CBSE
Three houses are available in a locality. Three persons apply for the houses. Each applies to one house without consulting others. The probability that all the three apply for the same house is
2/9
1/9
8/9
7/9
B.
1/9
For a particular house being selected
Probability = 1/3
Prob(all the persons apply for the same house) =
If are non -coplanar vector λ is a real number then
exactly one value of λ
no value of λ
exactly three values of λ
exactly two values of λ
B.
no value of λ
The angle between the lines 2x = 3y = − z and 6x = − y = − 4z is
0^{o}
90^{o}
45^{o}
30^{o}
B.
90^{o}
Angle between the lines 2x = 3y = - z & 6x = -y = -4z is 90°
Since a_{1}a_{2} + b_{1}b_{2} + c_{1}c_{2} = 0
If the plane 2ax − 3ay + 4az + 6 = 0 passes through the midpoint of the line joining the centres of the spheres
x^{2} + y^{2} + z^{2} + 6x − 8y − 2z = 13 and x^{2} + y^{2} + z^{2} − 10x + 4y − 2z = 8, then a equals
-1
1
-2
2
C.
-2
Plane 2ax – 3ay + 4az + 6 = 0 passes through the mid point of the centre of spheres x^{2} + y^{2} + z^{2} + 6x – 8y – 2z = 13 and x^{2} + y^{2} + z^{2} – 10x + 4y – 2z = 8 respectively centre of spheres are (-3, 4, 1) & (5, - 2, 1) Mid point of centre is (1, 1, 1) Satisfying this in the equation of plane,
we get 2a – 3a + 4a + 6 = 0
⇒ a = -2.
The distance between the line and the plane
10/9
3/10
10/3
B.
Distance between the line
equation of plane is x + 5y + z = 5 ∴ Distance of line from this plane = perpendicular distance of point (2, -2, 3) from the plane
If a vertex of a triangle is (1, 1) and the mid-points of two sides through this vertex are (-1, 2) and (3, 2), then the centroid of the triangle is
(-1, 7/3)
(-1/3, 7/3)
(1, 7/3)
(1/3, 7/3)
C.
(1, 7/3)
Vertex of triangle is (1, 1) and midpoint of sides through this vertex is (-1, 2) and (3, 2) ⇒ vertex B and C come out to be (-3, 3) and (5, 3)
therefore centroid is
only y
only x
both x and y
neither x nor y
D.
neither x nor y
Let a, b and c be distinct non-negative numbers. If the vectors
the Geometric Mean of a and b
the Arithmetic Mean of a and b
equal to zero
the Harmonic Mean of a and b
A.
the Geometric Mean of a and b