List of top Mathematics Questions asked in AP EAPCET

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 \(\lambda = ?\)

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, 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 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 \[ \cot \frac{A}{2} \cdot \cot \frac{C}{2} = ? \]

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

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

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

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

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:

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

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

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

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

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

Evaluate \[ \left(\frac{1-i}{1+i}\right)^{2022} + \left(\frac{1+i}{1-i}\right)^{2021} \]

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 \(x^2 + px + 1\) is a factor of \(ax^3 + bx + c\), then:

Area of the triangle formed by the complex numbers \(z\), \(iz\) and \(z+iz\) in the Argand diagram as vertices is:

The set of values of \(k\) for which the system of simultaneous equations \[ x+y+kz = 1, \quad 2x+2y-3, \quad x+2y+2kz = k \] has no real solution is: