Find the remainder when the $41$-digit number $1234\ldots$ is divided by $8$.
Find the value of $\log_{20} 100 + \log_{20} 1000 + \log_{20} 10000 \quad \bigl[\textit{Assume that } \log 2 = 0.3\bigr].$
If $\log x-5\log 3=-2$, then $x$ equals
The difference between compound interest (CI) and simple interest (SI) on a sum for $4$ years is ₹ $1282$. Find the sum.I. Amount of simple interest accrued after $4$ years is ₹ $4000$.II. Rate of interest is $10\%$ per annum.
A 540 m-long rectangular plot is to be fenced. Find the cost of fencing per square metre.I. Breadth of the plot is $60$ m.II. Length of the plot is $120$ m.
A shopkeeper sells some articles at a profit of $20\%$ on the cost price. Find the amount of profit.I. Cost price of the article is Rs. $2400$.II. Selling price of the article is Rs. $480$ more than the cost price.
The weights of $A$, $B$ and $C$ are in the ratio $8:7:5$. $A$'s weight is $60\%$ more than $C$'s. Find the weight of $B$.I. Total weight of $A,B,C$ is $300$ kg.II. Difference between $A$'s and $C$'s weight is $45$ kg.
A train running at a certain speed crosses a platform in $30$ seconds. What is the speed of the train?I. Length of the train is $240$ m.II. The train crosses a man who is on the platform in $12$ seconds.
$X=$ Marked price of Laptop; $Y=$ Marked price of A.C. Decide the relation between $X$ and $Y$.
$X=$ Profit amount of Mobile; $Y=$ Discount amount of Mobile. Decide the relation between $X$ and $Y$.
$X=$ Cost price of Cooler; $Y=$ Profit amount of Laptop. Decide the relation between $X$ and $Y$.
$X=$ Average profit amount of all items; $Y=$ Average discount amount of all items. Decide the relation between $X$ and $Y$.
$X=$ Average cost price of A.C and Mobile; $Y=$ Cost price of Laptop. Decide the relation between $X$ and $Y$.
Find the remainder when \[6^{\underbrace{66\cdots6}_{100 \text{ times}}}\] is divided by 10.
Find the value of $1(1!)+2(2!)+3(3!)+\cdots+20(20!)$.
If $(67^{67}+67)$ is divided by $68$, the remainder is:
What is the remainder when $1!+2!+3!+\cdots+100!$ is divided by $7$?
There are two integers 34041 and 32506, when divided by a three-digit integer $n$, leave the same remainder. What is the value of $n$?
Mantle of the earth crust is ?