List of top Questions asked in AP EAPCET

Let \( A = \begin{bmatrix} 1 & 2 2 & 1 \end{bmatrix} \) and \( B = \begin{bmatrix} x & y 1 & 2 \end{bmatrix} \) be two matrices such that \( (A + B)(A - B) = A^2 - B^2 \).
If \( C = \begin{bmatrix} x & 2 1 & y \end{bmatrix} \), then trace \((C) = \)

Let \(S\) be a symmetric matrix obtained from \[ A= \begin{bmatrix} 1 & 2 & -3\\ 2 & -2 & 1\\ 3 & 1 & -1 \end{bmatrix} \] and \(T\) be a skew-symmetric matrix obtained from \[ B= \begin{bmatrix} 4 & 2 & 0\\ 1 & -1 & 3\\ 0 & 2 & -3 \end{bmatrix} \] If trace of \(S=-4\) and the non-zero elements of \(T\) are \(-1,1\), then \(S+T=\)

If \[ \vec a=\hat i-\hat j+2\hat k,\qquad \vec b=-\hat i+2\hat j \] and \(\vec c\) are three vectors such that \(\vec a+\vec b\) is parallel to \(\vec c\) and \[ (\vec c+\vec a)\cdot(\vec c+\vec b)=7, \] then the vector \(\vec c\) having minimum length is

In a triangle $ABC$, if $a = 13$, $b = 14$, $c = 15$, then the area of the triangle is:

If $\Delta$ denotes the area of triangle $ABC$ and $s$ is its semi-perimeter, then

In a \(\triangle ABC\), if \[ \cot\frac{A}{2}:\cot\frac{B}{2}:\cot\frac{C}{2} = 3:5:7, \] then \[ \cos A:\cos B:\cos C= \]

In a triangle $ABC$, $C=90^\circ$. If $r$ is the inradius and $R$ is the circumradius of the triangle, then \[ 2(r+R)= \]

In a \(\Delta ABC\) if \( a:b:c = 5:6:7 \), then the ratio of the radius of the circumcircle to that of the incircle is:

In a triangle \(ABC\), if \(r_1=\dfrac{5}{\sqrt2},\ r_2=2\sqrt2,\ r=r\sqrt2\), then \(\dfrac{a+c}{b}=\)

If the angles of triangle ABC are in arithmetic progression and the sides a, b and c satisfy \( \frac{\sqrt{3}}{2} < \frac{b}{a} < 1 \) and \( c < b \), then the possible values of the side c are:

In a \(\triangle ABC\), let \(r\) be the inradius and \(r_1,r_2,r_3\) be the exradii opposite to vertices \(A,B,C\) respectively. Match the items of List-I with List-II. \[ \begin{array}{|c|c|} \hline \text{List-I} & \text{List-II}\\ \hline \text{A. } rr_1=r_2r_3 & \text{I. } \Delta^2\\ \text{B. } r_1+r_2=r_3-r & \text{II. } \angle A=90^\circ\\ \text{C. } \dfrac1{r_1}+\dfrac1{r_2}+\dfrac1{r_3} & \text{III. } \angle C=90^\circ\\ \text{D. } rr_1r_2r_3 & \text{IV. } s^2\\ & \text{V. } \dfrac1r\\ \hline \end{array} \]

If the sides of a triangle \(ABC\) are in arithmetic progression, then \[ b\cos\left(\frac{A-C}{2}\right)= \]

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

In \( \Delta ABC \), if \( A+B=120^{\circ} \), \( a=\sqrt{3}+1 \) and \( b=\sqrt{3}-1 \), then \( A:B= \)

The sides of a triangle are in the ratio \[ 1:\sqrt3:2. \] Then the angles opposite to these sides are in the ratio

2 is a zero of the polynomial function \[ f(x)=x^4+kx^3+22x^2-6x-20. \] If \(-2,\alpha,\beta\) are the roots of the equation \[ x^3+3x^2+2kx-40=0 \] and \(\alpha<\beta\), then \(2\alpha+3\beta=\)

If \( x^5 + ax^4 + bx^3 + cx^2 + 5x + d = 0 \) is an odd order reciprocal equation of second type and \( \frac{1+\sqrt{3}i}{2} \) is a root, then \( b-c = \)

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

If \( x^{5}+ax^{4}+b death^{3}+cx^{2}+5x+e=0 \) is a reciprocal equation of second kind such that \( a+b=4 \) then the number of complex roots of this equation is

The equation formed with the roots obtained by diminishing the roots of the equation \( x^{4}+3x^{3}-7x^{2}+4x+1=0 \) by 'h', does not contain the \( x^{2} \) term. If the possible values of such 'h' are \( h_{1}<0 \) and \( h_{2}>0, \) then which one of the following is true?

If \(5\) is the remainder when \[ 2x^5+kx^4+5x^3-3x^2+2x-1 \] is divided by \[ x^2+x+1, \] then the quotient is:

If the coefficient of \(x^2\) in the expansion of \[ (1+x)^5(1-x)^4 \] is \(k\), then \(k\) is equal to:

The coefficient of \(x^{12}\) in the expansion of \[ (x^2+x+2)^8 \] is

If the coefficients of the first, second, and third terms in the expansion of \( (1+x)^n \) are in the ratio \(1:20:190\), then \(n\) is equal to: