List of top Mathematics Questions asked in AP EAPCET

If $z = \frac{\sqrt{3} + i}{2}$, then $z^{101} + z^{103} =$

Given that \[ \sum_{k=1}^{n} k(k-1)=\frac{n(n-1)(n+1)}{3} \] and $\omega$ and $\omega^2$ are complex cube roots of unity. If \[ \sum_{k=1}^{2026} \left( k+\frac{1}{\omega} \right) \left( k+\frac{1}{\omega^2} \right) = \frac{2026}{3}(N+3), \] then $N=$

If \[ \cos\alpha+\cos\beta+\cos\gamma=0 \] and \[ \sin\alpha+\sin\beta+\sin\gamma=0, \] then which of the following is true?

If $\omega$ is a complex cube root of unity, then $(1 - \omega + \omega^2)^5 + (1 + \omega - \omega^2)^5 =$

The modulus of the product of all the values of \( (2+3i)^{3/5} \) is:

If \(z_1=8+4i,\; z_2=6+4i\) and \[ \operatorname{Arg}\left(\frac{z-z_1}{z-z_2}\right)=\frac{\pi}{4}, \] then \(z\) satisfies

If $z_1,z_2$ are two roots of the equation \[ z^2+az+b=0 \] and on the Argand plane the points represented by $z_1,z_2$ and the origin form an equilateral triangle, then $a^2=$

Among the solutions of the equation \( x^6 = 64 \), the sum of all those solutions whose real part is negative is:

If \(1,i\in\mathbb{C}\), the set of complex numbers, then the value of \[ \sqrt{1+\sqrt{i}} \] cannot be

If \( \text{Arg}(\frac{z-1}{z+5}) = \pi/3 \) and \( |z-1|=|z+5| \), then \( |z|^2 = \)

Among the roots of \[ 3\sqrt{3}\,z^3-i=0, \] the sum of the squares of the two roots having non-zero real part is

If \[ (1+\sin\alpha+i\cos\alpha)^8 = A(\cos\theta+i\sin\theta), \] then $A$ and $\theta$ are respectively

If \( z_{1}=x+iy \), \( z_{2}=a+ib \) and \( x^{2}+y^{2}=a^{2}+b^{2} \), then \( z_{2} = \)

The value of \[ \lim_{n \to \infty} \left\{ \frac{1}{n+m} + \frac{1}{n+2m} + \frac{1}{n+3m} + \dots + \frac{1}{n+nm} \right\} \] is:

If \[ \sin\theta+\cos\theta=\sqrt{2}\cos\alpha, \] where \(0<\theta<\frac{\pi}{2}\), then the value of \[ \sin2\theta \] is:

If \[ \sin\theta+\cos\theta=1, \] then the value of \[ \sin\theta\cos\theta \] is:

If \(A\) and \(B\) are the minimum and maximum values of \[ \sin^6 x+\cos^6 x, \] then \(A+B=\)

The value of \[ \sin20^\circ\sin40^\circ\sin80^\circ \] is:

Evaluate \[ \frac{\cos\theta}{1-\cos\theta} + \frac{\sec\theta}{1+\sec\theta}. \]

The value of \[ \sin^2 15^\circ+\cos^2 15^\circ \] is

If \[ \tan\theta+\cot\theta=4, \] then the value of \[ \sec^2\theta+\csc^2\theta \] is:

If \[ \int \frac{dx}{2\sin^2x+\sin2x} = \frac12\log|f(x)|+C \] and \[ f\!\left(\frac{\pi}{4}\right)=\frac12, \] then \(f(x)\) is

Evaluate $\int \frac{x-1}{(x+1)^3}e^x dx$:

If \( F(x)=\int x(\log x)^{2} \, dx \) and \( F(e)=\frac{e^{2}}{4} \), then \( F(1) = \)

If $\int \frac{\cos 8x + 1}{\cot 2x - \tan 2x} dx = A\cos 8x + c$, then $A =$