1
JEE Main 2022 (Online) 29th June Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $$A = [{a_{ij}}]$$ be a square matrix of order 3 such that $${a_{ij}} = {2^{j - i}}$$, for all i, j = 1, 2, 3. Then, the matrix A2 + A3 + ...... + A10 is equal to :

A
$$\left( {{{{3^{10}} - 3} \over 2}} \right)A$$
B
$$\left( {{{{3^{10}} - 1} \over 2}} \right)A$$
C
$$\left( {{{{3^{10}} + 1} \over 2}} \right)A$$
D
$$\left( {{{{3^{10}} + 3} \over 2}} \right)A$$
2
JEE Main 2022 (Online) 29th June Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let a set A = A1 $$\cup$$ A2 $$\cup$$ ..... $$\cup$$ Ak, where Ai $$\cap$$ Aj = $$\phi$$ for i $$\ne$$ j, 1 $$\le$$ j, j $$\le$$ k. Define the relation R from A to A by R = {(x, y) : y $$\in$$ Ai if and only if x $$\in$$ Ai, 1 $$\le$$ i $$\le$$ k}. Then, R is :

A
reflexive, symmetric but not transitive.
B
reflexive, transitive but not symmetric.
C
reflexive but not symmetric and transitive.
D
an equivalence relation.
3
JEE Main 2022 (Online) 29th June Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The distance between the two points A and A' which lie on y = 2 such that both the line segments AB and A' B (where B is the point (2, 3)) subtend angle $${\pi \over 4}$$ at the origin, is equal to :

A
10
B
$${48 \over 5}$$
C
$${52 \over 5}$$
D
3
4
JEE Main 2022 (Online) 29th June Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

A wire of length 22 m is to be cut into two pieces. One of the pieces is to be made into a square and the other into an equilateral triangle. Then, the length of the side of the equilateral triangle, so that the combined area of the square and the equilateral triangle is minimum, is :

A
$${{22} \over {9 + 4\sqrt 3 }}$$
B
$${{66} \over {9 + 4\sqrt 3 }}$$
C
$${{22} \over {4 + 9\sqrt 3 }}$$
D
$${{66} \over {4 + 9\sqrt 3 }}$$
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