List of top Questions asked in AP EAPCET

From the set \[ \{2,3,5,7\} \] two numbers are selected one after the other with replacement. If \(X\) is the random variable representing the absolute difference of the two numbers selected, then the mean of \(X\) 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

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 \(x+y+z=\)

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 \(x=\)

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

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

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

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

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

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

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 \(\beta-\alpha=\)

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

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

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

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 \[ \alpha^3+\beta^3+\gamma^3+\delta^3= \]

The solutions of the equation \[ 2\sqrt{2}\,x^4=(\sqrt{3}-1)+i(\sqrt{3}+1) \] are