List of top Mathematics Questions asked in AP EAPCET

The number of points of discontinuity of the function \[ f(x)=[x]+|x-2|, \qquad -3<x<3 \] is

If \[ \lim_{x\to\infty} \left(\frac{ax^2+bx+c}{lx^2+mx+n}\right) \left(\frac{lx-1}{lx+a}\right)^{\frac{x}{2}} = \frac{3}{\sqrt{16e}}, \] then \[ \lim_{x\to0} \frac{l+mx+cx^2}{a+bx+nx^2} = \]

If \[ f(x)= \begin{vmatrix} 2+\dfrac{\sin x}{x} & 1 & 3
[4pt] 2 & 1+\dfrac{\sin x}{x} & 3
[4pt] 2 & 1 & 3+\dfrac{\sin x}{x} \end{vmatrix}, \] then \[ \lim_{x\to 0} f(x)= \]

If the distance between the foci of an ellipse \[ \frac{x^2}{a^2}+\frac{y^2}{b^2}=1 \] is \(6\) and the distance between its directrices is \(10\), then the equation of one of the tangents of the ellipse drawn parallel to the line \[ y=\sqrt2\,x+5 \] is

PSQ is a focal chord of the parabola \[ y^2=12x. \] \(A\) and \(B\) are respectively the feet of the perpendiculars drawn from \(P\) and \(Q\) on the directrix of the parabola. If the length of \(AB\) is \(7\sqrt3\) and \[ P=(3t^2,6t), \qquad (0<t<1), \] then \(t=\)

Let \(O\) and \(S\) be the vertex and focus of the parabola \[ y^2=4ax \] respectively and \(x=k\) be its double ordinate of length \(2\sqrt6\,a\). If the line \(x=k\) cuts the \(X\)-axis at \(P\), then the length of the double ordinate drawn through \(O\) to the parabola having \(P\) and \(S\) as vertex and focus is

Let \[ A(1,2,1),\qquad B\left(\frac95,\frac85,\frac95\right),\qquad C(\alpha,\beta,\gamma) \] and \[ D(-3,4,-3) \] be four collinear points. If \(B\) divides \(AC\) in the ratio \(m:n\), and \(D\) divides \(AC\) in the ratio \(m:-n\), then \[ \alpha+\beta+\gamma= \]

The acute angle between the lines whose direction cosines satisfy \[ l^2-5m^2+n^2=0 \] and \[ l+m-n=0 \] is

From a point \[ P(x_1,-1), \qquad (x_1<0), \] two tangents are drawn to the hyperbola \[ \frac{x^2}{2}-\frac{y^2}{3}=1. \] If the sum of the slopes of the tangents is \(2\), then \(x_1=\)

If \[ x^2+y^2-2x+2fy+c=0 \] intersects the two circles \[ x^2+y^2+2x-4y+1=0 \] and \[ x^2+y^2-4x-2y-11=0 \] orthogonally, then \[ f+c= \]

If the tangent drawn at \((\sqrt2,1)\) on the circle \[ x^2+y^2=3 \] is also a tangent to the two circles of equal radius \(2\sqrt3\) with centres at \[ (0,\beta_1) \quad \text{and} \quad (0,\beta_2), \] then \[ |\beta_1-\beta_2|= \]

If \(A,B\) are the feet of the perpendiculars drawn from \(P(3,1)\) on the pair of lines \[ 2x^2+3xy-2y^2+3x+y+1=0 \] and \(Q\) is the point of intersection of the pair of lines, then the area of the quadrilateral \(PAQB\) is

The external centre of similitude of the two circles \[ x^2+y^2-4x+6y+4=0 \] and \[ x^2+y^2-2x+2y-2=0 \] is

The point of intersection of the lines \[ 2x+3y-12=0 \] and \[ 3x-2y-5=0 \] is the centre of a circle \(S=0\). If \(AB\) is a chord of \(S=0\) and it is a diameter of the circle \[ x^2+y^2-10x+4y+13=0, \] then the radius of the circle \(S=0\) is

If the angular bisectors of the lines \[ 3x-4y-5=0 \] and \[ 8x-6y+1=0 \] are \[ x+y+c=0 \] and \[ x-y+k=0, \] then \[ 7(c+k)= \]

If \(O\) is the origin and \(H\) is the orthocenter of a triangle formed by the lines \[ x+y=1, \] \[ 6x^2-13xy+6y^2=0, \] then \[ OH= \]

If the equation of a line passing through \[ \left(\frac13,-\frac12\right) \] and making an angle of \(60^\circ\) with the line \[ 2x-3y+4=0 \] is \[ (2+3\sqrt3)x+by=c, \] then \(c=\)

The origin is shifted to the point \((1,1)\) by translation of axes and then the axes are rotated through an angle \[ \frac{\pi}{3} \] about \((1,1)\) in the positive direction. After these two transformations, if the point \[ P(3,2) \] becomes \(P(\alpha,\beta)\), then \[ 4\alpha+2\beta= \]

In a binomial distribution \[ P(X=2)\div P(X=23)=\left(\frac{2}{3}\right)^{21}, \] then the mean of the binomial distribution is

If \(P(3,4)\) is a fixed point and \(Q\) is a variable point on the circle \[ x^2+y^2=16, \] then the locus of the midpoint of \(PQ\) is

If a number \(x\) is to be chosen randomly from the set \[ \{1,2,3,\ldots,30\}, \] then the probability of getting an \(x\) that is a multiple of \(3\) such that \[ \left(x-\frac{26}{x}\right)>25 \] is

If \(A\), \(B\), \(C\) are independent events of a random experiment such that \[ P(A)=\frac34,\qquad P(B)=\frac56,\qquad P(C)=\frac23, \] then the probability that exactly one of the events occurs is