1
JEE Main 2023 (Online) 10th April Morning Shift
+4
-1

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
2
JEE Main 2023 (Online) 8th April Evening Shift
+4
-1

$$25^{190}-19^{190}-8^{190}+2^{190}$$ 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
3
JEE Main 2023 (Online) 8th April Evening Shift
+4
-1

The absolute difference of the coefficients of $$x^{10}$$ and $$x^{7}$$ in the expansion of $$\left(2 x^{2}+\frac{1}{2 x}\right)^{11}$$ is equal to :

A
$$11^{3}-11$$
B
$$13^{3}-13$$
C
$$12^{3}-12$$
D
$$10^{3}-10$$
4
JEE Main 2023 (Online) 8th April Morning Shift
+4
-1
Out of Syllabus

If the coefficients of three consecutive terms in the expansion of $$(1+x)^{n}$$ are in the ratio $$1: 5: 20$$, then the coefficient of the fourth term is

A
3654
B
1827
C
5481
D
2436
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