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

$$\overline{\mathrm{a}}, \overline{\mathrm{b}}, \overline{\mathrm{c}}$$ are vectors such that $$|\overline{\mathrm{a}}|=5,|\overline{\mathrm{b}}|=4,|\overline{\mathrm{c}}|=3$$ and each is perpendicular to the sum of the other two, then $$|\overline{\mathrm{a}}+\overline{\mathrm{b}}+\overline{\mathrm{c}}|^2=$$

A
60
B
12
C
47
D
50
2
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
3
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
$$\mathrm{(\sim p\wedge q)\to (r \wedge s)}$$
4
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
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