List of top Mathematics Questions asked in AP EAPCET

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 \( \vec{a} = 3\hat{i} - 2\hat{j} \) 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 \( \tan \theta = \frac{4}{3} \), find the value of \( \sin \theta \) in the first quadrant.
If \( \sin \theta + \cos \theta = \sqrt{2} \cos \theta \), then the value of \( \tan \theta \) is
Find the midpoint of the line segment joining the points (3, 4) and (7, -2).
A bag contains 5 red and 3 blue balls. If one ball is drawn at random, what is the probability that it is red?
If $ \sin \theta + \cos \theta = 1 $, find the value of $ \sin \theta \cos \theta $.
A bag contains 3 red and 4 blue balls. If one ball is drawn at random, what is the probability that it is red?
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 $.

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

The function \( f(x) = \frac{x^2 - 4x + 3}{x^2 - 5x + 6} \) is defined for all real values of \( x \) except:

If the equation of a straight line passing through the point (1,2) and perpendicular to the line $3x + 4y = 7$ is:

The number of real Solution of the equation \[ \sqrt{x + 4} + \sqrt{5 - x} = 5 \] \text{is:}
The general solution of the equation \[ 2\sin^2 \theta - \cos^2 \theta = \sin \theta \]
The mean of 6 numbers is 15, and the standard deviation is 2. If each number is increased by 5, what is the new standard deviation?
The sum of the first 10 terms of an arithmetic progression is 145, and the first term is 1. Find the common difference.
If the arithmetic mean of the terms \(a, a + d, a + 2d, ..... a + (2n)d\) is 35 and the sum of the series is 735, then the value of \(n\) is:
If $ \sin \theta = \frac{3}{5} $ and $ \theta $ is in the first quadrant, find the value of $ \tan \theta $.
Let \( f(x) = 2x^3 - 3x \neq 4 \). Then the inverse function \( f^{-1}(x) \) is:
If \( \vec{a} = 2\hat{i} - \hat{j} + 3\hat{k} \), \( \vec{b} = \hat{i} + 2\hat{j} - \hat{k} \), then the angle \( \theta \) between \( \vec{a} \) and \( \vec{b} \) is:
Let a circle pass through the point \( (1, 2) \) and touch the \( x \)-axis at \( (3, 0) \). Then the equation of the circle is:
If \( f(x) = 2x^3 - 3x^2 + 4 \), then the minimum value of \( f(x) \) in the interval \( [0, 3] \) is: