1
MHT CET 2022 11th August Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $$\tan ^{-1}\left(\frac{1-x}{1+x}\right)=\frac{1}{2} \tan ^{-1} x$$, then $$x$$ has the value

A
3
B
1
C
$$\frac{1}{\sqrt{3}}$$
D
$$\sqrt{3}$$
2
MHT CET 2022 11th August Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $$p: \forall n \in I N, n^2+n$$ is an even number $$q: \forall n \in I N, n^2-n$$ is an odd numer, then the truth values of $$p \wedge q, p \vee q$$ and $$p \rightarrow q$$ are respectively

A
$$F, T, F$$
B
$$F, F, T$$
C
$$T, T, F$$
D
$$F, T, T$$
3
MHT CET 2022 11th August Evening Shift
MCQ (Single Correct Answer)
+2
-0

If the function $$f(x)=x^3-3(a-2) x^2+3 a x+7$$, for some $$a \in I R$$ is increasing in $$(0,1]$$ and decreasing in $$[1,5)$$, then a root of the equation $$\frac{f(x)-14}{(x-1)^2}=0(x \neq 1)$$ is

A
14
B
7
C
$$-$$14
D
$$-$$7
4
MHT CET 2022 11th August Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $$\bar{a}=\hat{\boldsymbol{i}}-\hat{\boldsymbol{k}}, \bar{b}=x \hat{\boldsymbol{i}}+\hat{\boldsymbol{j}}+(1-x) \hat{\boldsymbol{k}}$$ and $$\bar{c}=y \hat{\boldsymbol{i}}+x \hat{\boldsymbol{j}}+(1+x-y) \hat{\boldsymbol{k}}$$, then $$[\bar{a} \bar{b} \bar{c}]$$ depends on

A
only $$y$$
B
neither $$x$$ nor $$y$$
C
both $$x$$ and $$y$$
D
only $$x$$
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