1
JEE Main 2021 (Online) 18th March Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
In a triangle ABC, if $$|\overrightarrow {BC} | = 8,|\overrightarrow {CA} | = 7,|\overrightarrow {AB} | = 10$$, then the projection of the vector $$\overrightarrow {AB} $$ on $$\overrightarrow {AC} $$ is equal to :
A
$${{25} \over 4}$$
B
$${{127} \over 20}$$
C
$${{85} \over 14}$$
D
$${{115} \over 16}$$
2
JEE Main 2021 (Online) 18th March Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Define a relation R over a class of n $$\times$$ n real matrices A and B as

"ARB iff there exists a non-singular matrix P such that PAP$$-$$1 = B".

Then which of the following is true?
A
R is reflexive, transitive but not symmetric
B
R is symmetric, transitive but not reflexive.
C
R is reflexive, symmetric but not transitive
D
R is an equivalence relation
3
JEE Main 2021 (Online) 18th March Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Let the centroid of an equilateral triangle ABC be at the origin. Let one of the sides of the equilateral triangle be along the straight line x + y = 3. If R and r be the radius of circumcircle and incircle respectively of $$\Delta$$ABC, then (R + r) is equal to :
A
$$7\sqrt 2 $$
B
$${9 \over {\sqrt 2 }}$$
C
$$2\sqrt 2 $$
D
$$3\sqrt 2 $$
4
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
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