List of top Mathematics Questions asked in AP EAPCET

If \(2\sin x - \cos 2x = 1\), then \( (3 - 2\sin^2x) = \)
Evaluate: \(\tan\left(2\tan^{-1}\left(-\frac{1}{3}\right) + \tan^{-1}\left(\frac{1}{7}\right)\right) =\)
If \( {}^{27}P_{r+7} = 7722 \cdot {}^{25}P_{r+4} \), then r =
If \( \vec{a} = 2\vec{i} - \vec{j} + 6\vec{k} \); \( \vec{b} = \vec{i} - \vec{j} + \vec{k} \) and \( \vec{c} = 3\vec{j} - \vec{k} \), then \( \vec{a} \times \vec{b} + \vec{b} \times \vec{c} + \vec{c} \times \vec{a} = \)
If the transformed equation of the equation \[ 2x^2 + 3xy - 2y^2 - 17x + 6y + 8 = 0 \] after translating the coordinate axes to a new origin \((\alpha, \beta)\) is \[ aX^2 + 2h XY + bY^2 + c = 0, \] then find \(3\alpha + c\).
Evaluate $ \lim_{x \to 2} \frac{x^2 - 4}{x - 2} $.
If g is the inverse of the function f(x) and \( g(x) = x + \tan x \) then, \( f'(x) = \)
$\int \frac{\sin 2x}{\sin^2 x + 3 \cos x - 3} \, dx =$
Identify the correct option from the following:
The tangents drawn to the hyperbola \(5x^2 - 9y^2 = 90\) through a variable point \(P\) make angles \(\alpha\) and \(\beta\) with its transverse axis. If \(\alpha\) and \(\beta\) are complementary angles, then the locus of \(P\) is
The radius of the circle passing through the points of intersection of the circles \( x^2+y^2+2x+4y+1=0 \), \( x^2+y^2-2x-4y-4=0 \), and intersecting the circle \( x^2+y^2=6 \) orthogonally is:
If \[ \int \frac{dx}{(x \tan x + 1)^2} = f(x) + c, \] then \(\lim_{x \to \frac{\pi}{2}} f(x)\) is?
If the surface area of a spherical bubble is increasing at the rate of 4 sq.cm/sec, then the rate of change in its volume (in cubic cm/sec) when its radius is 8 cms is
The general solution of the equation \( \cos(2x) = \frac{1}{2} \) is:
Given \(f(x) = x^2 - 5x + 4\). Out of first 20 natural numbers, if a number \(x\) is chosen at random, then the probability that the chosen \(x\) satisfies the inequality \(f(x)>10\) is
Evaluate the limit: \[ \lim_{x \to \infty} \frac{3x+4\cos^2x}{\sqrt{x^2-5\sin^2x}} \]
If $$ \int \frac{a \cos x + 3 \sin x}{5 \cos x + 2 \sin x} dx = \frac{26}{29} x - \frac{k}{29} \log |5 \cos x + 2 \sin x| + c, $$ then find $ |a + k| $.
If P(\(\alpha, \beta\)) is the radical centre of the circles \(S=x^2+y^2+4x+7=0\), \(S'=2x^2+2y^2+3x+5y+9=0\) and \(S''=x^2+y^2+y=0\), then the length of the tangent drawn from P to S' = 0 is
The slope of one of the direct common tangents drawn to the circles \(x^2 + y^2 - 2x + 4y + 1 = 0\) and \(x^2 + y^2 - 4x - 2y + 4 = 0\) is
A straight line passing through a fixed point (2, 3) intersects the coordinate axes at points \( P \) and \( Q \). If \( O \) is the origin and \( R \) is a variable point such that \( OPRQ \) is a rectangle, then the locus of \( R \) is
X denotes the number of heads in $ n $ tosses of a fair coin. If $ P(X = 4),\ P(X = 5),\ P(X = 6) $ are in arithmetic progression, find the largest possible value of $ n $.
If \( \alpha, \beta, \gamma \) are the roots of the equation \[ x^3 + px^2 + qx + r = 0, \] then \[ (\alpha + \beta)(\beta + \gamma)(\gamma + \alpha) =\ ? \]
If \( \frac{1}{2} \leq \frac{x^2+x+a}{x^2-x+a} \leq 2 \ \forall x \in \mathbb{R} \), then \( a = \)
If $X$ is a binomial variate with mean $\frac{16}{5}$ and variance $\frac{48}{25}$, then $P(X \leq 2) =$
Evaluate: \( \int_0^{400\pi} \sqrt{1 - \cos 2x} \, dx \)
If the average number of accidents occurring at a particular junction on a highway in a week is 5, then the probability that at most one accident occurs in a particular week is: