List of top Mathematics Questions asked in AP EAPCET

In \(\triangle ABC\), if \(a : b : c = 4 : 5 : 6\), then \( \dfrac{\cos A + 3 \cos C}{\cos B} = \)
Length of the common chord of two circles of same radius is \( 2\sqrt{17} \). If one of the two circles is \( x^2 + y^2 + 6x + 4y - 12 = 0 \), then the acute angle between the two circles is:
Assertion (A): $S_3 = 55 \times 2^9$
Reason (R): $S_1 = 90 \times 2^8$ and $S_2 = 10 \times 2^8$
Evaluate: \[ \sin^3 10^\circ + \sin^3 50^\circ - \sin^3 70^\circ = ? \]

If $\tan A + \tan B = m$ and $\tan A \tan B = n$, then $\tan(A + B)$ is: 

If \( x \ne (2n+1)\frac{\pi}{4} \), then the general solution of \( \cos x + \cos 3x = \sin x + \sin 3x \) is
If \[ \frac{x^2}{(x^2 + 2)(x^4 - 1)} = \frac{A}{x^2 - 1} + \frac{B}{x^2 + 1} + \frac{C}{x^2 + 2}, \text{ then } A + B - C =\ ? \]
If the direction ratios of two lines \(L_1\) and \(L_2\) are \((1,-2,2)\) and \((-2,3,-6)\) respectively, then the direction ratios of the line which is perpendicular to both \(L_1\) and \(L_2\) are?
Find the area (in square units) of the region bounded by the lines \( x=0 \), \( x=\frac{\pi}{2} \), and the curves \( f(x) = \sin x \), \( g(x) = \cos x \):
If the volume of a sphere is increasing at the rate of 12 \( \text{cm}^3/\text{sec} \), then the rate (in \( \text{cm}^2/\text{sec} \)) at which its surface area is increasing when the diameter of the sphere is 12 cm is:
If \( \sqrt{x-xy} + \sqrt{y-xy} = 1 \), then \( \frac{dy}{dx} = \)
\( \int \frac{x}{(1-x^2)\sqrt{2 - x^2} dx = \)}
Evaluate the integral: \[ \int \frac{\sec^2 x}{(\sec x+\tan x)^{5/2}}dx \]
If \(\cos\theta = -\frac{3}{5}\) and \(\theta\) does not lie in second quadrant, then \(\tan\frac{\theta}{2} =\)
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 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.

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

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 $ \alpha $, $ \beta $, and $ \gamma $ are the angles made by a vector with the $ x $-, $ y $-, and $ z $-axes respectively, then find the value of $ \sin^2\alpha + \sin^2\beta $.
\( \int \frac{dx}{12\cos x + 5\sin x} = \)
If the area of a right angled triangle with hypotenuse 5 is maximum, then its perimeter is
If \( \sinh^{-1}(2) + \sinh^{-1}(3) = \alpha \), then \( \sinh\alpha = \) ?
Let \( A(5,4) \) and \( B(5,-4) \) be two points. If \( P \) is a point in the coordinate plane such that \( |APB| = \frac{\pi}{4} \), then the point \( P \) lies on the curve:
$\sin\left(\frac{\pi}{5}\right) + \sin\left(\frac{2\pi}{5}\right) + \sin\left(\frac{3\pi}{5}\right) + \sin\left(\frac{4\pi}{5}\right) =$
If a hyperbola has asymptotes \(3x-4y-1=0\) and \(4x-3y-6=0\), then the transverse and conjugate axes of that hyperbola are