List of top Questions asked in AP EAPCET

The mean deviation about the median for the following data: \(6,3,4,9,2,7,11\) is:

Let \(\vec{e_1}, \vec{e_2}\) be two non-collinear unit vectors such that \(|\vec{e_1}+\vec{e_2}| = \sqrt{3}\). Then evaluate \[ (2\vec{e_1}-5\vec{e_2}) \cdot (3\vec{e_1}+\vec{e_2}). \]

\(A(2,1,2), B(1,0,0), C(1+\sqrt{3},\sqrt{3},-\sqrt{6})\) are vertices of a triangle. If the length of the median drawn through \(A\) is \(\lambda\sqrt{9-2\sqrt{3}+2\sqrt{6}}\), then \(\lambda=\)

A, B, C, D are any 4 points and \[ |AB \times CD + BC \times AD + CA \times BD| = \lambda (\text{Area of } \Delta ABC) \] then \(\lambda = ?\)

Let \[ \vec{a} = a_1 \hat{i} + a_2 \hat{j} + a_3 \hat{k}, \quad \text{where } a_1, a_2, a_3 \text{ and } |\vec{a}| \text{ are rational numbers.} \] If \(\vec{a}\) makes an angle of \(45^\circ\) with \[ \vec{b} = \sqrt{2} \hat{i} + 3 \sqrt{2} \hat{j} + 4 \hat{k}, \] then \(\vec{a}\) lies in which plane?

If \(G(2,-1,2)\) is the centroid of tetrahedron \(OABC\) where \(O = (0,0,0)\) and \(G_1\) is the centroid of \(\Delta ABC\), then \(|OG_1| = ?\)

In a triangle ABC, if \(a = 13, b = 14, c = 15\), then \[ \sin \frac{A}{2} = ? \]

In a triangle ABC, if \(a - 2b + c = 0\), then \[ \cot \frac{A}{2} \cdot \cot \frac{C}{2} = ? \]

In a triangle ABC, the expression \[ (b+c) \sin \frac{A}{2} \] is equal to:

If one solution of the equation \[ \cosh x - \frac{4}{5} \sinh x = 1 \text{ is } x = 0, \] then the other solution is:

If \[ 2 \sin 2\theta = \sqrt{3}, \] then \(\theta =\)?

In any triangle ABC, the inequality \[ \sin \frac{A}{2} \leq \frac{a}{2\sqrt{bc}} \] holds. Determine the correct expression.

If \[ \frac{x}{(x-1)(x^2+1)^2} = \frac{1}{4} \left[\frac{1}{x-1} - \frac{x+1}{x^2+1}\right] + y, \] then \(y =\)

Evaluate \[ \cos \frac{7\pi}{12}. \]

Evaluate \[ \cos \frac{\pi}{12}. \]

Evaluate \[ \cos^4 \frac{\pi}{24} - \sin^4 \frac{\pi}{24}. \]

If \(^{10}P_r = 604800\) and \(^{10}C_r = 120\), then \(r\) is:

The number of 5-card combinations out of a deck of 52 cards if there is exactly one ace in each combination is:

The product of real roots of the equation \[ 4x^4 - 24x^3 + 57x^2 + 18x - 45 = 0 \] if one of the roots is \(3 + i\sqrt{6}\) is:

A question paper consists of two sections having 3 and 4 questions respectively. One question from each section is compulsory. In how many ways can a candidate select the questions?

What is the rank of the word ``MOTHER'' when all possible words are formed using all its letters and arranged in dictionary order?

The quadratic equation whose sum of roots is 11 and sum of squares of roots is 61 is:

The sum of the complex roots of the equation \[ x^4 - 2x^3 + x - 380 = 0 \] is:

If \(1, \omega, \omega^2\) are the cube roots of unity, then the value of \[ (x+y)^2 + (x\omega + y\omega^2)^2 + (x\omega^2 + y\omega)^2 \] is:

If \(\Arg z_1\) and \(\Arg z_2\) are \(\frac{\pi}{3}\) and \(\frac{\pi}{5}\) respectively, then the value of \(\Arg z_1 + \Arg z_2\) is: