List of top Questions asked in AP EAPCET

If \(g(x)\) is the inverse of the function \(f(x)\) and \(f'(x) = \dfrac{1}{h(x)}\), then what is the value of \(g'(x)\)?

If the slope of the tangent on a curve at any point \((x, y)\) is equal to \[ \frac{y^2 - x^2}{2xy} \] then the equation of the normal at the point \(\left(1, \frac{\sqrt{3}}{2}\right)\) is

Let \(A(1,15),\ B(3,-12),\ C(6,12)\) be three consecutive turning points of a continuous curve \(y = f(x)\). If \(f(x) = 0\) only for \(x = \alpha\) and \(x = \beta\), then \[ |\beta - \alpha| < ? \]

Evaluate the integral \[ \int \frac{\sin^{-1} \sqrt{x} - \cos^{-1} \sqrt{x}}{\sqrt{x} \left( \sin^{-1} \sqrt{x} + \cos^{-1} \sqrt{x} \right)} \, dx \]

Let the transverse axis of a hyperbola \( H \) be parallel to the X-axis and \( x^2 + y^2 - 2x - 4y + 3 = 0 \) be the equation of the auxiliary circle of \( H \). If the asymptotes of \( H \) are at right angles, then the equation of the hyperbola is:

Assertion (A): Every rational function is continuous at every real number \(x\) at which it is defined.
Reason (R): Every rational function is a quotient of two polynomials.

If \(x^2 \tan^{-1}\left(\frac{y}{x}\right) - y^2 \tan^{-1}\left(\frac{x}{y}\right) = k\), then \(\left(\frac{dy}{dx}\right)_{(1,1)} =\) ?

If a focal chord of the ellipse \(\frac{x^2}{25} + \frac{y^2}{16} = 1\) meets its minor axis at the point \((0, 3)\), then the perpendicular distance from the centre of the ellipse to this focal chord is:

If \( PS \) is the median of the triangle with vertices \( P(2, 2) \), \( Q(6, -1) \), and \( R(7, 3) \), then the equation of the line passing through \( (1, -1) \) and parallel to \( PS \) is:

Two sides of a rhombus are along the lines \( x - y + 1 = 0 \) and \( 7x - y - 5 = 0 \). If its diagonals intersect at \( (-1, -2) \), then one of the vertices of this rhombus is:

If \(2x^2 - 5xy + 2y^2 = 0\) represents two sides of a triangle whose centroid is \((1,1)\), then the equation of the third side is:

A point on the plane passing through the points \((\sqrt{2},1,4), (0,-1,0)\) and \((0,0,1)\) is:

A box contains 5 white balls and 7 black balls. In how many ways can 3 balls be drawn from the box such that at least one black ball is included?}

Two dice are rolled. If \( A \) denotes the event that the same number shows on each die and \( B \) denotes the event that the sum of the numbers on both dice is greater than 7, then \( P(A \mid B) \) and \( P(B \mid A) \) respectively are:

The circumcentre of the triangle with vertices \( (-2,3), (2,-1), (4,0) \) is:

Let \[ \vec{a} = 2\hat{i} + \hat{j} - \hat{k} \quad \text{and} \quad \vec{b} = \hat{i} + 3\hat{j} - 5\hat{k} \] be two vectors, and \(\vec{r}\) be a vector along the vector \(3\vec{a} - 2\vec{b}\) such that \(|\vec{r}| = \sqrt{74}\). If the direction of \(\vec{r}\) is opposite to that of \(3\vec{a} - 2\vec{b}\), then \(\vec{r} =\)

If \(\vec{r}\) is the position vector of the centroid \(G\) of triangle \(ABC\) and \[ 2\hat{i} + \hat{j} - \hat{k} \quad \text{and} \quad 2\hat{i} + 4\hat{j} - 4\hat{k} \] are respectively the position vectors of its vertices \(A\) and \(B\), then \[ AG^2 + BG^2 + CG^2 =\ ? \]

If \[ \vec{a} = -2\hat{i} + 9\hat{j} - 6\hat{k}, \quad \vec{b} = t\hat{i} - 2\hat{j} + 6\hat{k} \] are vectors such that \(|\vec{a} + \vec{b}| = 25\), then the sum of the values of \(t =\ ?\)

If \[ \vec{a} = \hat{i} + 3\hat{j} + 13\hat{k}, \quad \vec{b} = 2\hat{i} - 4\hat{j} + 3\hat{k} \] are two vectors, then the component vector of \(\vec{a}\) perpendicular to \(\vec{b}\) is

Let \[ \vec{a} = 2\hat{i} - 3\hat{j} - 5\hat{k}, \quad \vec{b} = 3\hat{i} + 2\hat{j} - 5\hat{k} \] be two vectors and \(\vec{r}\) be a vector in the plane of \(\vec{a} \text{ and } \vec{b}\). If \(\vec{r}\) is orthogonal to \(5\hat{i} - 2\hat{j} + 3\hat{k}\) and the magnitude of \(\vec{r}\) is \(\sqrt{94}\), then \(|\vec{r} \cdot \vec{b}|\) is

If \(x_1, x_2, \ldots, x_n\) are 'n' observations and \(\bar{x}\) is their mean. If \[ \sum_{i=1}^{n}(x_i - \bar{x})^2 \text{ is almost zero, then a true statement among the following is} \]

If \( \cos^3 x \sin 4x = \sum_{r=0}^n a_r \sin rx \ \forall x \in \mathbb{R} \), then \( a_3 + a_5 : a_1 + a_7 = \)

In \(\triangle ABC\), if \(\angle A = 90^\circ\), then \((r_2 - r_1)(r_3 - r_1) = \)

The coefficient of \( x^3 \) in the expansion of \( (1 - 2x)^{\frac{1}{2}} (1 + 3x)^{\frac{1}{3}} \) is:

The number of arrangements of the letters of the word ARRANGEMENT in which two E’s do not occur adjacently is: