1
WB JEE 2021
MCQ (Single Correct Answer)
+2
-0.5
Change Language
The coefficient of a3b4c5 in the expansion of (bc + ca + ab)6 is
A
$${{12!} \over {3!4!5!}}$$
B
$${{6!} \over {3!}}$$
C
33
D
$$3\,.\,\left( {{{6!} \over {3!3!}}} \right)$$
2
WB JEE 2021
MCQ (Single Correct Answer)
+2
-0.5
Change Language
Three unequal positive numbers a, b, c are such that a, b, c are in G.P. while $$\log \left( {{{5c} \over {2a}}} \right),\log \left( {{{7b} \over {5c}}} \right),\log \left( {{{2a} \over {7b}}} \right)$$ are in A.P. Then a, b, c are the lengths of the sides of
A
an isosceles triangle
B
an equilateral triangle
C
a scalene triangle
D
a right-angled triangle
3
WB JEE 2021
MCQ (Single Correct Answer)
+2
-0.5
Change Language
The determinant $$\left| {\matrix{ {{a^2} + 10} & {ab} & {ac} \cr {ab} & {{b^2} + 10} & {bc} \cr {ac} & {bc} & {{c^2} + 10} \cr } } \right|$$ is
A
divisible by 10 but not by 100
B
divisible by 100
C
not divisible by 100
D
not divisible by 10
4
WB JEE 2021
MCQ (Single Correct Answer)
+2
-0.5
Change Language
Let R be the real line. Let the relations S and T or R be defined by

$$S = \{ (x,y):y = x + 1,0 < x < 2\} ,T = \{ (x,y):x - y$$ is an integer}. Then
A
both S and T are equivalence relations on R
B
T is an equivalence on R but S is not
C
neither S nor T is an equivalence relation on R
D
S is an equivalence relation on R but T is not
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