List of top Questions asked in AP EAPCET

If $y=mx+c$, $m>0$ is a common tangent to the parabolas $y^{2}=8x$ and $y^{2}=1+4x$, then $m+c=$

A perpendicular is drawn through the vertex \(O\) of the parabola \(y^2=8x\) to any non-vertical tangent meeting the parabola at \(P\). Then \(OP.OQ=\)

An ellipse intersects the hyperbola \(2x^2-2y^2=1\) orthogonally. The eccentricity of the ellipse is reciprocal to that of the hyperbola. If the axes of the ellipse are along the coordinate axes, then the equation of the ellipse is:

The equation of the conjugate hyperbola of the hyperbola $x^{2}-4y^{2}-2x-8y-19=0$ is

If the major axis of an ellipse subtends an angle of $120^{\circ}$ at one end of its minor axis and the length of its semi latus rectum is $\frac{4}{\sqrt{3}}$, then the sum of the lengths of its axes is

Let S be the focus of the parabola \( y^{2}=36x \) and let the line \( x+by+c=0 \) intersect the parabola at the points Q and R. If the centroid of \( \triangle QRS \) is (57,0), then -c is

If the eccentricity of a hyperbola is $\sqrt{3}$, then the eccentricity of its conjugate hyperbola is:

If \[ \begin{bmatrix} 1 & -\tan\frac{\theta}{2}
[4pt] \tan\frac{\theta}{2} & 1 \end{bmatrix} \begin{bmatrix} 1 & \tan\frac{\theta}{2}
[4pt] -\tan\frac{\theta}{2} & 1 \end{bmatrix}^{-1} = ? \]

If the distance of a variable point $P$ from the fixed line \[ 2x-y+1=0 \] is twice the distance of $P$ from another fixed line \[ 2x+y-2=0, \] then a point on the locus of $P$ is

The number of terms in the expansion of $(x + y + z)^{10}$ is:

If the expansion of \[ \left(\frac{1+15x}{1-3x}\right) \] is valid and the coefficient of \(x^3\) in its expansion is \(k(3^3)\), then \(k=\)

If \( C_{o},C_{1},C_{2},...,C_{n} \) represent the coefficients in the binomial expansion of \( (1+x)^{n} \), then \( C_{o}+\frac{c_{2}}{3}+\frac{c_{4}}{5}+\cdot\cdot\cdot+\frac{c_{16}}{17}= \)

In the binomial expansion of $(x+a)^{15}$, if the eleventh term is the geometric mean of the eighth and twelfth terms, then the numerically greatest term in its expansion is

The value of $n$ for which the sum \[ \frac{{}^nC_0}{2^n} + 2\frac{{}^nC_1}{2^n} + 3\frac{{}^nC_2}{2^n} +\cdots+ (n+1)\frac{{}^nC_n}{2^n} =16 \] is

The coefficient of $x^{12}$ in the expansion of \[ (3+2x)^{-5} \] is

Evaluate \[ \sum_{r=1}^{\infty} \frac{1\cdot3\cdot5\cdots(2r-1)} {2^{2r}r!} (\sqrt{3})^r : \]

If $x$ is so small that the values of $x^n$, $n\geq2$ are negligible, then the approximate value of \[ \frac{\sqrt{2-3x}}{(3+2x)}(x+1) \] is

If $a_n = \sum_{r=0}^n \frac{1}{^{n}C_r}$ and $b_n = \sum_{r=0}^n \frac{r}{^{n}C_r}$, then $\frac{b_n}{a_n} =$

If \( 0<x<1 \), then first negative term in the expansion of \( (1+x)^{\frac{47}{5}} \) is

Let \[ f(x)=\int \frac{\sqrt{x}}{(1+x)^2}\,dx \quad (x\geq 0) \] Then \[ f(3)-f(1) \] is equal to:

The value of the integral \(\int_{0}^{\pi} \frac{x \sin x}{\sin^2 x + 2 \cos^2 x} \, dx\) is:

If \( [ ] \) denotes the greatest integer function, then \( \int_{1}^{2} [x^2] dx = \)

If $f(x)=\left|\frac{x}{3}-3^{-x}\right|$ and $\int_{0}^{5}f(x)dx=K+\frac{3^{n}+1}{3^{5}\log 3}$, then $nK=$

Evaluate: \[ \lim_{n\to\infty}\sum_{r=n}^{2n}\left(\frac{n^3+r^3}{n^4}\right) \]