List of top Mathematics Questions asked in AP EAPCET

The value of $c$ of Rolle's theorem for the function $f(x) = 2 \sin x + \sin 2x$ in the interval $[0, \pi]$ is
Identify the correct option from the following:

If $\int \left[ 3t^2 \sin^{-1} \left( \frac{1}{-t \cos t} \right) \right] \, dt = f(t) \left( \sin^{-1} \left( \frac{1}{t} \right) \right) + c$, then $f(2) =$
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$\lim_{x \to 0} \frac{(\sqrt{2})^{-\sqrt{1 + \cos x}}}{15 + \cos 2x - 4} =$
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$\lim_{x \to 0} \frac{x \tan 2x - 2x \tan x}{(1 - \cos 3x) (\cos x - \cot x)^2} =$
Identify the correct option from the following\nobreakspace the following:

The derivative of $\sec^{-1} \left( \frac{1}{2x^2 - 1} \right)$ with respect to $\sqrt{1 - x^2}$ at $x = \frac{1}{2}$ is
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If $5f(x) + 3f \left( \frac{1}{x} \right) = x + 2$ and $y = x f(x)$, then $\frac{dy}{dx}$ at $x = 1$ is
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If a real valued function \[ f(x) = \begin{cases} \frac{x^2 (a + 3) x (a + 1)}{x + 3}, & x \neq -3
-\frac{5}{2}, & x = -3 \end{cases} \] is continuous at $x = -3$, then $\lim_{x \to -3} [x^2 x + 1] =$ Identify the correct option from the following:

Match the functions in Column I with their properties in Column II.
\[ \begin{array}{ll} \text{Column I} & \text{Column II}
\text{A) } |x| & \text{I. Strictly increasing and continuous in } (-1,1)
\text{B) } \sqrt{|x|} & \text{II. Continuous but not differentiable in } (-1,1)
\text{C) } x + |x| & \text{III. Differentiable in } (-1,1)
\text{D) } |x - |x|| + |x + 1| & \text{IV. Differentiable in } (-1,0), (0,1) \end{array} \] The correct match is: Identify the correct option from the following:

If the sum of the distances of the point (3, 4, 0), $\alpha \in \mathbb{R}$ from X-axis, Y-axis and Z-axis is minimum, then $\sec \alpha$ =
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If the equation of the plane passing through the point (2, -1, 3) and perpendicular to each of the planes $3x - 2y + z = 8$ and $x + y + z = 6$ is $lx + my + nz = 1$, then $4m + 2n - 3l$ =
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If the equation of the hyperbola having foci at \((8,3)\), \((0,3)\) and eccentricity \( \frac{4}{3} \) is \[ \frac{(x-\alpha)^2}{p} - \frac{(y-\beta)^2}{q} = 1, \] then find \( p + q \). Options:

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:

The slope of the non-vertical tangent drawn from the point $(3,4)$ to the circle $x^2 + y^2 = 9$ is:

Problem: If one of the lines represented by \(ax^2 + 2hxy + by^2 = 0\) bisects the angle between the positive coordinate axes, then identify the correct relationship between \(a\), \(b\), and \(h\). Identify the correct option from the following:

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:

Problem: From a point \( P \) on the circle \( x^2 + y^2 = 4 \), two tangents are drawn to the circle \( x^2 + y^2 - 6x - 6y + 14 = 0 \). If \( A \) and \( B \) are the points of contact of those lines, then the locus of the center of the circle passing through the points \( P \), \( A \), and \( B \) is: Identify the correct option from the following:

If the intercepts made by a variable circle on the X-axis and Y-axis are 8 and 6 units respectively, then the locus of the center of the circle is:

If the straight line \[ 2x + 3y + 1 = 0 \] bisects the angle between two other straight lines, one of which is \[ 3x + 2y + 4 = 0, \] then the equation of the other straight line is:

If the slopes of both the lines given by \[ x^2 + 2hxy + 6y^2 = 0 \] are positive and the angle between these lines is \[ \tan^{-1} \left(\frac{1}{7}\right), \] then the product of the perpendiculars drawn from the point \((1,0)\) to the given pair of lines is:

Point \(P(6,4)\) lies on the line \(x - y - 2 = 0\). If \(A(\alpha, \beta)\) and \(B(\gamma, \delta)\) are two points on this line lying on either side of \(P\) at a distance of 4 units from \(P\), then find \(\alpha^2 + \beta^2 + \gamma^2 + \delta^2\).

A random variable \(X\) follows a binomial distribution in which the difference between its mean and variance is 1. If \(2P(x=2) = 3P(x=1)\), then \(n^2 P(x>1)\) is:

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 \(3\alpha + c\).

70% of the total employees of a factory are men. Among the employees of that factory, 30% of men and 15% of women are technical assistants. If an employee chosen at random is found to be a technical assistant, then the probability that this employee is a man is:

Two cards are drawn at random from a pack of 52 playing cards. If both the cards drawn are found to be black in colour, then the probability that at least one of them is a face card is: