List of top Questions asked in AP EAPCET

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 \[ \sqrt{5}y-\sqrt{8}=0 \] 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 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

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

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:

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

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

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

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

If two distinct points lying at a unit distance from \[ 4x+3y-10=0 \] and passing through \[ x+y=4 \] are separated by a distance \(d\), then the value of \(d\) 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

Suppose the pairs of straight lines \[ 2x^2+axy+3y^2=0 \] and \[ 2x^2+bxy-3y^2=0 \] are such that they have one common line with the other two remaining perpendicular. Then the values of \(a\) and \(b\) respectively are:

The locus of the incentre of the triangle formed by the lines \[ xy-4x-4y+16=0 \] and \[ x+y=5 \] 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:

Suppose a point \(P\) moves so that \[ BP^2-AP^2=121, \] where \(A\) and \(B\) are \((2,5)\) and \((5,11)\) respectively. Then the locus of \(P\) is a straight line, whose slope is:

It is given that the discrete random variable \[ X\sim B(n,p) \] and \[ P(X=2)=P(X=3). \] Then mean of \(X\) is

If \(3\) is the variance of Poisson distribution, then \[ P(1\lt x\lt 4)= \] is:

Two dice are thrown simultaneously. The probability of getting two numbers whose product is even is:

From a pack of \(52\) cards, \(3\) cards are drawn at random. Then, the probability that one is ace, one is queen and one is jack is:

There are \(4\) hotels in a town. If \(3\) men check into the hotels in a day, then the probability that each checks into a different hotel is

In \(\triangle ABC\), \(O\) is the circumcenter and \(G\) is the centroid, then \[ OG^2= \] is:

The mean deviation about the mean for the following data:

is: