List of top Mathematics Questions asked in AP EAPCET

Investigate the values of $\lambda$ and $\mu$ for the system $x+2 y+3 z=6, x+3 y+5 z=9$, $2 x+5 y+\lambda z=\mu$ and match the values in List - I with the items in List - II.
List I List II
(A) $\lambda=8, \mu \neq 15$ 1. Infinitely many solutions
(B) $\lambda \neq 8, \mu \in R$ 2. No solution
(C) $\lambda=8, \mu=15$ 3. Unique solution

Given below are two statements, one is labelled as Assertion A and the other is labelled as Reason R
Assertion (A) : (1) \(+(1+2+4)+(4+6+9) +(9+12+16)+\ldots+(81+90+100)=1000\) 

Reason (R) : \(\displaystyle \sum_{r=1}^{n}\left(r^{3}-[r-1]^{3}\right)=n^{3}\) for any natural number \(n\)

In the light of the above statements, choose the correct answer from the options given below

If $z = x + iy , x , y \in R$ and the imaginary part of $\frac{\bar{z} - 1}{\bar{z} - i}$ is $1$ then the locus of $z$ is
Which of the following is divisible by $x^{2}-y^{2}, \forall x\ne y$?