Algebra
Let x - 1/x = 3, find x^2 + 1/x^2
11
If a rectangle has a length of 30 cm and a width of 16 cm, what is the length of its diagonal?
34 cm
Amy, Chintan, Ayush, and Rudra have to choose a group of 2 between them to join the soccer team with Kartik. What number of combinations are possible?
6
What is ∫x2 dx?
x^3/3 + C
What is the GCD of 18, 24
6
Let x+y+z = 6, xy+yz+xz = 11, xyz = 6, find x^2+y^2+z^2
14
A circle has a radius of 12 cm. What is the area of the sector formed by a central angle of 40°?
16 pi cm^2
This is the number of different ways to rearrange the letters KARTIK.
360
What is ∫ 3x*sqrt(x2 + 4) dx?
(x2+4)3/2 + C
What is the (LCM of 67, 2, 5)/10
67
Solve for x: log3(x)+ log9(x) = 3
x = 9
If a regular hexagon is inscribed in a circle of radius 14 cm, what is the area of the hexagon?
294*sqrt(3)
Kartik, Amy, Chintan, and Ayush (sorry Rudra) have to enter a car. When they get into the car, two people will sit in the front, and the other two will sit in the back. Either Kartik or Ayush must sit in the driver's seat. This is the number of seating arrangements that are possible.
12
What is ∫x*e-2x dx?
-e-2x * (x/2 + 1/4) + C
What is 1^3 + 2^3 + ... + 10^3?
3025
Let f(x+1)-f(x)=6x+7 and f(0)=6, find f(10)
346
A rhombus has diagonals with lengths 24 and 10. A circle is inscribed in the rhombus. What is the area of the inscribed circle?
3600 pi/169
A game is played. In each round, the player with the most tokens gives one token to each of the other players and also places one token in a discard pile. The game ends when any player runs out of tokens. Players A, B, and C start with 15, 14, and 13 tokens, respectively. This is the number of rounds there will be in the game.
37
What is ∫1∞ ln(x)/x3 dx?
1/4
How many divisors does 2^66 have?
67
Let r and s be the roots of x^2-6x+10=0, find (r^2+1)(s^2+1)
117
What is the area of the green traingle? (Show Image on Slides)
225*sqrt(3)
Round-robin tournament with 6 teams, each team plays one game against each other team. Each game results in one team winning and one team losing. At the end, teams are ranked by the number of games won. This number is the max teams that could be tied for the most wins at the end of the tournament.
5
What is ∫ (5x + 7)/[(x - 1)*(x2 + 4)] dx?
12/5*ln|x - 1| - 6/5*ln(x2+4) + 13/10*tan-1(x/2) + C
What is the remainder when 7^67 is divided by 100?
43