List of top Questions asked in AP EAPCET

If \( \int_0^{2024\pi} \frac{2023^{\sin^2 x}}{2023^{\sin^2 x} + 2023^{\cos^2 x}} dx = k \), then \( \left( \frac{2k}{\pi} + 1 \right) = \)
In $ \triangle ABC $, if $ r = 1 $, $ R = 4 $, and $ \Delta = 8 $, then \[ \frac{1}{ab} + \frac{1}{bc} + \frac{1}{ca} = \]
If the extremities of a diagonal of a square are \( (1, -2, 3) \) and \( (2, -3, 5) \), then the length of its side is:
Let \( (1, 2) \) be the focus and \( x + y + 1 = 0 \) be the directrix of a hyperbola. If \( \sqrt{3} \) is the eccentricity of the hyperbola, then its equation is:
Among the following, the correct statement is
Assertion (A): \(\displaystyle \int_0^{\frac{\pi}{2}} (\sin^6 x + \cos^6 x)\, dx\) lies in the interval \(\left(\frac{\pi}{8}, \frac{\pi}{2}\right)\) Reason (R): \(\sin^6 x + \cos^6 x\) is a periodic function with period \(\dfrac{\pi}{2}\)
If \[ \frac{x + 2}{x^2 - 3} \text{ is one of the partial fractions of } \frac{3x^3 - x^2 - 2x + 17}{x^4 + x^2 - 12}, \text{ then the other partial fraction of it is:} \]
The suitable reagent to carry out the following reaction is:
suitable reagent to carry out the following reaction
A cylindrical rod made of aluminum has length 1 meter and diameter of 10 cm. The rod is subjected to a tensile force of 100 kN. The elongation in the rod is:
The coefficient of \( x^3 \) in the expansion of \( (1 - x)^{\frac{3}{2}} \), where \( |x|<1 \), is:
6 g of urea (molar mass = 60 g mol$^{-1}$) and 9 g of glucose (molar mass = 180 g mol$^{-1}$) were dissolved in 35 g of water. The mass percent of urea and glucose is respectively.
Match the following
hybridisation
Identify the correct statements with respect to cis / trans-2-butene from the following
I. cis-2-Butene is more polar than trans - 2 Butene
II. melting point of cis-2-Butene is greater than that of trans -2- Butene
III. boiling point of cis-2- Butene is greater than that of trans - 2- Butene
If \( A = \frac{\pi}{24} \), then \[ \frac{\cos A + \cos 3A + \cos 5A + \cos 7A}{\sin A + \sin 3A + \sin 5A + \sin 7A} \]
A metal wire with circular cross section and length one metre is pulled with tensile force of 1000 N on each side. For the wire to be stretched not more than 0.25 cm, the minimum diameter of the wire required is:
(Young's modulus of the metal $= 10^{11}$ \text{ Pa, take } $\sqrt{\pi} = 1.77$)
The set \( \{ x \in \mathbb{R} : 4 + 11x - 3x^2>0 \} \) is the interval:
If \( P, Q \) and \( R \) are \( 3 \times 3 \) matrices such that} \[ P = \begin{bmatrix} 3x^2 + x + 3 & 2x^2 - x + 4 & 7x^2 + 8x + 5 \\ 5x^2 + 3x + 2 & 4x^2 - 2x - 1 & 7x^2 + 5x + 8 \\ 3x^2 + 2x + 5 & 4x^2 - x - 2 & 3x^2 + 8x + 7 \end{bmatrix} = Px^2 + Qx + R \] then det \( R = \) ?
The equation of a tangent to the circle \(x^2 + y^2 + 2x - 12y - 132 = 0\) which is perpendicular to the line \(12x + 5y + k = 0\) is:
The number of natural numbers less than 10000 which are divisible by 5 and that no digit is repeated in the same number, is
Planes $\pi_1$ and $\pi_2$ are defined by vectors. If $|\vec{a}| = \sqrt{14}$ and $\vec{a}$ is parallel to their intersection, then $|\vec{a} \cdot (\hat{i} + \hat{j} + \hat{k})| = $
If \( \sqrt{-3 - 4i} = re^{i\theta} \), then \( r^2 \tan \theta = \)
If \( 1, \omega, \omega^2 \) are the cube roots of unity and \( f(x, y) = (x + y)(x\omega + y\omega^2)(x\omega^2 + y\omega) \), then \( f(2, 3) \) is:
Assertion (A): The difference of the slopes of the lines represented by \( y^2 - 2xy \sec^2 \alpha + (3 + \tan^2 \alpha) \left( 1 + \tan^2 \alpha \right) \cos^2 \theta = 0 \) is 4. Reason (R): The difference of the slopes represented by \( ax^2 + 2hxy + by^2 = 0 \) is \( \frac{2\sqrt{h^2 - ab}}{|b|} \).
Given below are two statements
Assertion (A): Ethylamine is stronger base than ammonia
Reason (R): It is due to $-$I effect of ethyl group
The correct answer is
Arrange the following in order of increasing number of unpaired electrons in them:
  1. \([Fe(CN)_6]^{3-}\)
  2. \([MnCl_6]^{3-}\)
  3. \([FeF_6]^{3-}\)
  4. \([Co(NH_3)_6]^{3+}\)