List of top Mathematics Questions asked in AP EAPCET

The 10th term of an arithmetic progression is 35 and the 20th term is 65. What is the first term?
A box contains 5 defective and 15 non-defective bulbs. Two bulbs are drawn at random without replacement. What is the probability that at least one bulb is defective?
If \( \tan \theta = \frac{3}{4} \) and \( \theta \) is acute, find \( \sin 2\theta \):
The equation of the line passing through the point \((1, 2)\) and perpendicular to the line \(3x + 4y - 12 = 0\) is:
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?
The mean of 10 numbers is 18. If one number is excluded, the mean becomes 17. What is the excluded number?
If \( \vec{a} = 3\hat{i} - 2\hat{j} \) and \( \vec{b} = \hat{i} + 4\hat{j} \), find the magnitude of \( 2\vec{a} - 3\vec{b} \).
How many 4-digit numbers (between 1000 and 9999) can be formed using the digits \(2, 3, 5, 7, 8\) such that:
  • Each number contains both \(3\) and \(7\) exactly once,
  • No digit is repeated.
If the roots of the quadratic equation \( 2x^2 - 4x + k = 0 \) are real and equal, find the value of \( k \).
If \( \tan \theta = \frac{4}{3} \), find the value of \( \sin \theta \) in the first quadrant.
If the roots of the quadratic equation \( ax^2 + bx + c = 0 \) are in the ratio 3:4, then which of the following relationships holds between the coefficients?
Find the derivative of the function \( f(x) = \sin^{-1} \big( 2x \sqrt{1 - x^2} \big) \) with respect to \( x \), for \( x \in \left(-\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right) \).
If \( \sin \theta + \cos \theta = \sqrt{2} \cos \theta \), then the value of \( \tan \theta \) is
The equation of the circle passing through the points (1, 1), (2, 2), and (3, 1) is
A bag contains 5 red and 3 blue balls. If one ball is drawn at random, what is the probability that it is red?
Find the midpoint of the line segment joining the points (3, 4) and (7, -2).
If the sum of the roots of the quadratic equation $ x^2 - 5x + k = 0 $ is 5, find the value of $ k $.
If $ \sin \theta + \cos \theta = 1 $, find the value of $ \sin \theta \cos \theta $.
Find the slope of the line perpendicular to the line $ 3x + 4y - 12 = 0 $.
A bag contains 3 red and 4 blue balls. If one ball is drawn at random, what is the probability that it is red?
Evaluate $ \int_{0}^{1} (3x^2 + 2x) \, dx $.
Find the equation of the circle with center at (2, -3) and radius 5.
If $ \cos \theta = \frac{5}{13} $ and $ \theta $ is in the fourth quadrant, find the value of $ \tan \theta $.
Evaluate $ \lim_{x \to 3} \frac{x^2 - x - 6}{x - 3} $.

If $x^2 + y^2 = 25$ and $xy = 12$, then what is the value of $x^4 + y^4$?