Class12|Mean Value Theorem|WBJEE|AIEEE|WBJEE Main|Suggestion

 

Topics: 

How do you calculate MVT?

Two procedure mentioned here

Q1.Description of Rolle's Theorem :

All possible questions:

QA.How do you do Rolle's theorem?

QB.What are the three conditions of Rolle's theorem?

QC.What is the conclusion of Rolle's theorem?

QD.How do you find C in Rolle's theorem?

1.Rolle's Theorem

a.$\small f(x)$ is continuous at $\small [a,b]$

b.$\small f(x)$ is differentiable at $\small (a,b)$

c.$\small f(a)=f(b)$, there is $\small a<c<b$ for which $\small f^{'}(c)=0$.

Q2.Description of Lagranges Mean Value Theorem:

QA.What is LMV Theorem?

QB.How do you verify Lagrange's value theorem?

2.Lagranges Mean Value Theorem

All possible questions:

a.$\small f(x)$ is continuous at $\small [a,b]$

b.$\small f(x)$ is differentiable at $\small (a,b)$

c.$\small f(a)=f(b)$, there is $\small a<c<b$ for which $\small f^{'}(c)=\frac{f(b)-f(a)}{b-a}$.

Q3.If $\small a+b+c=0$, then the equation $\small 3ax^2+2bx+c=0$ has 

a.Exist only one solution

b.There exist no solution

c.There exist maximum one solution

d.No Solution

Ans:b

Q4.If $\small a_{n}x^n+a_{n-1}x^{n-1}+....+a_{1}$ equation has a positive solution say,$\small \alpha$,then the solution is 

a.$\small < \alpha$

b.$\small > \alpha$

c.$\small =\alpha$

d.$\small \geq \alpha$

Ans:a

Q5.$\small xlogx=3-x$ this equation has _______________ number of solution in this interval of (1,3)

a.Only one solution

b.Exactly one solution

c.No Solution

d,.Maximum one solution

Ans:a

Q6.$\small \phi(x)=a^{sinx}$ for this function the Rolle's theorem will be applicable 

a.Any inetrval 

b.$\small [0,\frac{\pi}{2}]$

c.$\small [0,\pi]$

d.$\small (0,\pi)$

Ans:d

Q7.$\small \phi(x)=1-x^{\frac{2}{3}}$ for this function the Rolle's theorem will be applicable 

a.Any inetrval 

b.$\small [-1,1]$

c.$\small [-1,0]$

d.$\small (0,1)$

Ans:b

Q8.$\small y=|x|$ this function satisfy how many conditions of Rolle's Theorem in this interval $\small [-1,1]$

a.one condition

b.two condition

c.all condition

d.No condition

Ans:a,d

Q9.Find the value of $\small c$,If $\small f(x)=x^3-3x-1$ function satisfy all the condition of Lagrange's M-V theorem in this interval $\small [\frac{-11}{7},\frac{13}{7}]$

a.2

b.-1

c.0

d.1

Ans:b,d

Q10.Rolle's theorem will be applicable for $\small f(x)=x^3+bx^2+ax+5$ in this interval [1,3] when $\small c=2+\frac{1}{\sqrt 3}$

a.a=-11

b.a=11

c.b=6

d.b=-6

Ans:b,d

Q11.Rolle's theorem will be applicable for $\small f(x)=x^3+px^2-qx+4$ in this interval [-2,2] when $\small c=\frac{1}{3}(1+\frac{1}{\sqrt 13})$

a.p=-1

b.p=1

c.q=4

d.q=3

Ans:a,c

Q12.If$\small f(x)=(x-1)(x-2)(x-3)(x-4)$,$\small f^{'}(x)=0$ has three equation $\small \alpha,\beta,\gamma$

a.$\small 1<\alpha<2$

b.$\small 2<\beta<3$

c..$\small 3<\gamma<4$

d..$\small 4<\alpha<5$

Ans:a,b,c

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