WB JEE 2020 | Application of Derivatives Question 34 | Mathematics

WB JEE 2020

MCQ (Single Correct Answer)

-0.25

If the function $$f(x) = 2{x^3} - 9a{x^2} + 12{a^2}x + 1$$ [a > 0] attains its maximum and minimum at p and q respectively such that p² = q, then a is equal to

$${1 \over 2}$$

$${1 \over 4}$$

WB JEE 2020

MCQ (Single Correct Answer)

-0.25

Let $$f(x) = {x^{13}} + {x^{11}} + {x^9} + {x^7} + {x^5} + {x^3} + x + 12$$.

Then

f(x) has 13 non-zero real roots

f(x) has exactly one real root

f(x) has exactly one pair of imaginary roots

f(x) has no real root

WB JEE 2020

MCQ (Single Correct Answer)

-0.5

In open interval $$\left( {0,\,{\pi \over 2}} \right)$$

cos x + x sin x < 1

cos x + x sin x >1

no specific order relation can be ascertained between cos x + x sin x and 1

$$\cos \,x + x\,\sin \,x < {1 \over 2}$$

WB JEE 2020

MCQ (Single Correct Answer)

-0.5

Consider the curve $$y = b{e^{ - x/a}}$$, where a and b are non-zero real numbers. Then

$${x \over a} + {y \over b}$$ = 1 is tangent to the curve at (0, 0)

$${x \over a} + {y \over b}$$ = 1 is tangent to the curve, where the curve crosses the axis of y

$${x \over a} + {y \over b}$$ = 1 is tangent to the curve at (a, 0)

$${x \over a} + {y \over b}$$ = 1 is tangent to the curve at (2a, 0)

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