1
AP EAPCET 2022 - 4th July Morning Shift
MCQ (Single Correct Answer)
+1
-0

A person writes letters to 6 friends and addresses the corresponding envelopes. In how many ways can the letters be placed in the envelopes so that at least two of them are in the wrong envelopes? Notation $$D_n=n!\left(\sum_\limits{i=0}^n \frac{(-1)^i}{i!}\right)$$

A
$${ }^6 C_4 \cdot D_2$$
B
$$\sum_\limits{r=3}^6{ }^6 C_{6-r} \cdot D_r$$
C
$$\sum_\limits{r=2}^6{ }^6 C_{6-r} \cdot D_r$$
D
$${ }^6 C_1 D_5+{ }^6 C_0 \cdot D_6$$
2
AP EAPCET 2022 - 4th July Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $$\frac{x^4+24 x^2+28}{\left(x^2+1\right)^3}=\frac{A x+B}{x^2+1}$$ $$+\frac{C x+D}{\left(x^2+1\right)^2}+\frac{E x+F}{\left(x^2+1\right)^3},$$ then the value of $$A+B+C+D+E+F=$$

A
21
B
22
C
28
D
29
3
AP EAPCET 2022 - 4th July Morning Shift
MCQ (Single Correct Answer)
+1
-0

The value of $$\frac{\sin \theta+\sin 3 \theta}{\cos \theta+\cos 3 \theta}$$ is

A
$$\cos 2 \theta$$
B
$$\cot 2 \theta$$
C
$$\tan 2 \theta$$
D
$$\operatorname{cosec} \theta+\sin \theta$$
4
AP EAPCET 2022 - 4th July Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $$(1+\tan 1^{\circ})(1+\tan 2^{\circ}) \ldots(1+\tan 45^{\circ})=2^n,$$ then $$n=$$

A
0
B
32
C
23
D
2
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