1
WB JEE 2021
+1
-0.25
Let a, b, c be real numbers, each greater than 1, such that $${2 \over 3}{\log _b}a + {3 \over 5}{\log _c}b + {5 \over 2}{\log _a}c = 3$$. If the value of b is 9, then the value of 'a' must be
A
$$\root 3 \of {81}$$
B
$${{27} \over 2}$$
C
18
D
27
2
WB JEE 2021
+1
-0.25
Consider the real valued function h : {0, 1, 2, ...... 100} $$\to$$ R such that h(0) = 5, h(100) = 20 and satisfying h(p) = $${1 \over 2}$$ {h(p + 1) + h(p $$-$$ 1)} for every p = 1, 2 ..... 99. Then the value of h(1) is
A
5.15
B
5.5
C
6
D
6.15
3
WB JEE 2021
+1
-0.25
The digit in the unit's place of the number 1! + 2! + 3! + .... + 99! is
A
3
B
0
C
1
D
7
4
WB JEE 2021
+2
-0.5
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
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