List of top Mathematics Questions asked in AP EAPCET

Assertion (A): $S_3 = 55 \times 2^9$
Reason (R): $S_1 = 90 \times 2^8$ and $S_2 = 10 \times 2^8$
If all letters of the word COMBINATION are arranged to form 11-letter words with \( C \) and \( N \) at the ends and no vowel in the middle position, find the number of such words.
Find the area (in square units) of the region bounded by the lines \( x=0 \), \( x=\frac{\pi}{2} \), and the curves \( f(x) = \sin x \), \( g(x) = \cos x \):
Evaluate the integral: \[ \int \frac{\sec^2 x}{(\sec x+\tan x)^{5/2}}dx \]
If \( A = \begin{pmatrix} 1 & 2 & 3 \\ 1 & 3 & 5 \\ 2 & 1 & 6 \end{pmatrix} \) and \( |adj(adj(A))|(adj A)^{-1} = kA \), then k =
If \( x \) satisfies the equation \( 3x^2 - 7x + 2 = 0 \), then what is the value of \( \frac{1}{x_1} + \frac{1}{x_2} \), where \( x_1 \) and \( x_2 \) are the roots?

If the probability distribution of a random variable $X$ is as follows, then $P(X \leq 2) =$ 

The probability distribution of a discrete random variable \( X \) is given below: \[ \begin{array}{c|cccc} X = x & -1 & 0 & 1 & 2 \\ P(X = x) & \frac{1}{3} & \frac{1}{6} & \frac{1}{6} & \frac{1}{3} \end{array} \] Then the value of \( 6 \sum x^2 P(X = x) - \text{var}(X) \) is:

If \(\cos \alpha = \sec h \beta\), then \(\beta =\)

In \(\triangle ABC\), if \(a : b : c = 4 : 5 : 6\), then \( \dfrac{\cos A + 3 \cos C}{\cos B} = \)
G(1,0) is the centroid of the triangle ABC. If A = (1, -4, 2) and B = (3, 1, 0), then AG$^2$ + CG$^2$ =
Identify the correct option from the following:
Evaluate: \[ \sin^3 10^\circ + \sin^3 50^\circ - \sin^3 70^\circ = ? \]
If \(A\) and \(B\) are events of a random experiment such that \[ P(A \cup B) = \frac{3}{4}, \quad P(A \cap B) = \frac{1}{4}, \quad P(\overline{A}) = \frac{2}{3}, \] then \(P(\overline{A} \cap B)\) is:
If a hyperbola has asymptotes \(3x-4y-1=0\) and \(4x-3y-6=0\), then the transverse and conjugate axes of that hyperbola are
$\sin\left(\frac{\pi}{5}\right) + \sin\left(\frac{2\pi}{5}\right) + \sin\left(\frac{3\pi}{5}\right) + \sin\left(\frac{4\pi}{5}\right) =$
If $\alpha, \beta$ and $\gamma$ are the roots of the equation $5x^3 - 4x^2 + 3x - 2 = 0$, then $\alpha^3 + \beta^3 + \gamma^3$ equals
If the product of the lengths of the perpendiculars drawn from the ends of a diameter of the circle \( x^2 + y^2 = 4 \) onto the line \( x + y + 1 = 0 \) is maximum, then the two ends of that diameter are:
Consider an arithmetic progression where the sum of the first 5 terms is 85, and the sum of the next 5 terms is 235. Find the common difference of the AP.
The difference between the absolute maximum and absolute minimum values of the function \( f(x) = 2x^3 - 15x^2 + 36x - 30 \) on \( [-1, 4] \) is:
A family consists of 8 persons. If 4 persons are chosen at random and they are found to be 2 men and 2 women, then the probability that there are equal numbers of men and women in that family is:
In triangle \(ABC\), if \(a = 6\), \(b = 8\), and \(c = 10\), then \(\dfrac{2r_1}{r_2} =\)
If \( \theta \) is the angle between the tangents drawn from the point \( (-1, -1) \) to the circle \( x^2+y^2-4x-6y+c=0 \) and \( \cos\theta = -\frac{7}{25} \), then the radius of the circle is:
If $x^2 + y^2 + \sin y = 4$, then the value of $\frac{d^2y}{dx^2}$ at $x=-2$ is
If the lines \(x+y-2=0\), \(3x-4y+1=0\) and \(5x+ky-7=0\) are concurrent at \((\alpha, \beta)\), then equation of the line concurrent with the given lines and perpendicular to \(kx+y-k=0\) is
If a function \( f(x) \) is given as: \[ f(x) = \begin{cases} \frac{\sqrt{1+ax^2+bx^3}-\sqrt{1-ax^2-bx^3}}{x^2}, & x<0
5, & x = 0
\frac{\tan3x-\sin3x}{bx^3}, & x>0 \end{cases} \] and is continuous at \( x = 0 \), then the geometric mean of \( a \) and \( b \) is: