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 ≥ 2. The value of f(100) is Q 5049 C Suppose, f(n)= log 2(3) ⋅ log 3(4) ⋅ log 4(5) ldots ldots ldots log n-1(n) then the sum displaystyle∑ k =2100 f (2 k ) 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 π then ' k ' equals S 5100

Question

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 ≥ 2. The value of f(100) is Q 5049 C Suppose, f(n)= log 2(3) ⋅ log 3(4) ⋅ log 4(5) ldots ldots ldots log n-1(n) then the sum displaystyle∑ k =2100 f (2 k ) 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 π then ' k ' equals S 5100 (A) (A) Q ; (B) R ; (C) Q ; (D) P (B) (A) Q ; (B) R ; (C) Q ; (D) Q (C) (A) Q ; (B) R ; (C) Q ; (D) R (D) (A) Q ; (B) R ; (C) Q ; (D) S

Tardigrade Admin · Accepted Answer

Correct answer is (c) (A) Q ; (B) R ; (C) Q ; (D) R

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, $f (n) = lo g_{2} (3) \cdot lo g_{3} (4) \cdot lo g_{4} (5) \dots\dots\dots lo g_{n - 1} (n)$ then the sum $k = 2 \sum 100 f (2^{k})$ equals	R	5050
D	Concentric circles of radii $1, 2, 3 \dots\dots 100 c m s$ 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 $kπ$ then ' $k$ ' equals	S	5100