List of top Questions asked in AP EAMCET

If
\[ \lim_{x\to\infty}x^{\log_e x}=0, \] then \(\log_x12=\)

The \(x\)-intercept of a plane \(\pi\) passing through the point \((1,1,1)\) is \(\dfrac{5}{2}\) and the perpendicular distance from the origin to the plane \(\pi\) is \(\dfrac{5}{7}\). If the \(y\)-intercept of the plane \(\pi\) is negative and the \(z\)-intercept is positive, then its \(y\)-intercept is

If \((a,b,c)\) are the direction ratios of a line joining the points \((4,3,-5)\) and \((-2,1,-8)\), then the point \(P(a,3b,2c)\) lies on the plane

Let origin be the centre, \((\pm 3,0)\) be the foci and \(\dfrac{3}{2}\) be the eccentricity of a hyperbola. Then the line \(2x-y-1=0\)

The locus of a variable point whose chord of contact with respect to the hyperbola
\[ \frac{x^2}{a^2}-\frac{y^2}{b^2}=1 \] subtends a right angle at the origin is

The eccentric angle of a point on the ellipse \(x^2+3y^2=6\) lying at a distance of \(2\) units from its centre is

Suppose a parabola with focus at \((0,0)\) has
\[ x-y+1=0 \] as its tangent at the vertex. Then the equation of its directrix is

If the point \((a,8,-2)\) divides the line segment joining the points \((1,4,6)\) and \((5,2,10)\) in the ratio \(m:n\), then
\[ \frac{2m}{n}-\frac{a}{3}= \]

If the tangent at the point \(P\) on the circle
\[ x^2+y^2+6x+6y=2 \] meets the straight line
\[ 5x-2y+6=0 \] at a point \(Q\) on the \(y\)-axis, then the length of \(PQ\) is

For \(\alpha \in \left[0,\dfrac{\pi}{2}\right]\), the angle between the lines represented by \[ [x\cos\theta-y]\left[(\cos\theta+\tan\alpha)x-(1-\cos\theta \tan\alpha)y\right]=0 \] is

If the lines represented by
\[ ax^2+2hxy+by^2+2gx+2fy+c=0 \] intersect on the \(x\)-axis, which of the following is in general incorrect?

The locus of centers of the circles, passing the same area and having \(3x-4y+4=0\) and \(6x-8y+7=0\) as their common tangent, is

For any two nonzero real numbers \(a\) and \(b\), if the line
\[ \frac{x}{a}+\frac{y}{b}=1 \] is a tangent to the circle
\[ x^2+y^2=1, \] then which of the following is true?

The length of the intercept on the line \(4x-3y-10=0\) by the circle \(x^2+y^2-2x+4y-26=0\) is

The pole of the line \(\dfrac{x}{a}+\dfrac{y}{b}=1\) with respect to the circle \(x^2+y^2=c^2\) is

Starting from the point \(A(-3,4)\), a moving object touches \(2x+y-7=0\) at \(B\) and reaches the point \(C(0,1)\). If the object travels along the shortest path, the distance between \(A\) and \(B\) is

A stick of length \(r\) units slides with its ends on coordinate axes. Then the locus of the midpoint of the stick is a curve whose length is

The least distance from origin to a point on the line \(y=x+3\) which lies at a distance of \(2\) units from \((0,3)\) is

Suppose a triangle is formed by \(x+y=10\) and the coordinate axes. Then the number of points \((x,y)\), where \(x\) and \(y\) are natural numbers, lying inside the triangle is

If \(6\) is the mean of a Poisson distribution, then
\[ P(X\geq3)= \]

A box contains \(100\) balls, numbered from \(1\) to \(100\). If \(3\) balls are selected one after the other at random with replacement from the box, then the probability that the sum of the three numbers on the balls selected from the box is an odd number, is

In a lottery containing \(35\) tickets, exactly \(10\) tickets bear a prize. If a ticket is drawn at random, then the probability of not getting a prize is

A bag contains \(7\) green and \(5\) black balls. \(3\) balls are drawn at random one after the other. If the balls are not replaced, then the probability of all three balls being green is

If \(x\) is chosen at random from the set \(\{1,2,3,4\}\) and \(y\) is chosen at random from the set \(\{5,6,7\}\), then the probability that \(xy\) will be even is

The discrete random variables \(X\) and \(Y\) are independent from one another and are defined as
\[ X\sim B(16,0.25) \] and
\[ Y\sim P(2). \] Then the sum of the variances of \(X\) and \(Y\) is