List of top Mathematics Questions asked in AP EAPCET

If \[ \vec{a}=x\hat{i}+2\hat{j}-\hat{k}\quad (x>0) \] and \[ \vec{b}=2\hat{i}-\hat{j}+2\hat{k} \] are two vectors such that \[ |\vec{a}-2\vec{b}|=|2\vec{a}+\vec{b}|, \] then \(x=\)

If the unit vector which is perpendicular to the normals drawn to the planes \[ \vec r\cdot(2\hat{i}+\hat{j}-\hat{k})=3 \] and \[ \vec r\cdot(6\hat{i}+3\hat{j}+2\hat{k})=4 \] is \[ x\hat{i}+y\hat{j}+z\hat{k}, \] then \(x+y+z=\)

In \(\triangle ABC\), if \[ \overrightarrow{AB}=2\hat{i}-\hat{j}+2\hat{k} \] and \[ \overrightarrow{AC}=3\hat{i}-3\hat{j}+4\hat{k}, \] then the triangle \(ABC\) is

If \[ A(0,1,-2),\quad B(-1,2,-3),\quad C(2,-3,4) \] and \[ D(3,4,5) \] are the vertices of a tetrahedron \(ABCD\), then the volume of the tetrahedron is

Let \[ \overrightarrow{OA}=\hat{i}+2\hat{j}-4\hat{k} \] and \[ \overrightarrow{OB}=3\hat{i}-4\hat{j}-2\hat{k} \] be the position vectors of points \(A\) and \(B\). If a point \(C\) divides the line segment \(AB\) in the ratio \(1:3\) externally, then the position vector of a point which divides \(OC\) in the ratio \(4:1\) internally is

In a triangle \(ABC\), if \[ a=2,\qquad b=4,\qquad \cos C=-\frac{5}{16}, \] then the circumradius \(R\) is

In \(\triangle ABC\), if \[ c=9,\qquad s=10,\qquad \Delta=10\sqrt2, \] then \[ \sin\frac{C}{2} = \]

Evaluate \[ \tan^{-1}\left(\frac12\right) +\tan^{-1}\left(\frac18\right) +\tan^{-1}\left(\frac1{18}\right) +\tan^{-1}\left(\frac1{32}\right). \]

If \(\sin\theta\neq 0\) and \[ \frac{1}{2}\sin\theta,\quad \cos\theta,\quad \cot\theta \] are in geometric progression, then the number of values of \(\theta\) lying in the interval \((-2\pi,2\pi)\) is

If \[ \tanh x=\frac13, \] then \[ 6\sinh^4x+2\cosh^4x+2\sinh^2x+\cosh^2x= \]

In a triangle \(ABC\), if \[ r_1=\frac{12\sqrt5}{5}, \qquad r_2=3\sqrt5, \qquad r_3=4\sqrt5, \] then \[ 5s^2= \]

Evaluate \[ \cos\frac{\pi}{7}\cos\frac{2\pi}{7}\cos\frac{3\pi}{7} \cos\frac{4\pi}{7}\cos\frac{5\pi}{7}\cos\frac{6\pi}{7}. \]

For \(\theta\in\left(0,\frac{\pi}{2}\right)\), if the complete range of \[ (\cot^2\theta-\cos^2\theta)(\tan^2\theta-\sin^2\theta) \] is \((\alpha,\beta]\), then \(\beta-\alpha=\)

One of the partial fractions of \[ \frac{2x^2+x-3}{(x^2+2)(3x-1)} \] is

If \(|x|\) is so small that \(x^2\) and higher powers of \(x\) may be neglected, then the approximate value of \[ \left(\frac{3x+64}{3x+8}\right)^{\frac{2}{3}} \] is

Evaluate \[ \frac{\cos\theta}{1-\cos\theta} + \frac{\sec\theta}{1+\sec\theta}. \]

A divisor of \[ 3^{6n}+56n-1,\qquad n\in\mathbb{N} \] is

If \(\alpha\) is a root of the equation \[ x^4-4x^3+16x-16=0 \] of multiplicity \(m\), then \[ m^2-4m+2= \]

If \(\alpha,\beta,\gamma,\delta\) are the roots of the equation \[ x^4+x^3-x-1=0, \] then \[ \alpha^3+\beta^3+\gamma^3+\delta^3= \]

If for all \(x\in\mathbb{R}\), \[ \frac{1}{3} < \frac{x^2-2x+4}{x^2+2x+4} <3, \] then the values of \[ \frac{9\cdot 3^{2x}+6\cdot 3^x+4} {9\cdot 3^{2x}-6\cdot 3^x+4} \] lie between