If A is a 3x3 non- singular matrix such that AAT = ATA, then BBT is equal to
B-1
B-1
If f and ga re differentiable functions in (0,1) satisfying f(0) =2= g(1), g(0) = 0 and f(1) = 6, then for some c ε] 0,1[
2f'(c) = g'(c)
2f'(c) = 3g'(c)
f'(c) = g'(c)
f'(c) = g'(c)
D.
f'(c) = g'(c)
Given, f(0) = 2 = g(1), g(0) and f(1) = 6
f and g are differentiable in (0,1)
Let h(x) = f(x)-2g(x) .... (i)
h(0) = f(0)-2g(0)
h(0) = 2-0
h(0) = 2
and h(1) = f(1)-2g(1) = 6-2(2)
h(1) = 2, h(0) = h(1) = 2
Hence, using rolle's theorem
h'(c) = 0, such that cε (0,1)
Differentiating Eq. (i) at c, we get
f'(c) -2g'(c) = 0
f'(c) = 2g'(c)
If fk(x) = 1/k (sink x + cosk x), where x ε R and k ≥1, then f4 (x)-fo (x) equal to
1/6
1/3
1/4
1/4
Let A and B be two events such that where
. Then, the events A and B are
independent but not equally likely
independent and equally likely
mutually exclusive and independent
mutually exclusive and independent
If =-1 and x =2 are extreme points of f(x) =α log|x| + βx2 +x, then
α = -6, β = 1/2
α = -6, β = -1/2
α = 2, β = -1/2
α = 2, β = -1/2
Let the population of rabbits surviving at a time t be governed by the differential equation. If p(0) = 100 then p(t) is equal to