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During which of the following processes, does entropy decrease?

(A) Freezing of water to ice at 0°C (B) Freezing of water to ice at -10°C (C) N2(g) + 3H2(g)... View Article

The correct pair(s) of the ambident nucleophiles is (are)

(A) AgCN/KCN (B) RCOOAg/RCOOK (C) AgNO2/KNO2 (D) AgI/KI a. (A) and (C) only b. (B) only c. (B) and (C)... View Article

In the below reactions, enzyme A and enzyme B respectively are:

In the below reactions, enzyme A and enzyme B respectively are: a. Invertase and Amylase b. Amylase and Invertase c.... View Article

Match List-I with List-II.

Match List-I with List-II. List – I Chemical Compound List – II Used as (a) Sucralose (i) Synthetic detergent (b)... 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... 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 \(\begin{array}{l}\begin{array}{l} I=\int_{0}^{1} \frac{x^{3}}{1+x^{8}} d x \\ \text... View Article

The value of ∫₁^e {[1 + log x] / (3x)} dx =

1) 1/4 2) 1/2 3) 3/4 4) e 5) 1/e Solution: (2) ½ \(\begin{array}{l}\begin{array}{l} I=\int_{1}^{e} \frac{1}{3 x} d x+\frac{1}{3} \int_{1}^{e}... View Article

The value of ∫₀¹ [dx / (e^x + e)] is

1) (1 / e) log [(1 + e) / 2] 2) log [(1 + e) / 2] 3) (1 /... 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:... View Article

If ∫_a^b x³ dx = 0 and ∫_a^b 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 \(\begin{array}{l}\begin{array}{l} \text {... View Article

∫_-1¹ [cos hx / (1 + e^2x)] dx =

1) 0 2) 1 3) [e2 – 1] / 2e 4) [e2 + 1] / 2e Solution: (3) [e2 –... View Article

If f (x) = tan x – tan³ x + tan⁵ x – … ∞ with 0 < x < π/4, then ∫₀^π/4 f (x) dx =

1) 1 2) 0 3) 1/4 4) 1/2 5) – (1/4) Solution: (3) ¼ \(\begin{array}{l}\begin{array}{l} \text { Given } f(x)=\tan... View Article

If f (t) is an odd function, then ∫₀^x f (t) dt is

1) an odd function 2) an even function 3) neither even nor odd 4) 0 Solution: (2) an even function... View Article

∫_π/4^π/2 cosec² x dx =

1) -1 2) 1 3) 0 4) 1/2 Solution: (2) 1 \(\begin{array}{l}\int_{\frac{\pi}{4}}^{\frac{\pi}{2}} \operatorname{cosec}^{2} x d x \\=[-\cot x]_{\frac{\pi}{4}}^{\frac{\pi}{2}} \\ =[0+1]\\... View Article

∫₀^a √a² – x² dx =

1) πa2 2) (1 / 2) πa2 3) (1 / 3) πa2 4) (1 / 4) πa2 Solution: (4) (1... View Article

The value of ∫₀^π/2 (sin x + cos x)² / (√1 + sin 2x)] dx =

1) 0 2) 1 3) 2 4) 3 Solution: (3) 2 \(\begin{array}{l}I =\int_{0}^{\frac{\pi}{2}} \frac{(\cos x+\sin x)^{2}}{\sqrt{1+\sin 2 x}} d x... View Article

∫₀³ |x³ + x² + 3x| dx =

1) 171/2 2) 171/4 3) 170/4 4) 170/3 Solution: (2) 171/4 \(\begin{array}{l}I=\int_{0}^{3}\left|x^{3}+x^{2}+3 x\right| d x \\ =\int_{0}^{3}\left|x\left(x^{2}+x+3\right)\right| d x \\... 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 +... 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... View Article

The value of ∫₀^π/2 {[cos 3x + 1] / [2 cos x – 1]} dx =

1) 2 2) 1 3) 1/2 4) 0 Solution: (2) 1 \(\begin{array}{l}\begin{array}{l} \int_{0}^{\frac{\pi}{2}}\left(\frac{1+\cos 3 x}{2 \cos x-1}\right) d x \\... View Article

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