List of top Questions asked in AP EAMCET

The algebraic equation of degree 4 whose roots are the translates of the roots of the equation \( x^4 + 5x^3 + 6x^2 + 7x + 9 = 0 \) by \( -1 \) is:
If \( n \geq 2 \) is a natural number and \( 0<\theta<\frac{\pi}{2} \), then \[ \int \frac{(\cos^n \theta - \cos \theta)^{1/n}}{\cos^{n+1} \theta} \sin \theta \, d\theta = \]
The angle between the planes \( \vec{r} \cdot (12\hat{i} + 4\hat{j} - 3\hat{k}) = 5 \) and \( \vec{r} \cdot (5\hat{i} + 3\hat{j} + 4\hat{k}) = 7 \) is:
If $$ y = 1 + x + x^2 + x^3 + \dots \quad \text{and} \quad |x| < 1, \text{ then } y'' = $$
The solution of the differential equation \[ x dy - y dx = \sqrt{x^2 + y^2} dx \] when \( y(\sqrt{3}) = 1 \) is:
A test containing 3 objective type of questions is conducted in a class. Each question has 4 options and only one option is the correct answer. No two students of the class have answered identically and no student has written all correct answers. If every student has attempted all the questions, then the maximum possible number of students who have written the test is:
\(\int\frac{2x^{2}\cos(x^{2})-\sin(x^{2})}{x^{2}}dx=\)
If 5 letters are to be placed in 5-addressed envelopes, then the probability that at least one letter is placed in the wrongly addressed envelope is:
If five-digit numbers are formed from the digits 0, 1, 2, 3, 4 using every digit exactly only once, then the probability that a randomly chosen number from those numbers is divisible by 4 is
The differential equation formed by eliminating arbitrary constants \( A \) and \( B \) from the equation \[ y = A \cos 3x + B \sin 3x \] is:
Evaluate the integral: \[ \int \left[ (\log_2 x)^2 + 2 \log_2 x \right] dx. \]
The number of all the values of \( x \) for which the function \[ f(x) = \sin x + \frac{1 - \tan^2 x}{1 + \tan^2 x} \] attains its maximum value on \( [0, 2\pi] \).
If the function \[ f(x) = \frac{\sqrt{1+x} - 1}{x} \] is continuous at \( x = 0 \), then \( f(0) \) is:
If a variable straight line passing through the point of intersection of the lines x - 2y + 3 = 0 and 2x - y - 1 = 0 intersects the X and Y axes at A and B respectively, then the equation of the locus of a point which divides the segment AB in the ratio -2 : 3 is:
In a triangle ABC, if \( (r_1 + r_2) \csc^2 \frac{C}{2} = \)
A Circle S passes through the points of intersection of the circles \( x^2 + y^2 - 2x + 2y - 2 = 0 \) and \( x^2 + y^2 + 2x - 2y + 1 = 0 \). If the centre of this circle S lies on the line \( x - y + 6 = 0 \), then the radius of the circle S is:
The equation of a circle which touches the straight lines \[ x + y = 2, \quad x - y = 2 \] and also touches the circle \[ x^2 + y^2 = 1 \] is:
\(\int_{0}^{\pi}x \sin^4 x \cos^6 x dx = \)
If the roots of the equation \(x^3 + ax^2 + bx + c = 0\) are in arithmetic progression, then:

Evaluate the integral: $ I = \int e^{2x+3} \sin 6x \, dx $.

The real part of \( \frac{\left( \cos a + i \sin a \right)^6}{\left( \sin b + i \cos b \right)^8} \) is:
If the \(2^{\text{nd}}\), \(3^{\text{rd}}\), and \(4^{\text{th}}\) terms in the expansion of \( (x + a)^n \) are 96, 216, and 216 respectively, and \( n \) is a positive integer, then \( a + x \) is:
If Rolle’s theorem is applicable for the function \( f(x) \) defined by \( f(x) = x^3 + Px - 12 \) on \( [0,1] \), then the value of \( C \) of the Rolle's theorem is:
The equation of one of the tangents drawn from the point \( (0,1) \) to the hyperbola \( 45x^2 - 4y^2 = 5 \) is:
The general solution of the equation \( \sin^2 \theta + 3 \cos^2 \theta = 5 \sin \theta \) is: