List of top Mathematics Questions asked in AP EAPCET

Which of the following is differentiable at \(x=0\)?

If \[ \frac{d}{dx} \left( \frac{(x+1)^2\sqrt{x-1}} {(x+4)^3e^x} \right) = f(x) \left[ \frac{2}{x+1} +\frac{1}{2(x-1)} -\frac{3}{x+4} -1 \right], \] then \(f(5)=\)

The curve \[ y=ax^3+bx^2+cx+5 \] touches the \(x\)-axis at \(P(-2,0)\), then \(c=\)

The curves \[ y=x^2-1,\qquad y=8x-x^2-9 \]

The perimeter of a sector is constant. If its area is to be maximum, the sectorial angle should be

If \[ f(x)=\frac{e^{1/x}-1}{e^{1/x}+1}, \] then

Let \[ ax+by+cz+d=0 \] be the equation of a plane. Given that \[ 4a+4b+c=0 \] and \[ a+2b+c=0. \] Then \(d=\)

Evaluate \[ \lim_{x\to 0} \frac{\sqrt{11+|x|-6\sqrt{2+|x|}}} {6-2\sqrt{2+|x|}} \]

If \[ \lim_{x\to 0^+}x^2 \left( \frac{e^{1/x}-e^{-1/x}} {e^{1/x}+e^{-1/x}} \right)=k \] and \[ \lim_{x\to 0^-}x^2 \left( \frac{e^{1/x}-e^{-1/x}} {e^{1/x}+e^{-1/x}} \right)=l, \] then

Suppose \((l_1,m_1,n_1)\) and \((l_2,m_2,n_2)\) are the direction cosines of two lines and \(\theta\) is the angle between them such that \[ \cos\theta=\pm(l_1l_2+m_1m_2+n_1n_2) \] Let \(A=(1,-2,3)\), \(B=(3,1,-3)\) and \(C=(-3,1,3)\) be the vertices of a triangle \(ABC\). Then \(\cos A=\)

If the point \((3,4,5)\) divides the line segment joining the points \((1,2,3)\) and \((4,5,6)\) in the ratio \(\lambda:1\), then the point which divides the line segment joining the points \((3,4,5)\) and \((1,2,3)\) in the ratio \(-1:\lambda\) is:

An ellipse has \(6\) and \(2\) as lengths of major and minor axes respectively. If the centre is at \((5,6)\) and the major axis is along \[ x-y+1=0, \] then the ellipse is:

For a hyperbola \[ \frac{x^2}{a^2}-\frac{y^2}{b^2}=1, \] if the length of the transverse axis is \(8\) and the distance between the foci is \(2\sqrt{41}\), then the length of its latus rectum is:

If the product of the perpendicular distances from any point on the hyperbola \[ \frac{x^2}{a^2}-\frac{y^2}{b^2}=1 \] to its asymptotes is \(6\) and eccentricity of the hyperbola is \(\sqrt3\), then the length of the conjugate axis of the hyperbola is:

The equation of bisectors of the angle between the lines given by \[ 3x^2+5xy+4y^2=0 \] is:

If the point \((2,\lambda)\) lies inside the circles \(x^2+y^2=13\) and \(x^2+y^2+x-2y=14\), then \(\lambda\) lies in the set:

For different real non-zero numbers \(x_1,x_2,x_3\) and \(x_4\), suppose the points \[ \left(x_1,\frac{1}{x_1}\right),\left(x_2,\frac{1}{x_2}\right),\left(x_3,\frac{1}{x_3}\right) \textbf{ and } \left(x_4,\frac{1}{x_4}\right) \] lie on the boundary of a circle of radius \(4\). Then the value of \(x_1x_2x_3x_4\) is:

The equation of the tangent to the circle \[ x^2+y^2-9=0 \] making an angle \(60^\circ\) with the \(x\)-axis is:

The equation of the circle passing through \((0,0)\) and cutting orthogonally the circles \[ x^2+y^2+6x-15=0 \] and \[ x^2+y^2-8y-10=0 \] is:

Suppose \(d_1\) and \(d_2\) are respectively the lengths of intercepts of the circles \(x^2+y^2=4\) and \(x^2+y^2-10x-14y+65=0\) on the line \(2x-2y-3=0\). Then which of the following is true?

The triangle formed by \[ x^2-4xy+y^2=0 \] and \[ x+y+4\sqrt6=0 \] is:

On the locus of the point \(P(x,y)\) equidistant from \((3,0)\) and \((0,4)\), if \(A\) and \(B\) are two points that satisfy \(4x=3y\) and \(x=y\) respectively, then the distance between \(A\) and \(B\) is:

If one side of an isosceles triangle is given by \(y=2\) and the base is provided by the points \((2,0)\) and \((0,2)\), then its area (in sq. units) is:

The straight line passing through \((0,0)\) and the foot of perpendicular from \((2,4)\) onto \[ x+y-1=0 \] is:

If \(P(\sin\alpha,\cos\alpha)\) lies inside the triangle formed by the vertices \[ (0,0),\left(\frac{\sqrt3}{2},0\right),\left(0,\frac{\sqrt3}{2}\right), \] then \(\alpha\) lies in the interval: