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Questions asked by meena.p
Questions
14353
questions
1
answer selected
Verify the Rolles Theorem for the function $ f(x)=\sin x- \cos x, $in the interval $ \bigg[\Large\frac{\pi}{4},\frac{5\pi}{4}\bigg]$
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q50
p15
easy
math
asked
Jan 28, 2013
1
answer
Using LMV Theorem, find a point on the curve $ y=(x-3)^2,$ where the tangent is parallel to the chord joining (3,0) and (5,4).
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q49
p15
easy
math
asked
Jan 28, 2013
1
answer
If f(x) and g(x) are functions derivable in [a,b] such that f(a) = 4, f(b) = 10, g(a) =1, g(b) =3.Show that for a < c < b, we have $ f'(c)=3g'(c).$
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q48
p15
math
asked
Jan 28, 2013
1
answer
It is given that for the function $ f(x)=x^3-6x^2+px+q\;on\;[1,3].$Rolles theorem holds with $ c=2+\large\frac{1}{\sqrt 3}.$Find the values of p and q.
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q47
p15
easy
math
asked
Jan 28, 2013
1
answer
Verify Rolles theorem for the function $ f(x)=\Large e^{1-x^2}$in the interval [-1,1]
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q46
p14
easy
math
asked
Jan 28, 2013
1
answer
If $ x\sqrt{1+y}+y\sqrt{1+x}=0,\normalsize\; Prove\; that\; \Large\frac{dy}{dx}=\frac{-1}{(1+x)^2}$
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q45
p14
difficult
math
sec-b
asked
Jan 28, 2013
1
answer
If $ y=\sqrt{x^2-1} - log \bigg(\Large\frac{1}{x}+\sqrt{1+\frac{1}{x^2}}\bigg),\;\normalsize find\;\Large\frac{dy}{dx}$
cbse
class12
additionalproblem
ch5
q44
p14
medium
math
sec-b
asked
Jan 28, 2013
1
answer
Differentiate $ \cos^{-1} \bigg[\large\frac{3 \cos x-2 \sin x}{\sqrt {13}}\bigg] w.r.t \; \sin^{-1} \bigg[\large\frac{5\sin x +4 \cos x}{\sqrt{41}}\bigg]$
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q43
p14
p406
difficult
math
sec-a
asked
Jan 28, 2013
1
answer
If $ x=\cos \theta + log \tan \Large\frac{\theta }{2},\normalsize y=\sin \theta \;find\; \Large\frac {d^2y}{dx^2}\normalsize \;at\;\theta =\Large\frac{\pi}{4}$
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q42
p14
medium
math
sec-a
asked
Jan 28, 2013
1
answer
If $ y^{ \cos x}+(\tan^{-1}x)^y=1,find \Large\frac{dy}{dx}$
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q41
p14
difficult
math
sec-b
asked
Jan 28, 2013
1
answer
If $ y=f \bigg(\Large\frac{2x-1}{x^2+1}\bigg)\;\normalsize and\;f' (x)=\sin x^2,\;find\; \Large\frac{dy}{dx}$
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q40
p14
difficult
math
sec-b
asked
Jan 28, 2013
1
answer
Find $\Large\frac{dy}{dx}$when$y=\tan^{-1}\bigg[\Large\frac{x^{\frac{1}{3}}+a^{\frac{1}{3}}}{1-x^{\frac{1}{3}}a^{\frac{1}{3}}}\bigg]$
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q39
p14
easy
math
sec-a
asked
Jan 28, 2013
1
answer
If $ y=|\cos x|+|\sin x|,\;find\; \Large\frac{dy}{dx}\; \normalsize at\;x=\Large\frac{2\pi}{3}$
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q38
p14
medium
math
sec-b
asked
Jan 28, 2013
1
answer
If $ y=\Large\frac{1}{\sqrt{b^2-a^2}} \normalsize log \bigg[\Large\frac{\sqrt{b+a}+\sqrt{b-a}\tan \frac{x}{2}} {\sqrt{b+a}-\sqrt{b-a}\tan \frac{x}{2}}\bigg]$ prove that $ \Large\frac {dy}{dx}=\frac{\sec^2\frac{x}{2}}{(b+a)-(b-a) \tan^2\frac{x}{2}}$
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q37
p14
difficult
math
sec-b
asked
Jan 28, 2013
1
answer
If $ \sqrt { 1-x^2} +\sqrt {1-y^2}=a(x-y),\;prove\;that\;\Large\frac{dy}{dx}=\sqrt{\frac{1-y^2}{1-x^2}}$
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q36
p14
difficult
math
sec-b
asked
Jan 25, 2013
1
answer
Prove that $ \Large\frac{d}{dx}\bigg[\Large\frac{1}{4 \sqrt 2} \normalsize log\bigg|\Large\frac{x^2+\sqrt 2 x+1}{x^2- \sqrt 2 x+1} \bigg|+\Large\frac {1}{2 \sqrt 2} \normalsize \tan^{-1} \Large\frac{\sqrt 2 x}{1-x^2}\bigg]=\Large\frac{1}{1+x^4}$
cbse
class12
kvquestionbank2012
ch5
q34
p13
difficult
math
sec-a
asked
Jan 25, 2013
1
answer
Let $y= \tan^{-1}\bigg[\Large\frac{4x}{1+5x^2}\bigg] \normalsize +\tan^{-1}\bigg[\Large\frac{2+3x}{3-2x}\bigg],$ show that $ \Large\frac{dy}{dy}=\frac{5}{1+25x^2}$
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q33
p13
medium
math
sec-a
asked
Jan 25, 2013
1
answer
Given that $ \cos \frac{x}{2}.\cos \frac{x}{4}.\cos \frac{x}{8}.......=\Large\frac {\sin x}{x},$ \[Prove\;that\;\frac{1}{2^2}\sec^2\frac{x}{2}+\frac{1}{2^4}\sec^2\frac{x}{4}+.......=cosec^2x-\frac{1}{x^2}\]
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q31
p13
difficult
math
sec-a
asked
Jan 25, 2013
1
answer
Find $\Large\frac{dy}{dx},$ when $y=\sin^{-1}\bigg[x\sqrt{1-x}-\sqrt x \sqrt{1-x^2}\bigg]$
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q30
p13
medium
math
sec-a
asked
Jan 25, 2013
1
answer
Differentiate w.r.t. x, $ y=\tan^{-1}\bigg[\Large\frac{a\cos x-b\sin x}{b\cos x+a \sin x}\bigg]$
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q29
p13
medium
math
sec-a
asked
Jan 25, 2013
1
answer
If $ y=\frac{2}{\Large\sqrt {a^2-b^2}}\tan^{-1}\bigg[\sqrt{\frac{a-b}{a+b}}\tan \frac{x}{2} \bigg],$ prove that $ \Large\frac{dy}{dx}=\frac{1}{a+b \cos x}, \normalsize a>b>0 $
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q28
p13
difficult
math
sec-b
asked
Jan 25, 2013
1
answer
If $y=\sin ^{-1}\big [x^2\sqrt{1-x^2}+x\sqrt {1-x^4}\big],$ prove that $ \Large\frac{dy}{dx}=\frac{2x}{\sqrt{1-x^4}}+\frac{1}{\sqrt{1-x^2}}$
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q27
p13
easy
math
sec-a
asked
Jan 25, 2013
1
answer
Find$ \Large\frac{dy}{dx}\;\normalsize when\;y=\sin ^{-1} \bigg[\Large\frac{5x+12 \sqrt{1-x^2}}{13}\bigg]$
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q26
p13
easy
math
sec-a
asked
Jan 25, 2013
1
answer
Let $\phi(x)\;andh(x)$ be derivable at x = c. Show that necessary and sufficient condition for the function defined as :\[f(x)= \left\{ \begin{array}{1 1} \phi(x), & \quad x \leq c \\ h(x), & \quad x>c \end{array} \right. \]to be derivable at x= c are $(i)\phi(c)=h(c)\quad(ii)\phi'(c)=h'(c)$
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q25
p13
medium
math
sec-b
asked
Jan 25, 2013
1
answer
Let $f(x) = \left\{ \begin{array}{l l} \Large\frac{1-sin^3x}{3cos^2x}, & \quad if\; { x < \Large\frac{\pi}{2}}\\ a, & \quad if\; { x = \Large\frac{\pi}{2}} \\ \Large\frac{b(1-sin x)}{(\pi - 2x)^2}, & \quad if \;{ x > \Large\frac{\pi}{2}} \end{array}. \right.$ If f(x) is continuous function at x \( x = \Large\frac{\pi}{2} \), find a and b.
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q24
p13
medium
math
sec-b
asked
Jan 25, 2013
1
answer
Discuss the continuity of the following function at x = 0 $f(x)= \left\{ \begin{array}{1 1} \Large\frac{x^4+x^3+2x^2}{\tan ^{-1}x} & \quad ,\;x\neq0 \\ 10 & \quad ,\;x=0 \end{array} \right. $
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q23
p12
medium
math
sec-b
asked
Jan 25, 2013
1
answer
Let $ f(x)= \left\{ \begin{array}{1 1} |x|\cos \frac{1}{x} & \quad if\;x\neq0 \\ 0 & \quad if\;x=0 \end{array} \right. $ then discuss the continuity of f(x) at x = 0
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q22
p12
medium
math
sec-b
asked
Jan 25, 2013
1
answer
Find all the points of discontinuity of f defined by f(x) = | x | - | x+1|.
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q21
p12
easy
math
sec-a
asked
Jan 25, 2013
1
answer
The function $ \Large\frac{log(1+ax)-log(1-bx)}{x}$ is not defined at x = 0. Find the value of f(x) so that f(x) is continuous at x = 0.
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q20
p12
medium
sec-a
math
asked
Jan 25, 2013
1
answer
Show that the function $f(x) = | \sin x+\cos x| $ is continuous at $ x =\Large\pi$
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q19
p12
medium
math
sec-a
asked
Jan 25, 2013
1
answer
Determine the values of a, b and c for which the function :$f(x)= \left\{ \begin{array}{1 1} \Large\frac{\sin (a+1)x+\sin x}{x} & \quad ,\;x<0 \\ c & \quad ,\;x=0 \\ \Large\frac{\sqrt{x+bx^2}-\sqrt x}{b\sqrt{x^3}} & \quad ,\;x>0 \end{array} \right. $ may continuous at x = 0
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q18
p12
medium
math
sec-b
asked
Jan 25, 2013
1
answer
Show that the function $ f(x)= \left\{ \begin{array}{1 1} x+\lambda, & \quad x< 1 \\ \lambda x^2+1, & \quad x\geq1 \end{array} \right. $ is continuous function, regardless of the choice of $ \lambda \in R $
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q17
p12
easy
math
sec-a
asked
Jan 25, 2013
1
answer
Show that Sin | x | is continuous.
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q16
p12
easy
math
sec-a
asked
Jan 25, 2013
1
answer
Show that the function : $f(x)= \left\{ \begin{array}{1 1} |x|, & \quad x\leq2 \\ [x], & \quad x>2 \end{array} \right. $ is continuous [0,2].
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q15
p12
easy
math
sec-a
asked
Jan 25, 2013
1
answer
Find a and b if the function :$ f(x)= \left\{ \begin{array}{1 1} [1+| \sin x | ]^{\Large\frac{a}{\sin |x|}}, & \quad \Large\frac{-\pi}{6}< \normalsize x<0 \\ 6 & \quad ,x=0 \\ e^{\Large\frac{\tan 2x}{\tan 3x}}, & \quad 0<x<\Large\frac{\pi}{6} \end{array} \right. $ is continuous on $\bigg(\Large\frac{-\pi}{6},\frac{\pi}{6}\bigg).$
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q14
p12
math
sec-b
asked
Jan 25, 2013
0
answers
Is the function $ f(x)=\Large\frac{3x+4\tan x}{x}$ continuous at x = 0? If not, how may the function be defined to make it continuous at this point.
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q13
p11
easy
math
sec-b
asked
Jan 25, 2013
1
answer
Show that the function :$f(x)= \left\{ \begin{array}{1 1} \Large\frac{e^{\frac{1}{x}}-1}{e^{\frac{1}{x}}+1}, & \quad when\;x\neq0 \\ 0, & \quad when\; x=0 \end{array} \right. $ is discontinuous at x = 0.
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q12
p11
difficult
math
sec-b
asked
Jan 25, 2013
1
answer
Given that $ f(x)= \left\{ \begin{array}{1 1} \Large\frac{1- \cos 4x}{x^2}, & \quad if\;x<0 \\ a & \quad ,if\;x=0 \\ \Large\frac{\sqrt x}{\sqrt{16+\sqrt{x}}-4}, & \quad if\;x>0 \end{array}. \right. $ If f(x) is continuous at x = 0, find the value of a.
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q11
p11
medium
math
sec-b
asked
Jan 25, 2013
1
answer
Find $\Large \frac{dy}{dx}$ when $y=\tan^{-1}\Large\frac{1+x^2}{1-x^2}$
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q10
p11
easy
math
sec-a
asked
Jan 25, 2013
1
answer
Find $\Large \frac{dy}{dx}$ when $ y=a^x.x^a$
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q9
p11
easy
math
sec-a
asked
Jan 25, 2013
1
answer
Verify Rolles theorem for the function $f(x)=\sin 2x \;in\;\bigg[0,\Large\frac{\pi}{2}\bigg]$
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q8
p11
easy
math
sec-a
asked
Jan 25, 2013
1
answer
Let $y=y=\sqrt{e^\sqrt x },x>0\;find\;\large\frac{dy}{dx}.$
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q7
p11
easy
math
sec-a
asked
Jan 25, 2013
1
answer
If $ f(x)=\begin{vmatrix} x & x^2 & x^3 \\ 1 & 2x & 3x^2 \\ 0 & 2 & 6x \end{vmatrix}$ than find $ f' (x)$
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q6
p11
easy
math
sec-a
asked
Jan 25, 2013
1
answer
If $ f^1(x)=g(x)\;and\;g^1(x)=-f(x)$ for all n and $f(2)=f^1(2)=4,$ find the value of $f^2(24)+g^2(24)$
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q5
p11
math
sec-a
asked
Jan 24, 2013
1
answer
Find the set of all points where the function f(x) = 2x |x| is differentiable.
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q4
p11
easy
math
sec-a
asked
Jan 24, 2013
1
answer
Find $ \frac{dy}{dx}\;when\;y=\Large x^{x^{x^{x.....}}}$
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q3
p11
easy
math
sec-a
asked
Jan 24, 2013
1
answer
Let f be a non zero continuous function satisfying f(x+y) = f(x).f(y) for all x, y $ \epsilon$ R. If f(2) = 9 then find the value of f(3).
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q2
p11
easy
math
sec-a
asked
Jan 24, 2013
1
answer
Let f be continuous function on [1,3]. If f takes only rational values for all x and f(2) = 10 then find the value of f(1.5)
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q1
p11
easy
math
sec-a
asked
Jan 24, 2013
1
answer
For any square matrix verify A(adj A) = |A|I
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q50
p10
math
sec-b
asked
Jan 24, 2013
0
answers
If $ A=\begin{bmatrix} a & b \\ 0 & 1 \end{bmatrix}\;prove\;that\;A^n=\begin{bmatrix} \Large a^n & \Large\frac{b(a^n-1)}{a-1} \\ \normalsize 0 & 1 \end{bmatrix},n \epsilon N$
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q49
p10
math
sec-b
asked
Jan 24, 2013
0
answers
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