In a seating arrangement, 5 people (A, B, C, D, E) sit in a row. A and B must sit together, and C cannot sit at the ends. How many arrangements are possible?
What is the sum of the first 20 terms of the arithmetic sequence 3, 7, 11, ........?
A rectangle's length is twice its breadth. If the perimeter is 60 cm, what is its area?
In how many ways can 5 identical balls be distributed into 3 distinct boxes?
The roots of the quadratic equation $x^2 - 6x + k = 0$ are real and distinct. How many integer values of $k$ are possible if $k$ is positive?
A shopkeeper sells an item at a 20% discount but still makes a 20% profit. If the cost price is Rs. 100, what is the marked price?
What is the remainder when $7^{100}$ is divided by 8?
A train travels 360 km at a uniform speed. If the speed is increased by 5 km/h, the journey takes 1 hour less. Find the original speed.
If the sum of two numbers is 15 and their product is 56, what is the sum of their reciprocals?
If $\log_2 (x) + \log_4 (x) = 5$, what is $x$?
A circle is inscribed in an equilateral triangle with side length 12 cm. What is the radius of the circle?
What is the value of $2^{100} \mod 5$?
A and B can complete a task in 12 days, B and C in 15 days, and A and C in 20 days. How many days will A alone take?
What is the sum of the series $1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \ldots$?
If $3x + 4y = 12$ and $x - y = 1$, what is the value of $x + y$?
A bag contains 4 red and 5 blue balls. Two balls are drawn without replacement. What is the probability that both are red?
What is the value of $\sin 30^\circ + \cos 60^\circ$?
A number when divided by 7 leaves a remainder of 4. What is the remainder when its square is divided by 7?
The HCF of two numbers is 12, and their LCM is 144. If one number is 36, what is the other?
A car travels at 60 km/h for half the distance and 80 km/h for the other half. What is the average speed for the entire journey?
What is the number of solutions to $|x - 2| = |x - 4|$?
A pipe can fill a tank in 6 hours, and another pipe can empty it in 8 hours. If both are open, how long will it take to fill the tank?
The sum of the first $n$ natural numbers is 55. What is $n$?