1
JEE Main 2021 (Online) 18th March Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Let f : R $$-$$ {3} $$ \to $$ R $$-$$ {1} be defined by f(x) = $${{x - 2} \over {x - 3}}$$.

Let g : R $$ \to $$ R be given as g(x) = 2x $$-$$ 3. Then, the sum of all the values of x for which f$$-$$1(x) + g$$-$$1(x) = $${{13} \over 2}$$ is equal to :
A
3
B
5
C
2
D
7
2
JEE Main 2021 (Online) 18th March Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Let S1 be the sum of first 2n terms of an arithmetic progression. Let S2 be the sum of first 4n terms of the same arithmetic progression. If (S2 $$-$$ S1) is 1000, then the sum of the first 6n terms of the arithmetic progression is equal to :
A
7000
B
1000
C
3000
D
5000
3
JEE Main 2021 (Online) 18th March Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language
If P and Q are two statements, then which of the following compound statement is a tautology?
A
((P $$ \Rightarrow $$ Q) $$ \wedge $$ $$ \sim $$ Q) $$ \Rightarrow $$ (P $$ \wedge $$ Q)
B
((P $$ \Rightarrow $$ Q) $$ \wedge $$ $$ \sim $$ Q) $$ \Rightarrow $$ Q
C
((P $$ \Rightarrow $$ Q) $$ \wedge $$ $$ \sim $$ Q) $$ \Rightarrow $$ P
D
((P $$ \Rightarrow $$ Q) $$ \wedge $$ $$ \sim $$ Q) $$ \Rightarrow $$ $$ \sim $$ P
4
JEE Main 2021 (Online) 18th March Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language
Let a tangent be drawn to the ellipse $${{{x^2}} \over {27}} + {y^2} = 1$$ at $$(3\sqrt 3 \cos \theta ,\sin \theta )$$ where $$0 \in \left( {0,{\pi \over 2}} \right)$$. Then the value of $$\theta$$ such that the sum of intercepts on axes made by this tangent is minimum is equal to :
A
$${{\pi \over 6}}$$
B
$${{\pi \over 3}}$$
C
$${{\pi \over 8}}$$
D
$${{\pi \over 4}}$$
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