List of top Questions asked in AP EAPCET- 2026

If \( u=log_{e}[tan(\frac{\pi}{4}+\frac{\theta}{2})], \) then \( sinh~u= \)

Statement I: If \( x\in(0,\frac{\pi}{2}) \) and \( cos~3x+cos~x=cos~2x \), then \( x=\frac{\pi}{4} \) or \( \frac{\pi}{3} \)
Statement - II: If \( sin~x~sin~2x=cos~x~cos~2x-1 \), then \( x=\frac{n\pi}{3},n\in Z \)
Which of the following options is correct?

If the angles of a triangle are in the ratio 4: 1: 1, then the ratio between its largest side and its perimeter is

Match the items of List - I with those of List - II: \[ \begin{array}{ll} \text{List - I} & \text{List - II} \\ \hline \text{A) } Tan^{-1}3+Tan^{-1}x=Tan^{-1}8 \implies x= & \text{I) } \frac{\sqrt{5}}{3} \\ \text{B) } Sin^{-1}x-Cos^{-1}x=\frac{\pi}{6} \implies x= & \text{II) } \frac{1}{5} \\ \text{C) } sin^{-1}\frac{4}{5}+2~Tan^{-1}\frac{1}{3}= & \text{III) } \frac{\sqrt{3}}{2} \\ \text{D) } tan(Sec^{-1}\frac{1}{x})=sin(Tan^{-1}2), x>0 \implies x= & \text{IV) } \frac{\pi}{2} \\ & \text{V) } \frac{\pi}{3} \end{array} \] The correct match is:

If \( sin~A=\frac{3}{5} \) and A lies in the second quadrant, then \( \frac{tan~A-sec~A}{cot~A+cosec~A}= \)

If \( \cos x+\cos^{2}x=1 \) , then \( \sin^{6}x+3 \sin^{8}x+3 \sin^{10}x+\sin^{12}x= \)

If \( 0<x<1 \), then first negative term in the expansion of \( (1+x)^{\frac{47}{5}} \) is

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

If \( C_{o},C_{1},C_{2},...,C_{n} \) represent the coefficients in the binomial expansion of \( (1+x)^{n} \), then \( C_{o}+\frac{c_{2}}{3}+\frac{c_{4}}{5}+\cdot\cdot\cdot+\frac{c_{16}}{17}= \)

Assertion (A): \( cos^{2}5^{\circ}+cos^{2}10^{\circ}+cos^{2}15^{\circ}+...+cos^{2}85^{\circ}=\frac{17}{2} \)
Reason (R): If \( A+B=90^{\circ} \), then \( cos^{2}A+cos^{2}B=1 \)
Then, which one of the following is True?

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

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 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

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

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

The locus of \( |z-2i|+|z+4i|=10 \) 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 \( 12c-5b = \)

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

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

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:

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