List of top Mathematics Questions asked in AP EAMCET

If 7 and 8 are the lengths of two sides of a triangle and \( a \) is the length of its smallest side. The angles of the triangle are in AP and \( a \) has two values \( a_1 \) and \( a_2 \) satisfying this condition. If \( a_1<a_2 \), then \( 2a_1 + 3a_2 = \):

If \( a \) is in the 3rd quadrant, \( \beta \) is in the 2nd quadrant such that \( \tan \alpha = \frac{1}{7}, \sin \beta = \frac{1}{\sqrt{10}} \), then \[ \sin(2\alpha + \beta) = \]

Assertion (A): If \( A = 10^\circ, B = 16^\circ, C = 19^\circ \), then: \[ \tan(2A) \tan(2B) + \tan(2B) \tan(2C) + \tan(2C) \tan(2A) = 1. \] Reason (R): If \( A + B + C = 180^\circ \), then: \[ \cot\left(\frac{A}{2}\right) + \cot\left(\frac{B}{2}\right) + \cot\left(\frac{C}{2}\right) = \cot\left(\frac{A}{2}\right) \cot\left(\frac{B}{2}\right) \cot\left(\frac{C}{2}\right). \]

If \( A, B, C \) are the angles of a triangle, then \[ \sin 2A - \sin 2B + \sin 2C = \]

If \[ \frac{x + 2}{(x^2 + 3)(x^4 + x^2)(x^2 + 2)} = \frac{Ax + B}{x^2 + 3} + \frac{Cx + D}{x^2 + 2} + \frac{Ex^3 + Fx^2 + Gx + H}{x^4 + x^2}, \] then \[ (E + F)(C + D)(A) = \]

In the expansion of \( \frac{2x+1}{(1+x)(1-2x)} \), the sum of the coefficients of the first 5 odd powers of \( x \) is:

If the ratio of the terms equidistant from the middle term in the expansion of \( (1 + x)^{12} \) is \( \frac{1}{256} \), then the sum of all the terms of the expansion \( (1 + x)^{12} \) is:

Four digit numbers with all digits distinct are formed using the digits 1, 2, 3, 4, 5, 6, 7 in all possible ways. If \( p \) is the total number of numbers thus formed and \( q \) is the number of numbers greater than 3400 among them, then \( p : q = \):

If a five-digit number divisible by 3 is to be formed using the numbers 0, 1, 2, 3, 4, and 5 without repetition, then the total number of ways this can be done is:

There are 6 different novels and 3 different poetry books on a table. If 4 novels and 1 poetry book are to be selected and arranged in a row on a shelf such that the poetry book is always in the middle, then the number of such possible arrangements is:

The condition that the roots of \( x^3 - bx^2 + cx - d = 0 \) are in arithmetic progression is:

The equation \( x^4 - x^3 - 6x^2 + 4x + 8 = 0 \) has two equal roots. If \( \alpha, \beta \) are the other two roots of this equation, then \( \alpha^2 + \beta^2 = \):

If \( a \) is a common root of \( x^2 - 5x + \lambda = 0 \) and \( x^2 - 8x - 2\lambda = 0 \) (\( \lambda \neq 0 \)) and \( \beta, \gamma \) are the other roots of them, then \( a + \beta + \gamma + \lambda = \):

If \( n \) is an integer and \( Z = \cos \theta + i \sin \theta, \theta \neq (2n + 1)\frac{\pi}{2}, \) then: \[ \frac{1 + Z^{2n}}{1 - Z^{2n}} = ? \]

The square root of \( 7 + 24i \) is:

Imaginary part of \( \frac{(1 - i)^3}{(2 - i)(3 - 2i)} \) is:

Assertion (A): If \( B \) is a \( 3 \times 3 \) matrix and \( |B| = 6 \), then \( | {Adj}(B) | = 36 \).
Reason (R): If \( B \) is a square matrix of order \( n \), then \( |{Adj}(B)| = |B|^n \).

If

and \( AA^T = I \), then \( \frac{a}{b} + \frac{b}{a} = \):

If \( 1 \cdot 3 \cdot 5 + 3 \cdot 5 \cdot 7 + 5 \cdot 7 \cdot 9 + \dots \) (n terms) = \( n(n + 1)f(n) - 3n \), then \( f(1) = \):

The real valued function \( f: \mathbb{R} \to \left[ \frac{5}{2}, \infty \right) \) defined by \( f(x) = \left| 2x + 1 \right| + \left| x - 2 \right| \) is:

The range of the real-valued function \( f(x) = \sin^{-1} \left( \frac{1 + x^2}{2x} \right) + \cos^{-1} \left( \frac{2x}{1 + x^2} \right) \) is: