Coordinate Geometry
If the vertices of a triangle are (9,9) (10, 1) and (6,7) , find the co-ordinates of its orthocentre.
(A) (9,9)
(B) (6,7)
(C)(4,5)
(D)(25/3, 17/3)
Question of the day
1000 Rooms
There are 1000 rooms in a row along a long corridor. Initially the first room contains 1000 people and the remaining rooms are empty. Each minute, the following happens:
for each room containing more than one person, someone in that room decides it is too crowded and moves to the next room. All these movements are simultaneous (so nobody moves more than once within a minute). After one hour, how many different rooms will have people in them?
after 2n minutes, the first room contains 1000 − 2n people and the next n rooms each contain 2 people, and after 2n + 1 minutes, the first room contains 1000 − (2n + 1) people, the next n rooms each contain 2 people, and the next room after that contains 1 person. So, after 60 minutes, we have one room with 940 people and 30 rooms with 2 people each.
See our previous ‘Puzzles of the Day’:
Counting
In how many ways is it possible to choose two black square on a 8 × 8 chessboard so that the squares do not lie in the same row or column ?
A. 400
B. 200
C. 800
D. None of these
See our previous ‘Questions of the Day’:
Equal Products
Each of the seven digits from 0, 1 , 2 ,3 4, 5, 6, 7, 8 and 9 is :
[1] Represented by a different letter in the figure above.
[2] Positioned in the figure above so that A × B × C, B×G ×E ,
and D × E × F are equal.
Which digit does G represent ?
Algebra
The numbers 2, 5, a are the roots of the equation x3 − bx2 + 5x + c = 0. Find the values of b and c.
Arithmetic
Ghajini and Rajni love solving math problems and each one of them solves them at a constant rate. Ghajini can solve a particular assignment containing math problems working alone in 6 hours work whereas Rajni can solve the same assignment in 8 hours. If they solve together, they can discuss the problems and this helps to enhance their efficiency in solving problems . So, their combined problem solving rates is the sum of their individual rates plus 2 additional problems per hour. Working together, they complete the same problem assignment in 3 hours. How many problems are on the assignment?
Grouping and Selections
Three groups are formed from three professors – P, Q and R – three lecturers – A, B and C – and six students – U , V , W , X , Y and Z. Each group consists of exactly one professor , one lecturer and two students . W and X are in one group but not in the groups of P or Q. V and Y are not in the the same group. Q and B are in the same group . Which of the following can be a correct combination of one of the groups ?
(A) R – A – VU
(B) Q – B – WX
(C)P – A – YZ
(D) R – C – YZ
Each of the three groups consists of one professor out of P, Q, R; one lecturer out of A , B and C; two students out of U, V, W,X,Y,Z that means P, Q , R are in three different groups and so are A, B and C.
W and X are in one group but not in the group of P and Q, that means they are in R’s group.
U and Z are not in the same group.
V and Y are not in the same group.
Q and B are in the same group.
So A and C must be in the groups of P and R. So, the groups can be as follows:
Group – I | Group – II | Group – III |
| R ( A or C) WX | Q B ( VU or YZ) | P |
So the correct combination out of the given 4 choices is P – A – YZ.
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See our previous ‘Puzzles of the Day’:
Regular Polygon- Geometry
A regular polygon has an even number of sides . If the product of the length of its side and the distance between two opposite sides is 1/4th of its area. Find the number of sides it has .
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