List of top Questions asked in AP EAPCET

If \( \cos A + \cos(A + B) + \cos(A + 2B) + \cdots \) upto \( n \) terms \( = \cos \left( \frac{2A + (n-1)B}{2} \right) \frac{\sin \frac{nB}{2}}{\sin \frac{B}{2}} \), then \( \cos \frac{3\pi}{19} + \cos \frac{5\pi}{19} + \cos \frac{7\pi}{19} + \cdots + \cos \frac{17\pi}{19} = \)

In \( \triangle ABC \), if \( \tan \frac{A}{2} + \tan \frac{C}{2} = \frac{b}{s} \), then \( \sin \left( \frac{A + C}{3} \right) = \)

If \( 3 \cdot {}^5C_0 + 8 \cdot {}^5C_1 + 13 \cdot {}^5C_2 + 18 \cdot {}^5C_3 + 23 \cdot {}^5C_4 + 28 \cdot {}^5C_5 = k \cdot 2^5 \), then \( k = \)

If a seven digit number formed with distinct digits 4, 6, 9, 5, 3, \( x \) and \( y \) is divisible by 3, then the number of such ordered pairs \( (x, y) \) is

In \( \triangle ABC \), if \( \cos A \cos B \cos C = \frac{1}{5} \), then \( \tan A \tan B + \tan B \tan C + \tan C \tan A = \)

If \( \omega \) is a complex cube root of unity, then \( \cos \left( \sum_{k=1}^{2} (k - \omega)(k - \omega^2) \frac{\pi}{175} \right) = \)

Let the two values of \( z = \frac{1 - i}{\sqrt{1 + i}} \) be \( z_1 \) and \( z_2 \). If \( -\frac{\pi}{2}<\text{Arg}(z_1)<\text{Arg}(z_2)<\pi \), then \( \text{Arg}(z_1) + \text{Arg}(z_2) = \)

If \( \alpha \) and \( \beta \) are the roots of the equation \( ax^2 + bx + c = 0 \), then the equation whose roots are \( \alpha + \beta \) and \( \frac{1}{\alpha} + \frac{1}{\beta} \) is

If \( 2^n \) divides \( 16! \) and \( 2^{n+1} \) does not divide \( 16! \), then \( n = \)

If \( z_1 = 2 - 3i \) and the roots of the equation \( z^3 + bz^2 + cz + d = 0 \) are \( i, z_1 \) and \( \overline{z_1} \), then \( b + c + d = \)

Let \( f: \mathbb{R} \rightarrow \mathbb{R} \) be a function defined by \( f(x) = \frac{2x+1}{3} \). If \( \alpha \) is an element in the domain of \( f \) whose image is \( \frac{1}{\alpha} \), then the sum of all possible values of such \( \alpha \) is

What is the intermediate in the following reaction?
RCN + SnCl$_2$ + HCl $\longrightarrow$ RCHO

Which of the following is/are correct?
i. Cr$_2$O$_3$ is an acidic oxide
ii. Mo(VI) and W(VI) are more stable than Cr(VI)
iii. All Cu(II) halides are known except iodide
iv. The E$^\circ$ value for Cr$^{3+}$/Cr$^{2+}$ is much more positive than Mn$^{3+}$/Mn$^{2+}$

Identify the correct statements about order of reaction:
I) It is equal to the sum of the powers of concentration terms in rate equation
II) It is always a whole number
III) It is determined experimentally
IV) It is not applicable for complex reactions

Identify the macromolecular colloids from the list given below:
I. Synthetic rubber II. Rhombic sulphur III. Sodium stearate
IV. Cellulose V. Enzymes VI. Sodium lauryl sulphate