List of top Mathematics Questions asked in AP EAPCET

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:
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 \( \vec{a} = 2\hat{i} - \hat{j} + 3\hat{k} \), \( \vec{b} = \hat{i} + 2\hat{j} - \hat{k} \), then the angle \( \theta \) between \( \vec{a} \) and \( \vec{b} \) is:
If \( f(x) = 2x^3 - 3x^2 + 4 \), then the minimum value of \( f(x) \) in the interval \( [0, 3] \) is:
If $a$ and $b$ are the roots of the equation $2x^2 + 5x + 30 = 0$, find the value of $a^2 + b^2$.
Find the distance between the points $ (2, 3) $ and $ (5, 7) $ in the Cartesian plane.
If the roots of the equation \[ x^3 + p x^2 + q x + r = 0 \] are in arithmetic progression, then which of the following is always true?
A point P divides the line joining points $A(2, 3)$ and $B(10, 7)$ in the ratio 3:1 internally. What are the coordinates of point P?
A bag contains 4 red and 5 blue balls. One ball is drawn at random. What is the probability that it is red?
Find the determinant of the matrix: $$ \begin{bmatrix} 3 & 2 \\ 1 & 5 \end{bmatrix} $$
If $ a $ and $ b $ are the roots of the equation $ 4x^2 - 12x + 11 = 0 $, find the value of $ a^2 + b^2 $.
Let \( A(1,2), B(3,4) \) and \( C(k,6) \) be three points such that the area of triangle \( ABC \) is 5 square units. The possible values of \( k \) are:
If the tangent to the curve \( y = ax^2 + bx + c \) at the point \( (1,1) \) is parallel to the x-axis, and the curve passes through the point \( (2,3) \), then find the value of \( a + b + c \):
Let \[ f(x) = x^4 - 4x^3 + 6x^2 + k \] \text{If \(f(x) \geq 0\) for all real \(x\), then the value of \(k\) is:}
A rectangular garden has a length that is 3 meters more than its width. If the area of the garden is 88 square meters, what is the width of the garden?
Evaluate the limit: \[ \lim_{x \to 1} \frac{x + x^2 + x^3 + \dots + x^n - n}{x - 1}. \]
Bag A contains 3 white and 4 red balls, bag B contains 4 white and 5 red balls, and bag C contains 5 white and 6 red balls. If one ball is drawn at random from each of these three bags, then the probability of getting one white and two red balls is:
In \( \triangle ABC \), if \( (r_2 - r_1)(r_3 - r_1) = 2r_2r_3 \), then \( 2(r + R) = \):
Evaluate the expression: \[ \frac{\sin 1^\circ + \sin 2^\circ + \dots + \sin 89^\circ}{2(\cos 1^\circ + \cos 2^\circ + \dots + \cos 44^\circ) + 1} =\]
Evaluate the integral \[ I = \int_{-1}^{1} \left( \sqrt{1 + x + x^2} - \sqrt{1 - x + x^2} \right) \, dx \]
If \( 5 \sinh x - \cosh x = 5 \), then one of the values of \( \tanh x \) is:
If \[ 3f(x) - 2f\left(\frac{1}{x}\right) = x, \] then \( f'(2) \) is:

If the line segment joining the points \( (1,0) \) and \( (0,1) \) subtends an angle of \( 45^\circ \) at a variable point \( P \), then the equation of the locus of \( P \) is: