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

Let $$\Delta$$ $$\in$$ {$$\wedge$$, $$\vee$$, $$\Rightarrow$$, $$\Leftrightarrow$$} be such that (p $$\wedge$$ q) $$\Delta$$ ((p $$\vee$$ q) $$\Rightarrow$$ q) is a tautology. Then $$\Delta$$ is equal to :

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

Let $$\{ {a_n}\} _{n = 0}^\infty $$ be a sequence such that $${a_0} = {a_1} = 0$$ and $${a_{n + 2}} = 2{a_{n + 1}} - {a_n} + 1$$ for all n $$\ge$$ 0. Then, $$\sum\limits_{n = 2}^\infty {{{{a_n}} \over {{7^n}}}} $$ is equal to:

A
$${6 \over {343}}$$
B
$${7 \over {216}}$$
C
$${8 \over {343}}$$
D
$${{49} \over {216}}$$
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