Welcome to your Entry Test Preparation (ECAT) Math Mock Test 2If $\sin{x} + \cos{x} = 0$ 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 greater? $\frac{1}{1000} - \frac{1}{999}$ $\frac{1}{1001} - \frac{1}{1000}$ $\frac{1}{999} - \frac{1}{1000}$ $\frac{1}{1002} - \frac{1}{1001}$ None $\int [x\ln{x} + x(\ln{x})^2] \, dx = ?$ $\frac{x^2}{2} \ln(x) - \frac{x^2}{4} (\ln(x))^2 + x + c$ $\frac{x^2}{2} \ln(x) - \frac{x^2}{4} (\ln(x))^2 + c$ $\frac{(x\ln(x))^2}{2} + c$ None of these 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 If the vertices of a triangle are $A(0, 0)$ , $B(4, 3)$ , $C(3, 0)$ then centroid is; $(2.33, 1)$ $(3.50, 2.50)$ $(1.50, 3.50)$ $(0, 0)$ None If $A=\{a,b,c,d\}, B=\{0,1,2,3\}$ then $f=\{(0, a), (1, b), (2, c), (2, d)\}$ is; Not a function Bijective Onto One to one None The graph of $x=-16y^2$ opens towards; Down Up Right Left None $\int_{0}^{8} \left|x-5\right| \, dx=$ 17 12 $-8$ 25 None If area of circle is $100\pi$, then radius of circle is; $\pm10$ $\sqrt{10}$ $10$ None of these 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 If $f(x)=(x+1)^2$ and $g(x)=x-1$ then value of $fg(4)=?$ 4 25 16 9 None Which of the following is equation whose eccentricity is $1$? $2x^2+2xy+2y^2 =0$ None $2x^2+2x+4y+1=0$ $2x^2+2y^2+1=0$ None If $n$ is divisble by $5$ the remainder is 3. If $3n$ is divisible by $5$ then the remainder is; 5 2 3 4 None If $A$ is a square matrix of order $5$, and $\left|A\right|=3$ then $\left|2A\right|=?$ 40 27 96 125 None $\sum_{k=1}^{100} (-1)^k=$ 0 5050 50 56 None $\tan^{-1}(x) + \tan^{-1}(\frac{1}{x}) =?$ 1 $\frac{\pi}{2}$ None 0 None $\log_{10}(0.01)=?$ $-2$ $-3$ $-1$ None None Co-efficient of $x^n$ in the expansion of $(x^2 - \frac{1}{x})^n$ is; $(-1)^n \cdot64$ cannot be determine $(-1)^n \cdot32$ $-(-1)^n \cdot32$ None Bisma's Salary was reduced by $25\%$. Percentage increase to be effected to bring the salary to original level is; $32.3\%$ $33.3\%$ $30.3\%$ $31.3\%$ None The sum of Binomial coefficients in the expansion of $(1-3y)^7$ is; 128 256 64 32 None For $1 < n < 5$ , which is true? None $n^2 = 5n$ $n^2 > 5n$ $n^2 < 5n$ None The line $y = mx + c ,$ tangent to parabola $y^2 =x $ if; $m = -\frac{1}{3}$ $m = \frac{1}{4}$ $m = \frac{1}{2}$ $ m = 2$ None Which one is in range of $f(x)=\frac{2}{3} \sin{x} ?$ 0 $\frac{\pi}{2}$ 1 $\pi$ None Maximum value of $f(x)=2\sin{x} + 1$ is; 4 1 2 3 None If m, n are the roots of the equation $x^2 + 5x + 6 = 0$, then value of $m^2 + n^2$ is; 36 -13 14 13 None If $x-1$ is a factor of $x^3-x^2-ax+1$ then value of $a=?$ 1 2 -1 0 None Which one is monoid? None of these $(N, \cdot)$ $(N, +)$ $(E, \cdot)$ 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) $\frac{1}{221}$ $\frac{2}{169}$ $\frac{1}{220}$ $\frac{1}{169}$ None The center and radius of circle $x^2 + y^2 -6x + 10y -15 = 0$; $(3, -5), 49$ $(3, -5), 7$ $(5, -3), 7$ $(-5, -3), 7$ None If $\cos{2x} = 0.1$ then value of $\sin{x}$ is; Cannot be determine $\frac{1}{2\sqrt{5}}$ $\frac{2}{5\sqrt{3}}$ $\frac{3}{2\sqrt{5}}$ None When $y=p$ where $p$ is the distance from origin, then slope of $y$ is; 0 $\infty$ None 1 None Value of A and B in equation $\frac{x}{(x+3)(x+2)} = \frac{A}{(x+3)} + \frac{B}{(x+2)}$ respectively; $-3, 2$ $-2, 3$ $3, -2$ $-3, -2$ None $150^\circ$ equal to how many radians ? 2.515 2.45 2.715 2.615 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 Which of the following could be the equation of graph? $y=-x^6$ $y=x^3$ $y=x^4$ None $\sin({\cos^{-1}{\frac{5}{4}}})=?$ $-\frac{3}{5}$ $\frac{3}{5}$ $\frac{5}{6}$ Cannot be determine None None The sides of a triangle are $7, 4\sqrt{3}, \sqrt{13}$ . Then smallest angle would be; $45^\circ$ $20^\circ$ $15^\circ$ $30^\circ$ None Term independent of $x$ in the expansion of $(2x+\frac{1}{x})^4$ is; None such term exists 64 32 24 None $\cos{22 \frac{1}{2}^o} = ?$ $\sqrt{\frac{\sqrt{2}-1}{2\sqrt{2}}}$ $-\sqrt{1 + \frac{1}{2\sqrt{2}}}$ $\sqrt{\frac{\sqrt{2}+1}{2\sqrt{2}}}$ $\pm\sqrt{\frac{\sqrt{2}+1}{2\sqrt{2}}}$ None Time's up