Welcome to your Entry Test Preparation (ECAT) Math Mock Test 2Which of the following is not true? $2\pi$ is not in domain of $\tan{x}$ Domain of $\sin{\theta}$ is $\mathbb{R} $ Range of $y=\cos{\theta}$ is $[-1, 1]$ Period of $y=\sin{\theta}$ is $2\pi$ None If one root of the equation $3x^2 + 13x + k = 0$ is reciprocal of the other then $k=?$ $\frac{1}{5}$ 3 5 $-5$ None The value of $(1 + i)^4 (1 + \frac{1}{i})^4$ equals to: $2$ $16$ $-16$ $15$ None If $\sin{x} + \cos{x} = 0$ then $x=?$ $\{\frac{5\pi}{4} + 2n\pi \}$ $\{\frac{\pi}{4} + n\pi \}$ $\{\frac{3\pi}{4} + n\pi \}$ $\{\frac{\pi}{4} + 2n\pi \}$ None The equation $\frac{x^2}{16} + \frac{y^2}{81}=1$ is symmetric about; $y-$axis not $x-$axis $x-$axis Origin, $x-$axis and $y-$axis $x-$axis not $y-$axis None If $2, x, 6$ are in G. P, then value of $x$ is $-2\sqrt{3}$ None of these $\sqrt{6}$ $\sqrt{2}$ None Direction of Qibla can be determined by; Plane Geometry Solid Geometry Spherical Trigonometry none None The sum of Binomial coefficients in the expansion of $(1-3y)^7$ is; 256 32 64 128 None $\sum_{k=1}^{98} (\omega^k) =\,?$ 0 $\omega$ -1 $\omega^2$ None Distance between lines $3x+4y-4=0$ and $6x+8y+2=0$ is; 5 $\frac{1}{\sqrt{5}}$ 1 cannot be determine None For $1 < n < 5$ , which is true? $n^2 > 5n$ $n^2 < 5n$ None $n^2 = 5n$ None H. M between $\frac{1}{2} and \frac{1}{3} $ is; $\frac{7}{5}$ $\frac{5}{4}$ $\frac{2}{5}$ $\frac{1}{5}$ None The sum of 3 A.Ms between 5 and 11; 34 24 25 12 None If $x-1$ is a factor of $x^3-x^2-ax+1$ then value of $a=?$ 0 -1 1 2 None $x^2 -5xy + 4y^2$ is made from which of the following pairs? $(x - y)(x - 4y)$ None $(x + y)(x - 4y)$ $(x + 5y)(x - 4y)$ None If $f(x)=(x+1)^2$ and $g(x)=x-1$ then value of $fg(4)=?$ 16 4 9 25 None The sum of squares of first 18 natural numbers is; 1809 2109 1509 2209 None $\int \sin{x}\cos{x} \, dx = ?$ $\frac{\sin^2(x)}{2} + \lambda$ $-\frac{\cos2x}{4} + k$ All of these $\frac{1-\cos2x}{4} + c$ None The center and radius of circle $x^2 + y^2 -6x + 10y -15 = 0$; $(5, -3), 7$ $(-5, -3), 7$ $(3, -5), 7$ $(3, -5), 49$ None If $\cos{2x} = 0.1$ then value of $\sin{x}$ is; Cannot be determine $\frac{3}{2\sqrt{5}}$ $\frac{1}{2\sqrt{5}}$ $\frac{2}{5\sqrt{3}}$ None $\lim_{n \to \infty} \frac{n^3 + 4n}{4 - 3n^2} =?$ $-3$ 0 $-\frac{1}{3}$ $\infty$ None If the vertices of a triangle are $A(0, 0)$ , $B(4, 3)$ , $C(3, 0)$ then centroid is; $(1.50, 3.50)$ $(0, 0)$ $(2.33, 1)$ $(3.50, 2.50)$ 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 $\int_{0}^{8} \left|x-5\right| \, dx=$ 17 25 12 $-8$ None The fourth term in the expansion of $(1+x)^{-\frac{1}{2}}$ is; $\frac{1}{8}x^2$ $\frac{5}{16}x^3$ $-\frac{3}{16}$ $-\frac{5}{16}x^3$ None If area of circle is $100\pi$, then radius of circle is; $\sqrt{10}$ $\pm10$ None of these $10$ None Term independent of $x$ in the expansion of $(2x+\frac{1}{x})^4$ is; None such term exists 64 24 32 None If $x=2at^2 , y=at^3$ then $\frac{dy}{dx}=?$ $\frac{1}{2} t^2$ $\frac{3}{4} t$ $\frac{3}{2} a$ $-\frac{1}{2} t$ None If $n$ is divisble by $5$ the remainder is 3. If $3n$ is divisible by $5$ then the remainder is; 3 5 4 2 None $\tan^{-1}(x) + \tan^{-1}(\frac{1}{x}) =?$ 1 0 None $\frac{\pi}{2}$ None $\cos{22 \frac{1}{2}^o} = ?$ $\pm\sqrt{\frac{\sqrt{2}+1}{2\sqrt{2}}}$ $\sqrt{\frac{\sqrt{2}+1}{2\sqrt{2}}}$ $\sqrt{\frac{\sqrt{2}-1}{2\sqrt{2}}}$ $-\sqrt{1 + \frac{1}{2\sqrt{2}}}$ None $\sin({\cos^{-1}{\frac{5}{4}}})=?$ $\frac{3}{5}$ Cannot be determine $-\frac{3}{5}$ $\frac{5}{6}$ None The line $y = mx + c ,$ tangent to parabola $y^2 =x $ if; $m = \frac{1}{2}$ $m = \frac{1}{4}$ $ m = 2$ $m = -\frac{1}{3}$ None $a + ar + ar^2 + … + ar^n =? r>1$ $\frac{a(a^{n+1}-1)}{r-1}$ $\frac{a(r-1)}{r-1}$ $a(r^{n+1}-1)$ None None $\lim_{{x \to \infty}}\frac{3x^2 - 1}{4 - 2x^2} =\,?$ $1$ $-\frac{3}{2}$ $\frac{3}{4}$ $\infty$ None When $y=p$ where $p$ is the distance from origin, then slope of $y$ is; 1 0 $\infty$ None None $\frac{1}{2} \sin({-\pi-2\theta})=?$ $-\sin{\theta}\cos{\theta}$ $-2\sin{\theta}\cos{\theta}$ $\sin{2\theta}$ $\sin{\theta}\cos{\theta}$ None Maximum value of $f(x)=2\sin{x} + 1$ is; 2 4 1 3 None $\sum_{k=1}^{100} (-1)^k=$ 5050 56 50 0 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) $\frac{1}{169}$ $\frac{1}{220}$ $\frac{2}{169}$ $\frac{1}{221}$ None Time's up