Welcome to your Entry Test Preparation (ECAT) Math Mock Test 2

$\tan^{-1}(x) + \tan^{-1}(\frac{1}{x}) =?$

If $x-1$ is a factor of $x^3-x^2-ax+1$ then value of $a=?$

$\int [x\ln{x} + x(\ln{x})^2] \, dx = ?$

Which one is monoid?

$\cos{22 \frac{1}{2}^o} = ?$

Find the average of first 50 whole numbers.

$a + ar + ar^2 + … + ar^n =? r>1$

If $\vec{u} = 2\vec{i} + 6 , \vec{v} = -9\vec{i}+ 8\vec{j} + 4\vec{k}$ then $\vec{u} \cdot \vec{v} = ?$

$\sum_{k=1}^{100} (-1)^k=$

$\lim_{{x \to \infty}}\frac{3x^2 - 1}{4 - 2x^2} =\,?$

Direction of Qibla can be determined by;

$x^2 -5xy + 4y^2$ is made from which of the following pairs?

The number of points of intersection of the circle $x^2 + y^2 =7$ and the hyperbola $x^2 - y^2 =1$

$\sin({\cos^{-1}{\frac{5}{4}}})=?$

The middle term in the expansion of $(1+\frac{x}{2})^{20}$ is;

Bisma's Salary was reduced by $25\%$. Percentage increase to be effected to bring the salary to original level is;

For $1 < n < 5$ , which is true?

The value of $\vec{i}\cdot[(\vec{k}\times\vec{j})\cdot(\vec{i}\times\vec{k})]$ is;

The line $y = mx + c ,$ tangent to parabola $y^2 =x $ if;

Which one is in range of $f(x)=\frac{2}{3} \sin{x} ?$

When $y=p$ where $p$ is the distance from origin, then slope of $y$ is;

$\lim_{n \to \infty} \frac{n^3 + 4n}{4 - 3n^2} =?$

The center and radius of circle $x^2 + y^2 -6x + 10y -15 = 0$;

The equation $ax^2+by^2+2hxy+2gx+2fy+c=0$ may be a parabola if;

Term independent of $x$ in the expansion of $(2x+\frac{1}{x})^4$ is;

If $x=a\cos{\theta} + ib\sin{\theta}$ and $y=a\cos{\theta} + ib\sin{\theta}$ then $\left| xy \right|=?$

Co-efficient of $x^n$ in the expansion of $(x^2 - \frac{1}{x})^n$ is;

If $A=\{a,b,c,d\}, B=\{0,1,2,3\}$ then $f=\{(0, a), (1, b), (2, c), (2, d)\}$ is;

$\log_{10}(0.01)=?$

Term independent of $x$ in the expansion of $(2x+\frac{1}{x})^3$ is;

$\int x^3 e^{5x} \, dx = ?$

If $\frac{dy}{dx}=\frac{x^2 - 1}{x}$ then $y = ?$

Which of the following is not true?

The graph of $x=-16y^2$ opens towards;

If m, n are the roots of the equation $x^2 + 5x + 6 = 0$, then value of $m^2 + n^2$ is;

If $A$ is a square matrix of order $5$, and $\left|A\right|=3$ then $\left|2A\right|=?$

20 years ago my age was $\frac{1}{3}$ of what it is now, what is my present age?

Which of the following are the parametric questions of the ellipse $\frac{x^2}{a^2} +\frac{y^2}{b^2} = 1, a>b ?$

If $A=\{1, 2, 3, 5, 7\}, U=\{1, 2, 3, …, 11, 12\} \,and\, B= \{4, 5, 7, 9, 3\} \,then\, P(A \cup B)=?$

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