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

If one root of the equation $3x^2 + 13x + k = 0$ is reciprocal of the other then $k=?$

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

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

If $\sin{x} + \cos{x} = 0$ then $x=?$

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

The eccentricity of the hyperbola $x^2 - y^2 =1$ is;

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

The sides of a triangle are $7, 4\sqrt{3}, \sqrt{13}$ . Then smallest angle would be;

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

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 $\left| xy \right|=?$

If $(3,7)$ and $(8,9)$ belong to complex numbers then $(3,7)\div (8,9)=?$

If $f(x)=(x+1)^2$ and $g(x)=x-1$ then value of $fg(4)=?$

Which one is monoid?

Maximum value of $f(x)=2\sin{x} + 1$ is;

Which one is greater?

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

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)

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

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

$\int_{0}^{8} \left|x-5\right| \, dx=$

Number of real roots $x^2 + 4x + 6 = 0$ are;

$\sum_{k=1}^{98} (\omega^k) =\,?$

If $2, x, 6$ are in G. P, then value of $x$ is

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

If $A(2,1)$ and $B(4,3)$ are end points of diameter of circles, then radius of circle is

$a + ar + ar^2 + … + ar^n =? r>1$

$\int \sin{x}\cos{x} \, dx = ?$

The rank of the matrix $ \begin{bmatrix} 1 & -1 & 2 & -3 \\ 2 & 0 & 7 & -7 \\ 3 & 1 & 12 & -11 \\ \end{bmatrix} $ is;

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

Value of A and B in equation $\frac{x}{(x+3)(x+2)} = \frac{A}{(x+3)} + \frac{B}{(x+2)}$ respectively;

H. M between $\frac{1}{2} and \frac{1}{3} $ is;

If the width of rectangle is $4$ meters and its total area is $12$ meter square. What is its length?

The sum of squares of first 18 natural numbers is;

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

The minimum value of $y = 2x - x^2$ is

If $x=2at^2 , y=at^3$ then $\frac{dy}{dx}=?$

If the vertices of a triangle are $A(0, 0)$ , $B(4, 3)$ , $C(3, 0)$ then centroid is;

If area of circle is $100\pi$, then radius of circle is;

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