List of top Mathematics Questions asked in AP EAPCET

The point on the curve \[ y=x^2+4x+3 \] which is closest to the line \[ y=3x+2 \] is

If \[ y=x^3-ax^2+48x+7 \] is an increasing function for all real values of \(x\), then \(a\) lies in the interval

If \[ I_n=\int(\cos^n x+\sin^n x)\,dx \] and \[ I_n-\frac{n-1}{n}I_{n-2} = \frac{\sin x\cos x}{n}f(x), \] then \(f(x)=\)

If \[ \int \frac{3x+4}{x^3-2x+4}\,dx=\log f(x)+C, \] then \(f(3)=\)

If the normal drawn at a point \(P\) on the curve \[ 3y=6x-5x^3 \] passes through \((0,0)\), then the positive integral value of the abscissa of the point \(P\) is

The line joining the points \((0,3)\) and \((5,-2)\) is a tangent to the curve \[ y=\frac{C}{x+1} \] then \(C=\)

If \[ x=f(\theta) \] and \[ y=g(\theta), \] then \[ \frac{d^2y}{dx^2}= \]

Assertion (A): \[ \frac{d}{dx}\left(\frac{x^2\sin x}{\log x}\right) = \frac{x^2\sin x}{\log x} \left(\cot x+\frac{2}{x}-\frac{1}{x\log x}\right) \] Reason (R): \[ \frac{d}{dx}\left(\frac{uv}{w}\right) = \frac{uv}{w} \left[ \frac{u'}{u}+\frac{v'}{v}-\frac{w'}{w} \right] \]

If \[ 3f(\cos x)+2f(\sin x)=5x, \] then \[ f'(\cos x)+f'(\sin x)= \]

Evaluate \[ \lim_{x\to 0}\frac{3|x|-x}{|x|-2x} - \lim_{x\to 0}\frac{\log(1+x^3)}{\sin^3 x} \]

If \(P\) divides the line segment joining the points \(A(1,2,-1)\) and \(B(-1,0,1)\) externally in the ratio \(1:2\) and \(Q=(1,3,-1)\), then \(PQ=\)

If the direction cosines of a line are \[ \left( \frac{a}{\sqrt{83}}, \frac{5}{\sqrt{83}}, \frac{c}{\sqrt{83}} \right) \] and \(c-a=4\), then \(ca=\)

Let the plane \(\pi\) pass through the point \((1,0,1)\) and perpendicular to the planes \[ 2x+3y-z=2 \] and \[ x-y+2z=1. \] Let the equation of the plane passing through the point \((11,7,5)\) and parallel to the plane \(\pi\) be \[ ax+by-z+d=0. \] Then \[ \frac{a}{b}+\frac{b}{d}= \]

If \(e_1\) and \(e_2\) are the eccentricities of the hyperbola \[ 16x^2-9y^2=1 \] and its conjugate respectively, then \(3e_1=\)

Evaluate \[ \lim_{x\to -\infty}\log_e(\cosh x)+x \]

If \(a,b,c\) are three distinct real numbers and \[ \lim_{x\to \infty} \frac{(b-c)x^2+(c-a)x+(a-b)} {(a-b)x^2+(b-c)x+(c-a)} = \frac{1}{2} \] then \(a+2c=\)

Suppose that the \(x\)-coordinates of the points \(A\) and \(B\) satisfy \[ x^2+2x-a^2=0 \] and their \(y\)-coordinates satisfy \[ y^2+4y-b^2=0. \] Then the equation of the circle with \(AB\) as its diameter is

The radical centre of the three circles \[ x^2+y^2-1=0, \] \[ x^2+y^2-8x+15=0 \] and \[ x^2+y^2+10y+24=0 \] is

If the angle between the straight lines joining the foci and the ends of the minor axis of the ellipse \[ \frac{x^2}{a^2}+\frac{y^2}{b^2}=1 \] is \(90^\circ\), then its eccentricity is

Which of the following represents a parabola?

The locus of point of intersection of tangents at the ends of normal chord of the hyperbola \[ x^2-y^2=a^2 \] is

The radius of the circle having \[ 3x-4y+4=0 \] and \[ 6x-8y-7=0 \] as its tangents is

A circle is such that \[ (x-2)\cos\theta+(y-2)\sin\theta=1 \] touches it for all values of \(\theta\). Then the circle is

The least distance of the point \((10,7)\) from the circle \[ x^2+y^2-4x-2y-20=0 \] is

Suppose the slopes \(m_1\) and \(m_2\) of the lines represented by \[ ax^2+2hxy+by^2=0 \] satisfy \[ 3(m_1-m_2)-7=0 \] and \[ m_1m_2-2=0. \] Then which of the following is true?