JEE MATHEMATICS MCQ: INCREASING & DECREASING

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Analyzing +4 | -1

\frac{{{x^2}}}{{f\left( {4a} \right)}} + \frac{{{y^2}}}{{f\left( {{a^2} - 5} \right)}}

represents an ellipse with major axis as

y

-axis and

f

is a decreasing function, then

View answer and explanation

Correct option: D

a \in \left( { - 1,5} \right)

Option D (

a \in (-1,5)

) is correct because it satisfies the condition for the given equation to represent an ellipse with the major axis as the y-axis, considering that f is a decreasing function.

More Questions from INCREASING & DECREASING

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If the function

f\left( x \right) = \frac{{K\sin x + 2\cos x}}{{\sin x + \cos x}}

is increasing for all values of

x

, then The set of values of a for which the function

f\left( x \right) = {x^2} + ax + 1

is an increasing function on [1,2] is The value of

a

in order that

f(x)=

\sin x-\cos x-a x+b

decreases for all real values is given by The function

f(x)=x e^{x(1-x)}, x \in R

, is If

f

and

g

are two increasing functions such that

fog

is defined, then If

f\left( x \right) = {x^3} + b{x^2} + cx + d

and

0 < {b^2} < c

, then in

\left( { - \infty ,\;\infty } \right)