The ratio of ages of A and B is 3:4. After 6 years, their ages will be in the ratio 4:5. What is A's current age?
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?