Let . If , , then 3(b + c) is equal to [2025]
39
22
40
26
(1)
Given,
Let
b = 4 and c = 9
3(b + c) = 3(4 + 9) = 39.
Let , where C is the constant of integration. If , then equals: [2025]
47
62
48
55
(4)
So,
and
So, .
Let be a function which is differentiable at all points of its domain and satisfies the condition , with f(1) = 4. Then 2f(2) is equal to : [2025]
23
19
29
39
(4)
Given, and f(1) = 4
(Divide both sides by )
Using integration on both sides,
Since f(1) = 4
Now, we get f(x)
.
If , f(0) = – 6, then f(1) is equal to : [2025]
(2)
We have,
Putting
If where C is the constant of integration and m, n N, then m + n is equal to __________. [2025]
(379)
Let (On rationalising)
Let
So,
Then, m = 360, n = 19
m + n = 360 + 19 = 379.
If , x > 0, , where c is the constant of integration, then is equal to __________. [2025]
(19)
We have,
Put
Now,
On comparing, we get
.
If , where C is the constant of integration, then is equal to __________. [2025]
(16)
Given integral is
Using partial fraction decomposition, we get
Comparing terms, we get
On comparing, we get
Hence, .