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 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?
Input: fight for all 39 62 25 today 19Which of the following steps will be step IV?
At the end of a business conference, the ten people present all shake hands with each other once. How many handshakes will there be altogether?
The Supreme Court has recently asked to re-introduce the VVPAT in Electronic Voting Machines (EVMs) for 100% transparency in electronics. The VVPAT in EVM would ensure free and fair polls besides sorting out disputes. What does VVPAT stand for?
What is the symbol of Jammu & Kashmir People's Democratic Party which was founded by Mufti Mohammed Sayeed?
Who has been awarded as the Indian of the year award by Brands Academy in New Delhi this year?
Which bank has announced to acquire mobile payment wallet provider FreeCharge from e-commerce company Snapdeal for Rs. 385 crore?
What is the nick-name of famous Indian Personalities 'Sayeed Bandhu'?
'Salvex' is a military exercise between which two countries?
