List of top Questions asked in AP EAPCET

The partial fraction decomposition of \( \frac{x^{4}+24 x^{2}+28}{(x^{2}+1)^{3}} \) is

If all the letters of the word MESSI are permuted in all possible ways and the words [with or without meaning] thus formed are arranged in dictionary order, then the rank of the word MESSI is

A student has to answer 10 out of 13 questions in an examination choosing atleast 3 from the 5 particular questions. The number of choices available to the student is

If a and b are the greatest values of \( {}^{2n}C_{r} \) and \( {}^{(2n-1)}C_{r} \) respectively, then

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

If \( a, b, c \in \mathbb{R} \) and \( -a^{2}x^{2}+bx+c>0 \quad \forall x \in \left(\frac{3-\sqrt{14}}{2},\frac{3+\sqrt{14}}{2}\right) \), then \( c^{2}-\left(\frac{b}{4}\right)^{2} = \)

If \( z=(1+\sqrt{3}i)^{4/3} \), then the product of all the values of \( z \) is

If \( z_{1}=x+iy \), \( z_{2}=a+ib \) and \( x^{2}+y^{2}=a^{2}+b^{2} \), then \( z_{2} = \)

For a quadratic expression \( ax^{2}+bx+c \), if the minimum value \( \frac{49}{12} \) exists at \( x=\frac{-5}{6} \), then \( 12c-5b = \)

The locus of \( |z-2i|+|z+4i|=10 \) is

Let \( A, B \) be \( 3^{\text{rd}} \) order non-singular square matrices and \( K \) is a real number. Which of the following is true?

If \( A=\begin{bmatrix}1&-2&2\\ 2&1&-2\\ 2&K&4\end{bmatrix} \), \( B=\begin{bmatrix}2&4&3\\ 3&4&5\\ 1&2&2\end{bmatrix} \) and \( \text{Rank}(A)=2 \), then \( K + \text{Rank}(B) = \)

The augmented matrix of a non-homogeneous system of equations \( AX = B \) is reduced to the following form after applying a series of elementary row transformations: \[ \begin{bmatrix}1&1&1&5\\ 0&0&-3&4\\ 0&0&\mu+1&\lambda^{2}-2\lambda+1\end{bmatrix} \] Then, which of the following is correct?

The expression \( \frac{n(n + 1)^2(n+2)}{12} \) for all \( n \in \mathbb{N} \) is always:

If \( f:A\rightarrow B \), \( g:B\rightarrow C \) are two functions such that \( gof: A\rightarrow C \) is an onto function, then it is necessary that

The domain of the real valued function \( f(x)=\log_{x-1}(3x+1) \) is

In which of the following reactions mesityl oxide is formed?