What is the remainder when $1!+2!+3!+\cdots+100!$ is divided by $7$?
If $(67^{67}+67)$ is divided by $68$, the remainder is:
Find the value of $1(1!)+2(2!)+3(3!)+\cdots+20(20!)$.
Find the remainder when \[6^{\underbrace{66\cdots6}_{100 \text{ times}}}\] is divided by 10.
Find the value of $\log_{20} 100 + \log_{20} 1000 + \log_{20} 10000 \quad \bigl[\textit{Assume that } \log 2 = 0.3\bigr].$
Find the remainder when the $41$-digit number $1234\ldots$ is divided by $8$.
In a survey of $500$ TV viewers: $285$ watch football (F), $195$ hockey (H), $115$ basketball (B); $45$ watch F&B, $70$ watch F&H, $50$ watch H&B, and $50$ watch none. How many watch exactly one of the three games?
Nine squares are chosen at random on a chessboard. What is the probability that they form a square of size $3\times 3$?
$A,B,C,D$ are four towns, any three of which are non-colinear. In how many ways can we construct three roads (each road joins a pair of towns) so that the roads do not form a triangle?
In the figure, $\triangle APB$ is formed by three tangents to a circle with centre $O$. If $\angle APB=40^\circ$, then the measure of $\angle BOA$ is
If $1+\sin^2(2A)=3\sin A\cos A$, then what are the possible values of $\tan A$?
If \[ 2\sin\alpha + 15\cos^{2}\alpha = 7, \quad 0^\circ < \alpha < 90^\circ, \] find \(\cot\alpha\).
In the given figure, $ABCD$ is a rectangle. $P$ and $Q$ are the midpoints of sides $CD$ and $BC$ respectively. Then the ratio of area of shaded portion to the area of unshaded portion is:
In the adjoining figure, points $A,B,C,D$ lie on a circle. $AD=24$ and $BC=12$. What is the ratio of the area of $\triangle CBE$ to that of $\triangle ADE$?
In $\triangle ABC$, $D$ is a point on $BC$ such that $3BD=BC$. If each side of the triangle is $12\,$cm, then $AD$ equals
World Earth Day which is annually observed worldwide wherein various events are held to demonstrate support for environmental protection is celebrated on ______________ .
Which football superstar has been named as the World's Best Player for 2016 by FIFA?
Which mobile telecom company has launched the Asia-Africa-Europe (AAE-1) submarine cable system, the longest 100GBps technology-based submarine system?
Elephant has shown at Indian Museum on which day?
Which of the following animal is national animal of China?
Step III of an input is: take 17 mind game 29 73 18 loudHow many more steps are required to complete the sequence?
Input: by now 51 32 for 91 20 meWhich of the following steps will be the last?
Input: fight for all 39 62 25 today 19Which of the following steps will be step IV?
Input: queen mary 79 62 172 60 green westWhich of the following steps will be the last one?
What is the missing number in the sequence?
