New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Application of Derivatives question

2013 · Shift 0 · Q43

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

PYQ Library
JEE Main
Mathematics
Application of Derivatives
2013 · Shift 0 · Q43

Application of Derivatives question

2013 · Shift 0 · Q43

JEE MainMathematicsApplication of DerivativesMCQ+4 / −1

The real number

k

for which the equation,

2{x^3} + 3x + k = 0

has two distinct real roots in

\left[ {0,\,1} \right]

A
lies between 1 and 2
B
lies between 2 and 3
C
lies between $- 1$ and 0
D
does not exist.

More from Application of Derivatives

Let $a, b \in R$ be such that the function $f$ given by $f (x) = I n ∣ x ∣ + b x^{2} + a x, x e 0$ has extreme values at $x = - 1$ and $x = 2$ Statement-1 : $f$ has local maximum at $x = - 1$ and at $x = 2$ . Statement-2 : $a = \frac{1}{2}$ …2012 · MCQ
A line is drawn through the point $P$ to meet the coordinate axes at $P$ and $Q$ such that it forms a triangle $O P Q,$ where $O$ is the origin. If the area of the triangle $O P Q$ is least, then the slope of the line $P Q$ is :2012 · MCQ
A spherical balloon is filled with $4500 π$ cubic meters of helium gas. If a leak in the balloon causes the gas to escape at the rate of $72 π$ cubic meters per minute, then the rate (in meters per minute) at which the radius of the…2012 · MCQ
For $x \in (0, \frac{5 π}{2}),$ define $f (x) = 0 \int x t sin t d t .$ Then $f$ has2011 · MCQ
Let $f : R \to R$ be defined by $f (x) = {k - 2 x, i f 2 x + 3, i f x \leq - 1 x > - 1$ If $f$ has a local minimum at $x = - 1$ , then a possible value of $k$ …2010 · MCQ
Let $f : R \to R$ be a continuous function defined by $f (x) = \frac{1}{e ^{x} + 2 e ^{- x}}$ Statement - 1 : $f (c) = \frac{1}{3},$ for some $c \in R$ . Statement - 2 : $0 < f (x) \leq \frac{1}{2 2},$ …2010 · MCQ
Given $P (x) = x^{4} + a x^{3} + b x^{2} + c x + d$ such that $x = 0$ is the only real root of $P^{'} (x) = 0.$ If $P (- 1) < P (1),$ then in the interval $[- 1, 1] :$ 2009 · MCQ
Suppose the cubic $x^{3} - p x + q$ has three distinct real roots where $p > 0$ and $q > 0$ . Then which one of the following holds?2008 · MCQ