List of top Mathematics Questions asked in AP EAPCET

The number of ordered pairs \( (x, y) \) satisfying the equations: \[ \sin x + \sin y = \sin (x + y) \quad \text{and} \quad |x| + |y| = 1. \]

If \[ \cos \frac{ \pi }{8} + \cos \frac{3 \pi }{8} + \cos \frac{5 \pi }{8} + \cos \frac{7 \pi }{8} = k, \] then evaluate \[ \sin^{-1} \left( \frac{k}{\sqrt{2}} \right) + \cos^{-1} \left( \frac{k}{3} \right)= \]

Given the equation: \[ \frac{A}{x-a} + \frac{Bx + C}{x^2 + b^2} = \frac{1}{(x-a)(x^2 + b^2)} \] then \( C \)=

If \( a_n = \sum_{r=0}^{n} \frac{1}{\binom{n}{r}} \), then \( \sum_{r=0}^{n} r \binom{n}{r} = \):

The number of positive divisors of 1080 is:

If \( P(x) = x^5 + ax^4 + bx^3 + cx^2 + dx + e \) is a polynomial such that: \[ P(0) = 1, \quad P(1) = 2, \quad P(2) = 5, \] \[ P(3) = 10, \quad P(4) = 17, \] then find the value of \( P(5) \)=

If the sum of two roots of \( x^3 + px^2 + qx - 5 = 0 \) is equal to its third root, then \( p(q^2 - 4q) = \) ?

If \( 2x^2 + 3x - 2 = 0 \) and \( 3x^2 + \alpha x - 2 = 0 \) have one common root, then the sum of all possible values of \( \alpha \) is:

If \( \alpha \) and \( \beta \) are two double roots of the equation: x^2 + 3(a + 3)x - 9a = 0 for different values of \( a \) (where} \( \alpha>\beta \)), then the minimum value of the equation: \(x^2 + \alpha x - \beta = 0\) is:

If \(\cos \alpha + \cos \beta + \cos \gamma = \sin \alpha + \sin \beta + \sin \gamma = 0,\) then evaluate \((\cos^3 \alpha + \cos^3 \beta + \cos^3 \gamma)^2 + (\sin^3 \alpha + \sin^3 \beta + \sin^3 \gamma)^2 =\)

Sum of the positive roots of the equation: \[ \begin{vmatrix} x^2 + 2x + 2 & x + 2 & 1 \\ 2x + 1 & x - 1 & 1 \\ x + 2 & -1 & 1 \end{vmatrix} = is \; 0. \]

If \[ A = \begin{bmatrix} 1 & 0 & 2\\ 2 & 1 & 3 \\3 & 2 & 4 \end{bmatrix}, \] then evaluate \( A^2 - 5A + 6I \)=

Let \( a>1 \) and \( 0<b<1 \). -∞\( f : \mathbb{R} \to [0, 1] \) is defined by \( f(x) = \begin{cases} a^x & \text{if } x<0 b^x & \text{if } 0 \leq x \leq 1 \end{cases} \), then \( f(x) \) is:

Let \( f(x) = 3 + 2x \) and \( g_n(x) = (f \circ f \circ \dots \text{n times}) (x) \). If for all \( n \in \mathbb{N} \), the lines \( y = g_n(x) \) pass through a fixed point \( (a, \beta) \), then \( \alpha + \beta = ? \)

In a random experiment, two dice are thrown and the sum of the numbers appeared on them is recorded. This experiment is repeated 9 times. If the probability that a sum of 6 appears at least once is \( P_1 \) and a sum of 8 appears at least once is \( P_2 \), then \( P_1 : P_2 = \):

Let \( \overline{X} \) and \( \overline{Y} \) be the arithmetic means of the runs of two batsmen A and B in 10 innings respectively, and \( \sigma_A, \sigma_B \) are the standard deviations of their runs in them. If batsman A is more consistent than B, then he is also a higher run scorer only when

If \( P(A \cap B) + P(B \mid A \cap B) = \), then:

The distance of the point \( O(0,0,0) \) from the plane \( \overrightarrow{r} \cdot (\hat{i} + \hat{j} + \hat{k}) = 5 \) measured parallel to \( 2\hat{i} + 3\hat{j} - 6\hat{k} \) is?

If a circle is inscribed in an equilateral triangle of side \( a \), then the area of any square inscribed in this circle (in square units) is:

Let \( \overrightarrow{a}, \overrightarrow{b}, \overrightarrow{c} \) be non-coplanar vectors. If \( \alpha \overrightarrow{d} = \overrightarrow{a} + \overrightarrow{b} + \overrightarrow{c} \), \( \beta \overrightarrow{a} = \overrightarrow{b} + \overrightarrow{c} + \overrightarrow{d} \), then \( | \overrightarrow{a} + \overrightarrow{b} + \overrightarrow{c} + \overrightarrow{d} | = ? \)

Let \( \overrightarrow{u}, \overrightarrow{v}, \overrightarrow{w} \) be three unit vectors. Let \( \overrightarrow{p} = \overrightarrow{u} + \overrightarrow{v} + \overrightarrow{w} \), \( \overrightarrow{q} = \overrightarrow{u} \times (\overrightarrow{p} \times \overrightarrow{w}) \). If \( \overrightarrow{p} \cdot \overrightarrow{u} = \frac{3}{2} \), \( \overrightarrow{p} \cdot \overrightarrow{v} = \frac{7}{4} \), \( |\overrightarrow{p}| = 2 \), and \( \overrightarrow{v} = K \overrightarrow{q} \), then \( K = ? \)

Evaluate the expression: \[ \frac{\sin 1^\circ + \sin 2^\circ + \dots + \sin 89^\circ}{2(\cos 1^\circ + \cos 2^\circ + \dots + \cos 44^\circ) + 1} =\]

If \( 5 \sinh x - \cosh x = 5 \), then one of the values of \( \tanh x \) is:

Evaluate the expression: \[ \frac{\cos 10^\circ + \cos 80^\circ}{\sin 80^\circ - \sin 10^\circ}. \]

Evaluate the infinite series: \[ 1 + \frac{1}{3} + \frac{1.3}{3.6} + \frac{1.3.5}{3.6.9} + \dots \text{ to } \infty = \]