CBSE 11TH MATHEMATICS - Online Test
Equation of the line which is perpendicular to the given line x + y = 6 is x - y + k = 0
Since it passes through the point (4,3)
4 - 3 + k = 0
Therefore k = -1
Hence the equation of the line segment PQ is x - y - 1 = 0
On solving these two lines we get x = 7/2 and y = 5/2
This point of intersection is the midpoint of the line segement PQ
That is = 7/2 Hence x = 3
Similarly = 5/2. Hence y = 2
Hence the coordiates of the point Q is (3,2)
slope form of normal is y=mx-2am-am3
for the given parabola a = 2 and m = 1
therefore y = x -4 -2
i.e; x - y - 6 = 0
total no. of outcomes=62=36
The pair which shows 6 on either dice are {(6,1),(6,2),(6,3),(6,4),(6,5),(1,6),(2,6),(3,6),(4,6),(5,6),(6,6)}=11
So total number of sample points in sample space when 6 on either dice do not appear=36-11=25
represents
represents the plane z=0 as the equation can be written as 
| t th | th | h | t | o |
| 1 | 2 | 3 | 4 | 2 |
Since we need an even number , ones place can be occupied by only two numbers 2 and 4 in two ways.
Since repetition is not allowed tens place is occupied by remaining 4 numbers in 4 ways and the hundred's place by 3 ways and thousands place in 2 ways.
Hence total number of even numbers can be formed in 1x2x3x4x2 = 48.
