New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Application of Derivatives question

2023 · 10 Apr · Shift 1 · Q32

Guest · try one question or challengeGuest · try one question or challenge

PYQ Library
JEE Main
Mathematics
Application of Derivatives
2023 · 10 Apr · Shift 1 · Q32

Application of Derivatives question

2023 · 10 Apr · Shift 1 · Q32

JEE MainMathematicsApplication of DerivativesMCQ+4 / −1

A square piece of tin of side 30 cm is to be made into a box without top by cutting a square from each corner and folding up the flaps to form a box. If the volume of the box is maximum, then its surface area (in cm

^2

) is equal to :

A
1025
B
900
C
800
D
675

More from Application of Derivatives

Let $g (x) = f (x) + f (1 - x)$ and $f^{''} (x) > 0, x \in (0, 1)$ . If $g$ is decreasing in the interval $(α, 1)$ and increasing in the interval $tan^{- 1} (2 α) + tan^{- 1} (\frac{1}{α}) + tan^{- 1} (\frac{α + 1}{α})$ , then $tan^{- 1} (2 α) + tan^{- 1} (\frac{1}{α}) + tan^{- 1} (\frac{α + 1}{α})$ …2023 · MCQ
If the local maximum value of the function $f (x) = (\frac{3 e}{2 s i n x})^{s i n^{2} x}, x \in (0, \frac{π}{2})$ , is $\frac{k}{e}$ , then $(\frac{k}{e})^{8} + \frac{k ^{8}}{e ^{5}} + k^{8}$ is equal to2023 · MCQ
$max_{0 \leq x \leq π} {x - 2 sin x cos x + \frac{1}{3} sin 3 x} =$ 2023 · MCQ
Consider the triangles with vertices $A (2, 1), B (0, 0)$ and $C (t, 4), t \in [0, 4]$ . If the maximum and the minimum perimeters of such triangles are obtained at $t = α$ and $t = β$ respectively, then $6 α + 21 β$ is equal to …2023 · Numerical
Let $x = 2$ be a local minima of the function $f (x) = 2 x^{4} - 18 x^{2} + 8 x + 12, x \in (- 4, 4)$ . If M is local maximum value of the function $f$ in ( $- 4, 4)$ , then M =2023 · MCQ
Let $f : (0, 1) \to R$ be a function defined $f (x) = \frac{1}{1 - e ^{- x}}$ , and $g (x) = (f (- x) - f (x))$ . Consider two statements (I) g is an increasing function in (0, 1) (II) g is one-one in (0, 1) Then,2023 · MCQ
Let the function $f (x) = 2 x^{3} + (2 p - 7) x^{2} + 3 (2 p - 9) x - 6$ have a maxima for some value of $x 0$ . Then, the set of all values of p is2023 · MCQ
If the functions $f (x) = \frac{x ^{3}}{3} + 2 b x + \frac{a x ^{2}}{2}$ and $g (x) = \frac{x ^{3}}{3} + a x + b x^{2}, a e q 2 b$ have a common extreme point, then $a + 2 b + 7$ is equal to :2023 · MCQ