1
MHT CET 2021 20th September Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $$\frac{n !}{2 !(n-2) !}$$ and $$\frac{n !}{4 !(n-4) !}$$ are in the ratio $$2: 1$$, then $$n=$$

A
6
B
4
C
5
D
3
2
MHT CET 2021 20th September Evening Shift
MCQ (Single Correct Answer)
+2
-0

p : It rains today

q : I am going to school

r : I will meet my friend

s : I will go to watch a movie.

Then symbolic form of the statement "If it does not rain today or I won't go to school, then I will meet my friend and I will go to watch a movie" is

A
$$\mathrm{\sim(p\vee q)\to (r \vee s)}$$
B
$$\mathrm{(p\wedge q)\to (r \vee s)}$$
C
$$\mathrm{\sim(p\wedge q)\to (r \wedge s)}$$
D
$$\mathrm{(\sim p\wedge q)\to (r \wedge s)}$$
3
MHT CET 2021 20th September Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $$a=\lim _\limits{n \rightarrow \infty} \frac{1+2+3+\ldots+n}{n^2}$$ and $$b=\lim _\limits{n \rightarrow \infty} \frac{1^2+2^2+3^2+\ldots+n^2}{n^3}$$, then

A
a = b
B
2a = 3b
C
a = 2b
D
3a = 2b
4
MHT CET 2021 20th September Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $$\omega$$ is complex cube root of unity and $$(1+\omega)^7=A+B\omega$$, then values of A and B are, respectively

A
0, 1
B
1, 1
C
1, 0
D
$$-$$1, 1
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