List of top Questions asked in AP EAPCET- 2022

There exists \(\theta\) such that \[ a\gt |\sec\theta|, \] then \[ \int \frac{dx}{1+a\cos x} = \] is:

Evaluate \[ \int \frac{x^2}{x^3\sqrt{x^2-1}}\,dx = \]

\(f:\mathbb{R}\to\mathbb{R}\) is a function such that \[ |f(x)-f(y)|\leq \frac{1}{2}|x-y| \quad \forall x,y\in \mathbb{R} \] and \[ f'(x)\geq \frac{1}{2}\quad \forall x\in \mathbb{R},\quad f(1)=\frac{1}{2} \] Then the number of points of intersection of the curve \(y=f(x)\) and the curve \[ y=x^2-2x-5 \] is:

If \[ \frac{d^n y}{dx^n}=y_n \] and \[ y=e^{\sqrt{x}}+e^{-\sqrt{x}}, \] then \[ 4xy_2+2y_1= \]

If the two curves \[ y=a^x \] and \[ y=b^x \] intersect at angle \(\alpha\), then \[ \tan\alpha= \] is:

The area of the triangle formed by the tangent to the curve \[ xy=a^2 \] at \((x_1,y_1)\) on it and the axes is

If the slope of the line through \((0,0)\) which is tangent to the curve \[ y=x^2+x+16 \] is \(m\), then the value of \[ m-4 \] is:

Evaluate \[ \lim_{n\to\infty}\sqrt{2} \left[ \frac{(2+\sqrt{2})^n+(2-\sqrt{2})^n} {(2+\sqrt{2})^n-(2-\sqrt{2})^n} \right] \]

If \[ f(x)= \begin{cases} \dfrac{1-\sin^3 x}{3\cos^2 x}, & x\lt \dfrac{\pi}{2} \\[6pt] \alpha, & x=\dfrac{\pi}{2} \\[6pt] \dfrac{\beta(1-\sin x)}{(\pi-2x)^2}, & x\gt \dfrac{\pi}{2} \end{cases} \] is continuous at \(x=\dfrac{\pi}{2}\), then \(\alpha\beta=\)

If \[ -2,\ \frac{4}{3},\ -\frac{4}{5} \] are the intercepts made by a plane on \(X,Y,Z\)-axes respectively, then the direction cosines of a normal to this plane are:

If \(a\gt 0\), \([\,]\) denotes greatest integer function and \[ \lim_{x\to a} \left( \frac{[x]^3}{a}-\left[\frac{x}{a}\right]^3 \right)=k, \] \[ \lim_{x\to a} \left( \frac{[x]^5}{a}-\left[\frac{x}{a}\right]^3 \right)=l, \] then

Evaluate \[ \lim_{n\to\infty}\frac{A+e^{nx}}{x+Ae^{nx}} \]

If the centroid of triangle whose vertices are \[ (a,1,3),\ (-2,b,-5)\ \text{and}\ (4,7,c) \] be the origin, then \[ a^2+b^2+c^2= \] is:

The distance between the directrices of the ellipse \[ \frac{x^2}{36}+\frac{y^2}{20}=1 \] is

If \(\alpha,2\alpha,3\alpha\) are angles made by a ray with \(OX\), \(OY\), \(OZ\) axes respectively, then all the possible values of \(\alpha\) are:

The locus of the point of intersection of the tangents at the end-points of normal chords of the hyperbola \[ \frac{x^2}{a^2}-\frac{y^2}{b^2}=1 \] is

If \[ \sqrt{5}y-\sqrt{8}=0 \] is the equation of the directrix of a hyperbola \[ \frac{x^2}{a^2}-\frac{y^2}{b^2}+1=0 \] and \[ \frac{\sqrt{5}}{2} \] is its eccentricity, then \[ a= \] is:

The distance of the point \[ (6,4\sqrt{3}) \] from the focus of \[ y^2=8x \] is:

The circle touching the coordinate axes with its centre lying on \[ x-2y-3=0 \] is:

The set of all points that are at a distance of at least \(2\) units from \((-3,0)\) is

The circle touching the \(y\)-axis at a distance \(4\) units from the origin and cutting off an intercept \(6\) from \(x\)-axis is:

For a circle of diameter \(R\), touching \[ x^2+y^2-4y=0 \] and passing through \((4,5)\), which of the following is correct?

Suppose a circle passes through \((0,a)\) and \((b,h)\) having its centre at \((c,0)\). Then the value of \(c\) is

Suppose \(P(x,y)\) lying on \[ \sqrt{3}x-y+2=0 \] or \[ \sqrt{3}x+y-2=0 \] is at a distance of \(5\) units from their point of intersection. Then the distance from \((0,0)\) to the foot of the perpendicular of \(P\) onto the \(y\)-axis is

If \(A(-3,3)\), \(B(1,1)\), \(C(1,-1)\) and \(D(-2,-2)\) are the vertices of a quadrilateral, the angle between the diagonals \(AC\) and \(BD\) is: