Q.
Column I
Column II
A
In an A.P. the series containing 99 terms, the sum of all the odd numbered terms is 2550 . The sum of all the 99 terms of the A.P. is
P
5010
B
$f$ is a function for which $f(1)=1$ and $f( n )= n +f( n -1)$ for each natural number $n \geq 2$. The value of $f(100)$ is
Q
5049
C
Suppose, $f(n)=\log _2(3) \cdot \log _3(4) \cdot \log _4(5) \ldots \ldots \ldots \log _{n-1}(n)$ then the sum $\displaystyle\sum_{ k =2}^{100} f \left(2^{ k }\right)$ equals
R
5050
D
Concentric circles of radii $1,2,3 \ldots \ldots 100 cms$ are drawn. The interior of the smallest circle is coloured red and the annular regions are coloured alternately green and red, so that no two adjacent regions are of the same colour. The total area of the green regions in sq. cm is $k \pi$ then ' $k$ ' equals
S
5100
| Column I | Column II | ||
|---|---|---|---|
| A | In an A.P. the series containing 99 terms, the sum of all the odd numbered terms is 2550 . The sum of all the 99 terms of the A.P. is | P | 5010 |
| B | $f$ is a function for which $f(1)=1$ and $f( n )= n +f( n -1)$ for each natural number $n \geq 2$. The value of $f(100)$ is | Q | 5049 |
| C | Suppose, $f(n)=\log _2(3) \cdot \log _3(4) \cdot \log _4(5) \ldots \ldots \ldots \log _{n-1}(n)$ then the sum $\displaystyle\sum_{ k =2}^{100} f \left(2^{ k }\right)$ equals | R | 5050 |
| D | Concentric circles of radii $1,2,3 \ldots \ldots 100 cms$ are drawn. The interior of the smallest circle is coloured red and the annular regions are coloured alternately green and red, so that no two adjacent regions are of the same colour. The total area of the green regions in sq. cm is $k \pi$ then ' $k$ ' equals | S | 5100 |
Sequences and Series
Solution: