The distance of the point of intersection of the line x - 23 = y + 14 = z - 212 and the plane x - y + z = 5 from the point (- 1, - 5, - 10)is
13
12
11
8
If the direction cosines of a line are 1c, 1c, 1c, then
0 < c < 1
c > 2
c = ± 2
c = ± 3
The vector form of the sphere 2(x2 + y2 + z2) - 4x + 6y + 8z - 5 = 0 is
r→ . r→ - 2i^ + j^ + k^ = 25
r→ . r→ - 2i^ - 3j^ - 4k^ = 12
r→ . r→ - 2i^ + 3j^ + 4k^ = 52
r→ . r→ - 2i^ - 3j^ - 4k^ = 52
If the lines 1 - x3 = y - 22α = z - 32x - 13α = y - 1 = 6 - z5 are perpendicular, then the value of α is
- 107
107
- 1011
1011
The distance between the lines r→ = 4i^ - 7j^ - 9k^ + t3i^ - 7j^ + 4k^ and r→ = 7i^ - 14j^ - 5k^ + s- 3i^ + 7j^ - 4k^ is equal to
1
34
0
∫x31 + x435dx is equal to
1 + x3465 + c
1 + x4365 + c
581 + x4365 + c
161 + x436 + c
If u = - f''θsinθ + f'θcosθ and v = f''θcosθ + f'θsinθ, then ∫dudθ2 + dvdθ212dθ is equal to
fθ - f''θ + c
fθ + f''θ + c
f'θ + f''θ + c
f'θ - f''θ + c
∫e6logex - e5logexe4logex - e3logexdx is equal to
x33 + c
x22 + c
x23 + c
- x33 + c
∫ex1 - x1 + x22dx is equal to
ex1 - x1 + x2 + c
ex11 + x2 + c
ex1 + x1 + x2
ex1 - x1 + x22 + c
∫x4 - 1x2x4 + x2 + 112dx is equal to
x4 + x2 + 1x + c
x2x4 + x2 + 1 + c
xx4 + x2 + 132 + c
D.
∫x4 - 1x2x4 + x2 + 112dx= ∫2x4 + x2 - x4 + x2 + 1x2x4 + x2 + 1dx= ∫x4x3 + 2x2x4 + x2 + 1 - x4 + x2 + 1x2dx= ∫ddxx4 + x2 + 1x = x4 + x2 + 1x + c