Match List-I with List-II. Match List-I with List-II. List – I Chemical Compound List – II Used as (a) Sucralose (i) Synthetic... View Article
The value of ∫24 [(log t) / t] dt is 1) (1 / 2) (log 2)2 2) (5 / 2) (log 2)2 3) (3 / 2) (log 2)2 4) (log 2)2 5) (3 / 2) (log 2) Solution: (3) (3 / 2) (log 2)2... View Article
The value of ∫01 [x3 / (1 + x8)] dx is 1) π/8 2) π/4 3) π/16 4) π/6 5) π/12 Solution: (3) π/16... View Article
The value of ∫1e {[1 + log x] / (3x)} dx = 1) 1/4 2) 1/2 3) 3/4 4) e 5) 1/e Solution: (2) ½... View Article
The value of ∫01 [dx / (ex + e)] is 1) (1 / e) log [(1 + e) / 2] 2) log [(1 + e) / 2] 3) (1 / e) log (1 + e) 4) log [2 / (1 + e)] 5) (1 / e) log [2 / (1 + e)]... View Article
If 2 f (x) – 3 f (1 / x) = x, then ∫12 f (x) dx = 1) (3/5) log 2 2) (-3/5) (1 + log 2) 3) (-3/5) log 2 4) None of the above Solution: (2) (-3/5) (1 + log 2)... View Article
If ∫ab x3 dx = 0 and ∫ab x2 dx = 2 / 3, then the values of a and b are respectively, 1) 1, 1 2) -1, -1 3) 1, - 1 4) -1, 1 Solution: (4) -1, 1... View Article
∫-11 [cos hx / (1 + e2x)] dx = 1) 0 2) 1 3) [e2 - 1] / 2e 4) [e2 + 1] / 2e Solution: (3) [e2 - 1] / 2e... View Article
If f (x) = tan x – tan3 x + tan5 x – … ∞ with 0 < x < Ï€/4, then ∫0Ï€/4 f (x) dx = 1) 1 2) 0 3) 1/4 4) 1/2 5) - (1/4) Solution: (3) ¼... View Article
If f (t) is an odd function, then ∫0x f (t) dt is 1) an odd function 2) an even function 3) neither even nor odd 4) 0 Solution: (2) an even function If f (t) is an odd function,... View Article
∫0a √a2 – x2 dx = 1) Ï€a2 2) (1 / 2) Ï€a2 3) (1 / 3) Ï€a2 4) (1 / 4) Ï€a2 Solution: (4) (1 / 4) Ï€a2... View Article
The value of ∫0π/2 (sin x + cos x)2 / (√1 + sin 2x)] dx = 1) 0 2) 1 3) 2 4) 3 Solution: (3) 2... View Article
The value of ∫01 [x4 + 1] / [x2 + 1] dx = 1) (1 / 6) (3 - 4π) 2) (1 / 6) (3π + 4) 3) (1 / 6) (3 + 4π) 4) (1 / 6) (3π - 4) Solution: (4) (1 / 6) (3π - 4)... View Article
The value of ∫35 [x2 / (x2 – 4)] dx = 1) 2 - loge (15 / 7) 2) 2 + loge (15 / 7) 3) 2 + 4 loge 3 - 4 loge 7 + 4 loge 5 4) 2 - tan-1 (15 / 7) Solution: (2) 2 + loge (15 / 7)... View Article
The value of ∫0Ï€/2 {[cos 3x + 1] / [2 cos x – 1]} dx = 1) 2 2) 1 3) 1/2 4) 0 Solution: (2) 1... View Article
The value of ∫0∞ dx / [(a2 + x2)] is 1) π/2 2) π/2a 3) π/a 4) 1/2a Solution: (2) π/2a... View Article
3a ∫01 [(ax – 1) / (a – 1)]2 dx = 1) a - 1 + (a - 1)-2 2) a + a-2 3) a - a-2 4) a2 + 1/a2 Solution: (1) a - 1 + (a - 1)-2... View Article
∫0λ y / [√y + λ] dy = 1) (2 / 3) [2 - √2] λ √λ 2) (2 / 3) [2 + √2] λ √λ 3) (1 / 3) [2 - √2] λ √λ 4) (1 / 3) [2 + √2] λ √λ Solution: (1) (2 / 3) [2 - √2] λ... View Article
