Welcome to your Entry Test Preparation (ECAT) Math Mock Test 2 If $A=\{1, 2, 3, 5, 7\}, U=\{1, 2, 3, …, 11, 12\} \,and\, B= \{4, 5, 7, 9, 3\} \,then\, P(A \cup B)=?$ $\frac{7}{12}$ $\frac{5}{12}$ $\frac{1}{2}$ $\frac{7}{10}$ None The sum of Binomial coefficients in the expansion of $(1-3y)^7$ is; 64 256 128 32 None For $1 < n < 5$ , which is true? None $n^2 < 5n$ $n^2 > 5n$ $n^2 = 5n$ None If $2, x, 6$ are in G. P, then value of $x$ is $-2\sqrt{3}$ $\sqrt{2}$ $\sqrt{6}$ None of these None If the width of rectangle is $4$ meters and its total area is $12$ meter square. What is its length? 6 meters None 4 meters 2 meters None $\sin({\cos^{-1}{\frac{5}{4}}})=?$ Cannot be determine $\frac{3}{5}$ $-\frac{3}{5}$ $\frac{5}{6}$ None $\frac{1}{2} \sin({-\pi-2\theta})=?$ $-\sin{\theta}\cos{\theta}$ $\sin{2\theta}$ $\sin{\theta}\cos{\theta}$ $-2\sin{\theta}\cos{\theta}$ None The eccentricity of the hyperbola $x^2 - y^2 =1$ is; $e=\sqrt{2}$ $e=\infty$ $e>1$ $e=1$ None The center and radius of circle $x^2 + y^2 -6x + 10y -15 = 0$; $(3, -5), 7$ $(3, -5), 49$ $(-5, -3), 7$ $(5, -3), 7$ None The middle term in the expansion of $(1+\frac{x}{2})^{20}$ is; None $33th$ $11th$ $22th$ None Number of real roots $x^2 + 4x + 6 = 0$ are; 1 0 3 2 None Which of the following is equation whose eccentricity is $1$? $2x^2+2y^2+1=0$ None $2x^2+2x+4y+1=0$ $2x^2+2xy+2y^2 =0$ None Direction of Qibla can be determined by; Plane Geometry none Solid Geometry Spherical Trigonometry 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 1 5 None The equation $\frac{x^2}{16} + \frac{y^2}{81}=1$ is symmetric about; $x-$axis Origin, $x-$axis and $y-$axis $x-$axis not $y-$axis $y-$axis not $x-$axis 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 minimum value of $y = 2x - x^2$ is 1 0 2 -1 None Which one is in range of $f(x)=\frac{2}{3} \sin{x} ?$ 0 $\pi$ $\frac{\pi}{2}$ 1 None If one root of the equation $3x^2 + 13x + k = 0$ is reciprocal of the other then $k=?$ $\frac{1}{5}$ $-5$ 5 3 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 $A$ is a square matrix of order $5$, and $\left|A\right|=3$ then $\left|2A\right|=?$ 27 96 125 40 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) $\frac{1}{220}$ $\frac{1}{221}$ $\frac{1}{169}$ $\frac{2}{169}$ None $\tan^{-1}(x) + \tan^{-1}(\frac{1}{x}) =?$ $\frac{\pi}{2}$ None 1 0 None Maximum value of $f(x)=2\sin{x} + 1$ is; 2 3 1 4 None $\sum_{k=1}^{100} (-1)^k=$ 50 5050 56 0 None $\cos{22 \frac{1}{2}^o} = ?$ $\sqrt{\frac{\sqrt{2}+1}{2\sqrt{2}}}$ $-\sqrt{1 + \frac{1}{2\sqrt{2}}}$ $\pm\sqrt{\frac{\sqrt{2}+1}{2\sqrt{2}}}$ $\sqrt{\frac{\sqrt{2}-1}{2\sqrt{2}}}$ 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 $\lim_{{x \to \infty}}\frac{3x^2 - 1}{4 - 2x^2} =\,?$ $1$ $\infty$ $-\frac{3}{2}$ $\frac{3}{4}$ None Which one is monoid? $(N, \cdot)$ $(E, \cdot)$ None of these $(N, +)$ None $150^\circ$ equal to how many radians ? 2.715 2.45 2.515 2.615 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 $\lim_{n \to \infty} \frac{n^3 + 4n}{4 - 3n^2} =?$ 0 $-\frac{1}{3}$ $\infty$ $-3$ 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 $6, 5$ $1, -5$ $-3, 2$ $6, -5$ None The sum of 3 A.Ms between 5 and 11; 24 25 34 12 None $\log_{10}(0.01)=?$ $-1$ None $-2$ $-3$ None Distance between lines $3x+4y-4=0$ and $6x+8y+2=0$ is; cannot be determine 1 $\frac{1}{\sqrt{5}}$ 5 None 20 years ago my age was $\frac{1}{3}$ of what it is now, what is my present age? 36 33 66 30 None Value of A and B in equation $\frac{x}{(x+3)(x+2)} = \frac{A}{(x+3)} + \frac{B}{(x+2)}$ respectively; $-3, 2$ $3, -2$ $-3, -2$ $-2, 3$ None $\int \sin{x}\cos{x} \, dx = ?$ All of these $\frac{\sin^2(x)}{2} + \lambda$ $\frac{1-\cos2x}{4} + c$ $-\frac{\cos2x}{4} + k$ None The fourth term in the expansion of $(1+x)^{-\frac{1}{2}}$ is; $-\frac{3}{16}$ $\frac{1}{8}x^2$ $-\frac{5}{16}x^3$ $\frac{5}{16}x^3$ None {{#message}}{{{message}}}{{/message}}{{^message}}Your submission failed. The server responded with {{status_text}} (code {{status_code}}). Please contact the developer of this form processor to improve this message. Learn More{{/message}}{{#message}}{{{message}}}{{/message}}{{^message}}It appears your submission was successful. Even though the server responded OK, it is possible the submission was not processed. Please contact the developer of this form processor to improve this message. Learn More{{/message}}Submitting… Time's up