If [x] denotes the greatest integer less than or equal to x, then the value of the integral ∫02x2xdx equals
53
73
83
43
For non-zero vectors a and b, if a + b < a - b, then a and b are
collinear
perpendicular to each other
inclined at an acute angle
inclined at an obtuse angle
General solution of ydydx + by2 = acosx, 0 < x < 1 is
y2 = 2a2bsinx + cosx + ce- 2bx
4b2 + 1y2 = 2asinx + 2bcosx + ce- 2bx
4b2 + 1y2 = 2asinx + 2bcosx + ce2bx
B.
Given, ydydx + by2 = acosx, 0 < x < 1 ...(i)
Let y2 = z
⇒ 2ydydx = dzdx⇒ ydydx = dzdx ...(ii)∴ 12dzdx + by2 = acosx ∵ using Eq. (ii)⇒ dzdx + 2by2 = 2acosx
Now, IF = e2b∫dx = e2bx∴ z.e2bx = ∫2a4b2 + 1sinx + 2bcosxe2bx + C⇒ 4b2 + 1y2 = 2asinx + 2bcosx + Ce- 2bx
If ϕt = 1, for 0 ≤ t < 10, otherwise, then
∫- 30003000∑r' = 20142016ϕt - r'ϕt - 2016dt is
a real number
1
0
does not exist
If A, B are two events such that P(A ∪ B) ≥ 34 and 18 ≤ PA ∩ B ≤ 38 then
P(A) + PB ≤ 118
P(A) . P(B) ≤ 38
P(A) + P(B) ≥ 78
None of the above