If the function f(x) = [ e^x ( e^{tan x − x − 1} ) + logₑ(sec x + tan x) − x ] / ( tan x − x ) is continuous at x = 0, then the value of f(0) is equal to
If the function f(x) = [ e^x ( e^{tan x − x − 1} ) + logₑ(sec x + tan […]
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Let each of the two ellipses E₁ : x²/a² + y²/b² = 1, (a > b) and E₂ : x²/A² + y²/B² = 1, (A < B) have eccentricity 4/5. Let the lengths of the latus recta of E₁ and E₂ be l₁ and l₂, respectively, such that 2l₁² = 9l₂. If the distance between the foci of E₁ is 8, then the distance between the foci of E₂ is
Let each of the two ellipses x²/a² + y²/b² = 1 and x²/A² + y²/B² = 1 have eccentricity 4/5.
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Consider an A.P.: a₁, a₂, … , aₙ; a₁ > 0. If a₂ − a₁ = −3/4, aₙ = (1/4)a₁, and ∑ᵢ₌₁ⁿ aᵢ = 525/2, then ∑ᵢ₌₁¹⁷ aᵢ is equal to
Consider an A.P.: a₁, a₂, … , aₙ; a₁ > 0. If a₂ − a₁ = −3/4, aₙ = (1/4)a₁,
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Let A(1, 0), B(2, −1) and C(7/3, 4/3) be three points. If the equation of the bisector of the angle ABC is αx + βy = 5, then the value of α² + β² is
Let A(1, 0), B(2, −1) and C(7/3, 4/3) be three points. If the equation of the bisector of the angle
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If cot x = 5/12 for some x ∈ (π, 3π/2), then sin 7x ( cos 13x/2 + sin 13x/2 ) + cos 7x ( cos 13x/2 − sin 13x/2 ) is equal to
If cot x = 5/12 for some x ∈ (π, 3π/2), then sin 7x (cos 13x/2 + sin 13x/2) +
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The value of ( √3 cosec 20° − sec 20° ) / ( cos 20° cos 40° cos 60° cos 80° ) is equal to
The value of ( √3 cosec 20° − sec 20° ) / ( cos 20° cos 40° cos 60° cos
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Let f(t) = ∫ ( (1 − sin(logₑ t)) / (1 − cos(logₑ t)) ) dt , t > 1. If f(e^{π/2}) = −e^{π/2} and f(e^{π/4}) = α e^{π/4}, then α equals
Let f(t) = ∫ ( (1 − sin(logₑ t)) / (1 − cos(logₑ t)) ) dt, t > 1. If
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If the domain of the function f(x) = log_(10x² − 17x + 7) (18x² − 11x + 1) is (−∞, a) ∪ (b, c) ∪ (d, ∞) − {e}, then 90(a + b + c + d + e) equals:
If the domain of the function f(x) = log_(10x² − 17x + 7) (18x² − 11x + 1) is (−∞,
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Let S = 1/(2·5!) + 1/(3!·23!) + 1/(5!·21!) + … up to 13 terms. If 13S = 2^k / n!, k ∈ ℕ, then n + k is equal to
Let S = 1/(1!·25!) + 1/(3!·23!) + 1/(5!·21!) + … up to 13 terms. If 13S = 2^k / n!,
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From a lot containing 10 defective and 90 non-defective bulbs, 8 bulbs are selected one by one with replacement. Then the probability of getting at least 7 defective bulbs is
From a lot containing 10 defective and 90 non-defective bulbs, 8 bulbs are selected one by one with replacement. Then