List of top Questions asked in AP EAMCET- 2024

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
If the function \[ f(x) = \frac{\sqrt{1+x} - 1}{x} \] is continuous at \( x = 0 \), then \( f(0) \) is:
The differential equation formed by eliminating arbitrary constants \( A \) and \( B \) from the equation \[ y = A \cos 3x + B \sin 3x \] is:
In a triangle ABC, if \( (r_1 + r_2) \csc^2 \frac{C}{2} = \)
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 \( A = \int_0^{\infty} \frac{1 + x^2}{1 + x^4} dx \) and \( B = \int_0^1 \frac{1 + x^2}{1 + x^4} dx \), then:
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:

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 \( f(x) \) is given as: \( f(x) = \begin{cases} 3ax - 2b, & x<1 ax + b + 1, & x<1 \end{cases} \) and \( \lim_{x \to 1} f(x) \) exists, then the relation between \( a \) and \( b \) 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:
The general solution of the equation \( \sin^2 \theta + 3 \cos^2 \theta = 5 \sin \theta \) 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:
If $y = \tan^{-1} \frac{x}{1+2x^2} + \tan^{-1} \frac{x}{1+6x^2} + \tan^{-1} \frac{x}{1+12x^2}$, then $\left(\frac{dy}{dx}\right)_{x=\frac{1}{2}} =$
The equation of one of the tangents drawn from the point \( (0,1) \) to the hyperbola \( 45x^2 - 4y^2 = 5 \) 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:
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:
In \( \triangle ABC \), evaluate: \[ \frac{r_2 (r_1 + r_3)}{\sqrt{r_1 r_2 + r_2 r_3 + r_3 r_1}}. \]
If \( y = \sinh^{-1} \left(\frac{1 - x}{1 + x} \right) \), then \( \frac{dy}{dx} \) is given by:
Among the options given below, from which option a differential equation of order two can be formed?
For a dataset, if the coefficient of variation is 25 and the mean is 44, find the variance.
Evaluate the integral: \[ I = \int \frac{x+1}{\sqrt{x^2 + x + 1}} dx. \]
In a triangle ABC, if \( r_1 = 2r_2 = 3r_3 \), then \(\sin A\): \(\sin B\): \(\sin C\) = Options: