List of top Questions asked in AP EAPCET- 2026

A vector \( \vec{a} \) has components \( 2p \) and \( 1 \) with respect to a rectangular Cartesian system. This system is rotated through a certain angle about the origin in the positive direction. If with respect to the new system, \( \vec{a} \) has components \( p+1 \) and \( 1 \), then the values of \( p \) are:

O is the origin, \( \overline{OP} \) and \( \overline{OR} \) are vectors making angles \( 45^{\circ} \) and \( 135^{\circ} \) respectively with the positive direction of x-axis, \( |\overline{OP}|=3 \) and \( |\overline{OR}|=4 \). M is the midpoint of PQ in the rectangle OPQR. If OM meets the diagonal PR at T, then \( \overline{OT}= \)

If the lengths of the sides of a triangle a, b, c \( (a>b>c) \) are in arithmetic progression and the greatest angle is twice the smallest, then a: b: \( c= \)

If \( \overline{a}=\overline{i}+\overline{j}+\overline{k} \), \( \overline{a}.\overline{b}=1 \) and \( \overline{a}\times\overline{b}=\overline{j}-\overline{k} \), then \( \overline{b}= \)

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:

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

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

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

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

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

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

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

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

If 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

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

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

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