1
AP EAPCET 2025 - 24th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $y=\frac{3}{4}+\frac{3 \cdot 5}{4 \cdot 8}+\frac{3 \cdot 5 \cdot 7}{4 \cdot 8 \cdot 12}+\ldots+\infty$, then

A

$y^2-2 y+5=0$

B

$y^2+2 y-7=0$

C

$y^2-3 y+4=0$

D

$y^2+4 y-6=0$

2
AP EAPCET 2025 - 24th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

Sum of the coefficients of $x^4$ and $x^6$ in the expansion of $\left(1+x-x^2\right)^6$ is

A

121

B

-91

C

11

D

31

3
AP EAPCET 2025 - 23rd May Evening Shift
MCQ (Single Correct Answer)
+1
-0

If $11^{12}-11^2=k\left(5 \times 10^9+6 \times 10^9+33 \times 10^8\right. \left.+110 \times 10^7+\ldots+33\right)$, then $k=$

A

20

B

50

C

100

D

200

4
AP EAPCET 2025 - 23rd May Evening Shift
MCQ (Single Correct Answer)
+1
-0

If $C_0, C_2, \ldots, C_n$ are the binomial coefficients in the expansion of $(1+x)^n$, then

$$ \left(C_0+C_1\right)-\left(C_2+C_3\right)+\left(C_4+C_5\right)-\left(C_6+C_7\right)+\ldots= $$

A

$2^{n / 2}\left(\cos \frac{n \pi}{4}+i \sin \frac{n \pi}{4}\right)$

B

$2^{n / 2}\left(\cos \frac{n \pi}{3}+i \sin \frac{n \pi}{3}\right)$

C

$2^{n / 2}\left(\cos \frac{n \pi}{3}+i \sin \frac{n \pi}{3}\right)$

D

$2^{n / 2}\left(\cos \frac{n \pi}{4}+\sin \frac{n \pi}{4}\right)$

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