List of top Mathematics Questions asked in AP EAPCET

Suppose that a book of 600 pages contains 40 print mistakes. Assume that these errors are randomly distributed throughout the book and the number of errors per page follows a Poisson distribution. The probability that all the 10 pages selected at random have no print mistakes is:
From a well shuffled pack of 52 cards, two cards are drawn at random. Then, the probability of both the cards being kings is
Let z and w be two distinct non-zero complex numbers if \(|z|^2w - |w|^2z = z - w\), then
If $f(x) = \sqrt{2 - x^2}$ and $g(x) = \log(1 - x)$ are two real-valued functions, then the domain of the function $(f+g)(x)$ is:
Simplify: $\dfrac{\cos\theta}{1 - \tan\theta} + \dfrac{\sin\theta}{1 - \cot\theta}$
If the general solution of \( \frac{dy}{dx} = \frac{-y^2}{xy-y^2-x^2} \) is \( \tan^{-1}\left(\frac{x}{y}\right) = f(y) + C \), then \( f(e^3) = \)
If the lines represented by $ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0$ intersect on the x-axis, which of the following is in general incorrect
Find the locus of the point of intersection of tangents drawn at the ends of a **normal chord** of the hyperbola: $$ x^2 - y^2 = a^2 $$
The equation of the circle passing through the origin and cutting orthogonally the circles \( x^2 + y^2 + 6x - 15 = 0 \) and \( x^2 + y^2 - 8y - 10 = 0 \) is:
Find the locus of midpoints of points of intersection of the line $$ x \cos \theta + y \sin \theta = 1 $$ with the coordinate axes.
If \( x^3 - 2x^2y + 5x + y - 5 = 0 \), then at (1,1), \( y'(1) = \)
The condition that \( f(x) = ax^3 + bx^2 + cx + d \) has no extreme value is
If \( y = \tan(3\tan^{-1} x) \), then: \[ (1 - 3x^2)\frac{d^2y}{dx^2} - 12x \frac{dy}{dx} = \]
\(\tanh(\log x) = \) (Assuming \(\log x\) is natural logarithm \(\ln x\))
\( \lim_{x \to 0} x^3 (\sqrt{x^2+\sqrt{x^4+1}} - \sqrt{2}x) = \)
The standard deviation of first 10 multiples of 4 is
In an exam:
- Three subjects have maximum marks = $ n $ each
- Fourth subject has max marks = $ 2n $
- Find the number of ways to score total $ 3n $ marks.
If $\cosech\,x = \dfrac{4}{5}$, then $\sinh x = $ ?
In a triangle \( ABC \), the identity holds: \[ s \left( \frac{r_1 - r}{a} + \frac{r_2 - r}{b} + \frac{r_3 - r}{c} \right) = ? \]
If a number is chosen at random from the set \( \{1, 2, 3, \dots, 100\} \), then the probability that it is a perfect cube is:
If $A + B + C = \pi$, $\cos B = \cos A \cos C$, then $\tan A \tan C =$
For what values of $a \in \mathbb{Z}$, the quadratic expression $(x + a)(x + 1991) + 1$ can be factorised as $(x + b)(x + c)$, where $b, c \in \mathbb{Z}$?
For the parabola represented parametrically by \( x = t^2 + t + 1 \) and \( y = t^2 - t + 1 \), the length of the latus rectum is:
If the product of the perpendicular distances from any point on the hyperbola \( \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \) to its asymptotes is 6, and the eccentricity of the hyperbola is \( \sqrt{3} \), then the length of the conjugate axis is:
The straight line touching the circle \(x^2+y^2-2x-3=0\) and remaining normal to the circle \(x^2+y^2-4y-6=0\) is