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Economy This Week (16th Jun to 30th Jun 2021)

Economy is an important part of the UPSC prelims and mains exams; this series titled ‘Economy This Week’ has been initiated to address the need... View Article

05 July 2021: The Hindu Analysis

UPSC Current Affairs Preparation: The Hindu Analysis Watch expert analysis of ‘The Hindu’ dated 5th Jul 2021. Important news and views to boost... View Article

Provincial Kingdoms of Medieval India (Part 1)

At its zenith, the Delhi Sultanate included states like Bihar, Bengal, Malwa, Gujarat, the Deccan states of Warangal, the Yadavas of Devagiri,... View Article

The value of ∫₀² |x² – 1| dx is

1) 0 2) 2 3) - (1/3) 4) -2 Solution: (2) 2... View Article

∫_-2² |[x]| dx =

1) 1 2) 2 3) 3 4) 4 5) 5 Solution: (4) 4... View Article

The value of ∫₀^12a [f (x) / [f (x) + f (12a – x)]] dx is

1) a 2) 2a 3) 3a 4) 6a Solution: (4) 6a... View Article

The value of ∫₀^π/2 dx / (1 + cot x) is

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

∫_-π/2^π/2 sin |x| dx =

1) 0 2) 1 3) 2 4) π Solution: (3) 2... View Article

∫_-3² {|x + 1| + |x + 2| + |x – 1|} dx =

1) 31/2 2) 35/2 3) 47/2 4) 39/2 Solution: (3) 47/2... View Article

If I₁ = ∫₀^π/4 sin² x dx and I₂ = ∫₀^π/4 cos² x dx, then

1) I1 = I2 2) I1 < I2 3) I1 > I2 4) I2 = I1 + π / 4 Solution: (2) I1 < I2... View Article

∫₀^π/2 log sin x dx =

1) - π log 2 2) π log 2 3) - π/2 log 2 4) π/2 log 2 Solution: (3) - π/2 log 2... View Article

∫_-1² |x|³ dx =

1) 5/4 2) 17/4 3) 15/4 4) 4/5 Solution: (2) 17/4... View Article

∫₀^π [cot x] dx, [.] denotes the greatest integer function, =

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

The value of I = ∫_-π/2^π/2 |sin x| dx is

1) 0 2) 2 3) -2 4) -2 < I < 2 Solution: (2) 2... View Article

If I = ∫₀¹ dx / (1 + x^π/2), then

1) loge 2 < I < π / 4 2) loge 2 > I 3) I = π / 4 4) I = loge 2 Solution: (1) loge 2 < I < π / 4... View Article

If I₁ = ∫₀^3π f (cos² x) dx and I₂ = ∫₀^π f (cos² x) dx, then

1) I1 = I2 2) 3I1 = I2 3) I1 = 3I2 4) I1 = 5I2 Solution: (3) I1 = 3I2... View Article

If p(x) be a function defined on R such that p'(x) = p'(1 – x), ∀ x ϵ [0, 1], p(0) = 1 and p(1) = 41. Then, ∫₀¹ p (x) dx =

1) √41 2) 21 3) 41 4) 42 Solution: (2) 21... View Article

The value of ∫₀^π sin⁵⁰ x . cos⁴⁹ x dx is

1) 0 2) π/4 3) π/2 4) 1 Solution: (1) 0... View Article

∫_π^16π |sin x| dx =

1) 0 2) 32 3) 30 4) 28 Solution: (3) 30... View Article

If [x] denotes the greatest integer less than or equal to x, then the value of ∫₀² [|x – 2| + [x]] dx is

1) 2 2) 3 3) 1 4) 4 5) 3/2 Solution: (2) 3... View Article

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