1
WB JEE 2024
MCQ (Single Correct Answer)
+1
-0.25
Change Language

If $$\left(1+x+x^2+x^3\right)^5=\sum_\limits{k=0}^{15} a_k x^k$$ then $$\sum_\limits{k=0}^7(-1)^{\mathbf{k}} \cdot a_{2 k}$$ is equal to

A
25
B
45
C
0
D
44
2
WB JEE 2024
MCQ (Single Correct Answer)
+1
-0.25
Change Language

The coefficient of $$a^{10} b^7 c^3$$ in the expansion of $$(b c+c a+a b)^{10}$$ is

A
140
B
150
C
120
D
160
3
WB JEE 2022
MCQ (Single Correct Answer)
+1
-0.25
Change Language

The number of zeros at the end of $$\left| \!{\underline {\, {100} \,}} \right. $$ is

A
21
B
22
C
23
D
24
4
WB JEE 2021
MCQ (Single Correct Answer)
+1
-0.25
Change Language
For x$$\in$$R, x $$\ne$$ $$-$$1, if $${(1 + x)^{2016}} + x{(1 + x)^{2015}} + {x^2}{(1 + x)^{2014}} + ..... + {x^{2016}} = \sum\limits_{i = 0}^{2016} {{a_i}\,.\,{x^i}} $$, then a17 is equal to
A
$${{2016!} \over {17!1999!}}$$
B
$${{2016!} \over {16!}}$$
C
$${{2017!} \over {2000!}}$$
D
$${{2017!} \over {17!2000!}}$$
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