nth group starts with $(n-1)$$^{2}$ $+$ $1$ and ends with $n$$^{2}$ and every group consists $2n-1$ numbers $15th$ group starts with 196 and ends with $225$ $sum$ = $\frac{No of terms}{2}$ * $[first$ $term$+$last$ $term]$ = $\frac{29}{2} * [(196+1) + 225]$ = 6119 [...]

Some standard limits and property of logarithms,   $1)\lim_{x \to 0} \dfrac{\tan x}{x} = 1$   $2)\lim_{x \to 0} \dfrac{\ln (x + 1) }{x} = 1$   $3) \ln (ab) = \ln a + \ln b$   Given limit , $\lim_{x \to 0} \dfrac{\ln ((x^2 +1) \cos x)}{x^2}$ we can rewrite it as,   $\lim_{x \to 0} \left(\dfrac{\ln (x^2 +1)}{x^2} + \dfrac{\ln (\cos x)}{x^2}\right)$   now lets evaluate individually,   Let $y=x^2$ ,as $x \to 0$ $y \to 0$, for the limit below we can use substitution with $y=x^2$   $\lim_{x \to 0}\dfrac{\ln (x^2 +1)}{x^2}$ $=\lim_{y \to 0}\dfrac{\ln (y +1)}{y}$ [...]

1. "$Bothered$" signifies a mild level of discomfort or concern. 2. "$ Daunted $" implies a much stronger feeling of being intimidated or overwhelmed. To maintain the analogy with the progression from "walk" to "jog" to "sprint," we need a word that represents an intermediate level of intensity between being bothered and being daunted. "$Fazed$" fits this criterion as it suggests a level of perturbation or discomposure that is stronger than being bothered but not as intense as being daunted. $(C)$ is correct. [...]

acknowledge-Ignored [...]

Another Approach: It is given 4th term=8 so consider an AP with 7 terms as following a-3d , a-2d , a-d , a , a+d , a+2d , a+3d Here 4th term = a = 8 Sum of the above series= 7*8=56 Answer= 56 [...]

B [...]