac{x^2}{2} - \ln{x}$ $x + \frac{1}{x}$ $x + \frac{2}{x}$ None Term independent of $x$ in the expansion of $(2x+\frac{1}{x})^4$ is; None such term exists 64 32 24 None $x^2 -5xy + 4y^2$ is made from which of the following pairs? $(x - y)(x - 4y)$ None $(x + 5y)(x - 4y)$ $(x + y)(x - 4y)$ None Which one is in range of $f(x)=\frac{2}{3} \sin{x} ?$ $\pi$ 1 0 $\frac{\pi}{2}$ None $\lim_{n \to \infty} \frac{n^3 + 4n}{4 - 3n^2} =?$ 0 $\infty$ $-\frac{1}{3}$ $-3$ None If one root of the equation $3x^2 + 13x + k = 0$ is reciprocal of the other then $k=?$ 5 $-5$ 3 $\frac{1}{5}$ None The eccentricity of the hyperbola $x^2 - y^2 =1$ is; $e>1$ $e=\infty$ $e=1$ $e=\sqrt{2}$ None Which one is monoid? None of these $(E, \cdot)$ $(N, \cdot)$ $(N, +)$ None $\int_{0}^{8} \left|x-5\right| \, dx=$ 12 $-8$ 17 25 None $\tan^{-1}(x) + \tan^{-1}(\frac{1}{x}) =?$ None 0 1 $\frac{\pi}{2}$ None The sum of squares of first 18 natural numbers is; 1509 1809 2109 2209 None The graph of $x=-16y^2$ opens towards; Left Up Right Down None The line $y = mx + c ,$ tangent to parabola $y^2 =x $ if; $m = -\frac{1}{3}$ $m = \frac{1}{2}$ $ m = 2$ $m = \frac{1}{4}$ None Number of real roots $x^2 + 4x + 6 = 0$ are; 0 3 2 1 None Which of the following are the parametric questions of the ellipse $\frac{x^2}{a^2} +\frac{y^2}{b^2} = 1, a>b ?$ $x=a\cos{\theta} , y=b\sin{\theta}, \theta \in [0, 2\pi)$ $x=a\cos{\theta} , y=a\sin{\theta}$ $x=a\cos{\theta} , y=b\sin{\theta}, \theta \in [0, 2\pi]$ $x=a\cos{\theta} , y=b\sin{\theta}$ None $150^\circ$ equal to how many radians ? 2.715 2.615 2.45 2.515 None If $\cos{2x} = 0.1$ then value of $\sin{x}$ is; $\frac{3}{2\sqrt{5}}$ $\frac{2}{5\sqrt{3}}$ Cannot be determine $\frac{1}{2\sqrt{5}}$ None The minimum value of $y = 2x - x^2$ is 0 2 1 -1 None Time's up