An unbiased coin is tossed n times. Let X denotes the number of times head occurs. If P(X = 4 ), P(X = 5) and PX = 6) are in AP, then the value of n can be
7, 14
10, 14
12, 7
None of these
Let X and Y be two events such that P(X/Y) = 1/2, P(Y/X) = 1/3 and P(X ∩ Y) = 1/6. Which of the following is incorrect?
P(X Y) = 2/3
X and Y are independent
P(XC ∩ Y) = 2/3
X and Y are not independent
If a, b, c and a', b',c' form a reciprocal system of vectors, then a . a'+ b . b' + c · c' is equal to
0
1
2
3
If a, b, c are three non - zero vectors which are pairwise non-collinear. Also, a + 3b is collinear with c and b + 2c is collinear with a, then a + 3b + 6c is
c
0
a + c
a
The area between the curve y = 2x4 - x2, the X-axis and the ordinates of two minima of the curve is
7/120
9/120
11/120
13/120
The equation of the plane through the intersection of the planes x + y + z = 1 and 2x + 3y - z + 4 = 0 and parallel to X-axis, is
y - 3z + 6 = 0
3y - z + 6 = 0
y + 3z + 6 = 0
3y - 2z + 6 = 0
A.
y - 3z + 6 = 0
The equation of the plane through the intersection of the planes x + y + z = 1 and 2x + 3y - z + 4 = 0 is
(x + y + z - 1) + (2x + 3y - z + 4) = 0
or (2 + 1)x + (3 + 1)y + (1 - )z + 4 - 1 = 0 ...(i)
It is parallel to x-axis i.e., = z/0
On substituting = - 1/2 in Eq. (i) we get y - 3z + 6 = 0 as the equation of the required plane.