1
JEE Main 2023 (Online) 10th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let the number $$(22)^{2022}+(2022)^{22}$$ leave the remainder $$\alpha$$ when divided by 3 and $$\beta$$ when divided by 7. Then $$\left(\alpha^{2}+\beta^{2}\right)$$ is equal to :

A
13
B
10
C
20
D
5
2
JEE Main 2023 (Online) 10th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If the coefficients of $$x$$ and $$x^{2}$$ in $$(1+x)^{\mathrm{p}}(1-x)^{\mathrm{q}}$$ are 4 and $$-$$5 respectively, then $$2 p+3 q$$ is equal to :

A
66
B
60
C
69
D
63
3
JEE Main 2023 (Online) 10th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If the coefficient of $${x^7}$$ in $${\left( {ax - {1 \over {b{x^2}}}} \right)^{13}}$$ and the coefficient of $${x^{ - 5}}$$ in $${\left( {ax + {1 \over {b{x^2}}}} \right)^{13}}$$ are equal, then $${a^4}{b^4}$$ is equal to :

A
22
B
33
C
44
D
11
4
JEE Main 2023 (Online) 8th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

$$25^{190}-19^{190}-8^{190}+2^{190}$$ is divisible by :

A
14 but not by 34
B
neither 14 nor 34
C
both 14 and 34
D
34 but not by 14
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