List of top Questions asked in AP EAPCET

Let \(x,y,z\) be real numbers and \[ x\geq y\geq z\geq \frac{\pi}{12} \] If \[ x+y+z=\frac{\pi}{2}, \] then the minimum value of \[ \cos x\sin y\cos z \] is

For any real number \(n\in \mathbb{R}\), \[ (\cosh x+\sinh x)^n= \]

Let \(a\) and \(b\) be non-negative real numbers. If \[ \sin x+a\cos x=b, \] then \[ |a\sin x-\cos x|= \] is equal to:

The value of \[ \sqrt{\sin^4x+4\cos^2x} - \sqrt{\cos^4x+4\sin^2x} \] is

The value of \[ \sin22\frac{1}{2}^{\circ} \] is

How many words, with or without meaning, each of 2 vowels and 3 consonants can be formed from the letters of the word DAUGHTER?

If we resolve the rational fraction \[ \frac{1}{(1-2x)^2(1-3x)} \] into partial fractions of the form \[ \frac{A}{1-3x}+\frac{B}{1-2x}+\frac{C}{(1-2x)^2}, \] then what is the \(\min\{A,B,C\}=\)

The number of ways of distributing \(500\) dissimilar boxes equally among \(50\) persons is

The largest interval containing \(x\) for which \[ x^{12}-x^9+x^4-x+1\gt 0 \] is

The number of solutions of the equations \[ x+y+z=12,\quad x^2+y^2+z^2=50,\quad x^3+y^3+z^3=216 \] is

Let \(a_n,a_{n-1},\ldots,a_1,a_0\in \mathbb{C}\) and \[ f(x)=a_nx^n+a_{n-1}x^{n-1}+\cdots+a_1x+a_0 \] is a polynomial. If the polynomial \(f(x)\) is monic, then

The value of \[ {}^{34}C_5+\sum_{i=0}^{4}{}^{38-i}C_4 \] is

Number of four digit numbers that can be formed using all the digits except zero such that every number has exactly \(2\) distinct digits in it is

The number of distinct solutions of the equation \[ x^{11}-x^7+x^4-1=0 \] is

If \(f(x)=ax^2+bx+c\) satisfies \[ f(1)+2f(2)=0 \] and \[ 2f(1)+f(2)=0, \] then \(3a+b=\)

If \[ A= \begin{bmatrix} 1 & 1 & 3\\ 1 & 7 & 9\\ 2 & 3 & 7 \end{bmatrix} \] then \[ \mathrm{Tr}(A^2-A)= \] is equal to:

If \[ (x+iy)=\left(\frac{1+i}{1-i}\right)^3-\left(\frac{1-i}{1+i}\right)^3, \] then the true statement among the following is:

The number of complex numbers \(z\) satisfying \[ \overline{z}=iz^2 \] is

If \[ z=\cos\theta+i\sin\theta \] then \[ z^r+(\overline{z})^r= \] is equal to:

If \[ A=\begin{bmatrix} 3 & 4\\ 5 & 6 \end{bmatrix} \] and \[ B=\begin{bmatrix} x & 0\\ 0 & y \end{bmatrix}, \quad x,y\in \mathbb{N}, \] then:

If \(A\) and \(B\) are symmetric matrices of same order such that \[ AB+BA=X \] and \[ AB-BA=Y, \] then \((XY)^T=\)

If the ranks of the matrices \[ A= \begin{bmatrix} 1 & 0 & 1\\ 2 & 1 & 2\\ 1 & 0 & -1 \end{bmatrix} \] and \[ B= \begin{bmatrix} 1 & 2 & 3 & 4\\ 2 & 4 & 6 & -8 \end{bmatrix} \] are \(r_1\) and \(r_2\) respectively, then \(r_1-r_2=\)

Let \(f\) be a function defined by \[ f(xy)=\frac{f(x)}{y} \] for all positive real numbers \(x\) and \(y\). If \(f(30)=20\), then \(f(40)=\)

Let \(f:\mathbb{R}\to\mathbb{R}\) be defined by \[ f(x)=5^{x^4+2} \] Then:

Gabriel phthalimide synthesis is used for the preparation of which of the following?