List of top Questions asked in AP EAPCET

Let \(\vec{a}\), \(\vec{b}\) be position vectors of points \(A\) and \(B\) respectively. \(C\) and \(D\) are points on the line \(AB\) such that \(\overrightarrow{AB}, \overrightarrow{AC}\) and \(\overrightarrow{BD}, \overrightarrow{BA}\) are two pairs of like vectors. If \(\overrightarrow{AC} = 3 \overrightarrow{AB}\) and \(\overrightarrow{BD} = 2 \overrightarrow{BA}\), then \(\overrightarrow{CD} =\)

If \(\vec{a}, \vec{b}, \vec{c}\) are three unit vectors such that \[ |\vec{a} - \vec{b}|^2 + |\vec{b} - \vec{c}|^2 + |\vec{c} - \vec{a}|^2 = 15, \] then \[ |\vec{a} - \vec{b} - \vec{c}|^2 - 4(\vec{b} \cdot \vec{c}) = ? \]

Let \( H(x) = 3x^4 + 6x^3 - 2x^2 + 1 \) and \( g(x) \) be a linear polynomial. If \[ \frac{H(x)}{(x-1)(x+1)(x-2)} = f(x) + \frac{g(x)}{(x-1)(x+1)(x-2)}, \] then find \( H(-1) + 2H(2) - 3H(1) \).

If \(630^\circ<\theta<810^\circ\) and \(\tan \theta = -\frac{7}{24}\), then find \(\cos \left(\frac{\theta}{4}\right)\).

For \(\theta \in \left[-\frac{\pi}{2}, \frac{\pi}{2}\right]\), if \(2\cos \theta + \sin \theta = 1\), and \(7\cos \theta + 6 \sin \theta = k\), then the possible values of \(k\) are:

Evaluate \[ \sum_{k=0}^{12} \sin\left( (k+1) \frac{\pi}{6} + \frac{\pi}{4} \right) \sin \left( \frac{k \pi}{6} + \frac{\pi}{4} \right) \]

Number of solutions of the equation \[ 2 \sin^2 \theta - 3 \cos^2 \theta = \sin \theta \cos \theta \] in the interval \((- \pi, \pi)\) is:

Evaluate \[ \tan^{-1} \frac{\sqrt{8} - 2\sqrt{15}}{\sqrt{15} + 1} + \tan^{-1} \frac{1}{\sqrt{5}} \]

The number of all possible positive integral solutions of the equation \(xyz = 30\) is:

The number of ways of arranging all the letters of the word PERFECTION such that there must be exactly two consonants between any two vowels is:

If \(x\) is so large that terms containing \(x^{-3}\), \(x^{-4}\), \(x^{-5}\), \ldots can be neglected, then the approximate value of \[ \left(\frac{3x - 5}{4x^2 + 3}\right)^{-4/5} \] is:

If \(\alpha\) and \(\beta\) (\(\alpha>\beta\)) are the multiple roots of the equation \[ 4x^4 + 4x^3 - 23x^2 - 12x + 36 = 0, \] then find \(2\alpha - \beta\).

If \( z_1 \) and \( z_2 \) are two of the \( n^{th} \) roots of unity such that the line segment joining them subtends a right angle at the origin, then for a positive integer \( k \), \( n \) takes the form:

If the harmonic mean of the roots of the equation \[ \sqrt{2} x^2 - b x + \left( 8 - 2\sqrt{5} \right) = 0 \] is 4, then the value of \( b \) is:

If \( A \) and \( B \) are both \( 3 \times 3 \) matrices, then which of the following statements are true? \[ \begin{cases}

If $ S_n = 1^3 + 2^3 + \ldots + n^3 $ and $ T_n = 1 + 2 + \ldots + n $, then

An alcohol X $\mathrm{C_5H_{12}O}$ on dehydration gives Y (major product). Reaction of Y with HBr gave Z ($\mathrm{C_5H_{11}Br}$, major product). Z undergoes nucleophilic substitution in two steps. What are X and Y?

Which of the following exhibit ionization isomerism?
I) [Cr(NH$_3$)$_4$Cl$_2$]Cl
II) [Ti(H$_2$O)$_5$Cl]Cl(NO$_3$)$_2$
III) [Pt(en)(NH$_3$)$_4$]Cl(NO$_3$)
IV) [Co(NH$_3$)$_4$(NO$_3$)$_2$]NO$_3$

A polymer sample contains 10 molecules each with molecular mass 5,000 and 5 molecules each with molecular mass 50,000. The number average molecular mass of the polymer sample is

Which of the following do not reduce Tollens' reagent?
a) Fructose
b) Sucrose
c) Lactose
d) Cellulose

Consider the following statements:
Statement-I: Lysine, arginine are essential and basic amino acids.
Statement-II: Leucine, phenyl alanine are non-essential and neutral amino acids.
Which of the following is correct?

Consider the following statements:
Statement-I: Shaving soaps contain glycerol to prevent rapid drying.
Statement-II: Laundry soaps contain sodium carbonate as filler.
Which of the following is correct?