If $x_1 = -1$ and $x_m = x_{m+1} + (m+1)$ for every positive integer $m$, then $x_{100}$ equals

Let $N$, $x$ and $y$ be positive integers such that $N = x + y$, $2 < x < 10$ and $14 < y < 23$. If $N > 25$, then how many distinct values are possible for $N$?

Let $\log_a 30 = A$, $\log_a \dfrac{5}{3} = -B$ and $\log_2 a = \dfrac{1}{3}$, then $\log_3 a$ equals

A contractor agreed to construct a $6$ km road in $200$ days. He employed $140$ persons for the work. After $60$ days, he realized that only $1.5$ km road has been completed. How many additional people would he need to employ in order to finish the work exactly on time?

The area, in sq. units, enclosed by the lines $x = 2$, $y = |x-2| + 4$, the $X$-axis and the $Y$-axis is equal to

Dick is thrice as old as Tom and Harry is twice as old as Dick. If Dick's age is $1$ year less than the average age of all three, then Harry's age, in years, is

How many of the integers $1, 2, \ldots, 120$, are divisible by none of $2$, $5$ and $7$?

In the final examination, Bishnu scored $52\%$ and Asha scored $64\%$. The marks obtained by Bishnu is $23$ less, and that by Asha is $34$ more than the marks obtained by Ramesh. The marks obtained by Geeta, who scored $84\%$, is

If $f(x+y) = f(x)f(y)$ and $f(5) = 4$, then $f(10) - f(-10)$ is equal to

$2^{(\log_2 4)^2} \times 4^{(\log_4 8)^3} \times 8^{(\log_8 16)^4}$ equals