JEE Main 2019 (Online) 8th April Morning Slot | Application of Derivatives Question 81 | Mathematics

JEE Main 2019 (Online) 8th April Morning Slot

MCQ (Single Correct Answer)

-1

If S₁ and S₂ are respectively the sets of local minimum and local maximum points of the function,

ƒ(x) = 9x⁴ + 12x³ – 36x² + 25, x $$ \in $$ R, then :

S₁ = {–1}; S₂ = {0, 2}

S₁ = {–2}; S₂ = {0, 1}

S₁ = {–2, 0}; S₂ = {1}

S₁ = {–2, 1}; S₂ = {0}

JEE Main 2019 (Online) 8th April Morning Slot

MCQ (Single Correct Answer)

-1

Let ƒ : [0, 2] $$ \to $$ R be a twice differentiable function such that ƒ''(x) > 0, for all x $$ \in $$ (0, 2). If $$\phi $$(x) = ƒ(x) + ƒ(2 – x), then $$\phi $$ is :

decreasing on (0, 2)

decreasing on (0, 1) and increasing on (1, 2)

increasing on (0, 2)

increasing on (0, 1) and decreasing on (1, 2)

JEE Main 2019 (Online) 12th January Evening Slot

MCQ (Single Correct Answer)

-1

The tangent to the curve y = x² – 5x + 5, parallel to the line 2y = 4x + 1, also passes through the point :

$$\left\{ {{1 \over 4},{7 \over 2}} \right\}$$

$$\left( { - {1 \over 8},7} \right)$$

$$\left( {{7 \over 2},{1 \over 4}} \right)$$

$$\left( {{1 \over 8}, - 7} \right)$$

JEE Main 2019 (Online) 11th January Evening Slot

MCQ (Single Correct Answer)

-1

Let f(x) = $${x \over {\sqrt {{a^2} + {x^2}} }} - {{d - x} \over {\sqrt {{b^2} + {{\left( {d - x} \right)}^2}} }},\,\,$$ x $$\, \in $$ R, where a, b and d are non-zero real constants. Then :

f is an increasing function of x

f is neither increasing nor decreasing function of x

f ' is not a continuous function of x

f is a decreasing function of x

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