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Recent questions tagged additionalproblem
Questions
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
by
meena.p
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
by
meena.p
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
by
meena.p
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
by
meena.p
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
by
meena.p
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
by
meena.p
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
by
meena.p
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
by
meena.p
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
by
meena.p
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
by
meena.p
1
answer
Show that Sin | x | is continuous.
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q16
p12
easy
math
sec-a
asked
Jan 25, 2013
by
meena.p
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
by
meena.p
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
by
meena.p
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
by
meena.p
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
by
meena.p
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
by
meena.p
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
by
meena.p
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
by
meena.p
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
by
meena.p
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
by
meena.p
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
by
meena.p
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
by
meena.p
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
by
meena.p
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
by
meena.p
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
by
meena.p
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
by
meena.p
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
by
meena.p
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
by
meena.p
0
answers
Let $\begin{vmatrix} 3 & y \\ x & 1 \end{vmatrix} =\begin{vmatrix} 3 & 2 \\ 4 & 1 \end{vmatrix} $ find the possible values of x and y, find the values if x = y.
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q48
p10
math
sec-a
asked
Jan 24, 2013
by
meena.p
0
answers
If the points (2,0), (0,5) and (x,y) are collinear give a relation between x and y.
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q47
p10
math
sec-a
asked
Jan 24, 2013
by
meena.p
0
answers
Find x, if $ \begin{bmatrix} x & -5 & -1 \end{bmatrix} \begin{bmatrix} 1 & 0 & 2 \\ 0 & 2 & 1 \\ 2 & 0 & 3 \end{bmatrix} \begin{bmatrix} x \\ 4 \\ 1 \end{bmatrix} =0$
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q45
p10
math
sec-a
asked
Jan 24, 2013
by
meena.p
0
answers
If $ A=\begin{bmatrix} 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{bmatrix} \;find\;A^2\;Hence\;find\;A^6.$
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q44
p10
math
sec-b
asked
Jan 24, 2013
by
meena.p
0
answers
If $A=\begin{bmatrix} \cos \theta & \sin \theta & \\ -\sin \theta & \cos \theta \end{bmatrix} $ then show that $A^n=\begin{bmatrix} \cos 2\theta & \sin 2\theta & \\ -\sin 2\theta & \cos 2\theta \end{bmatrix} $
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q43
p10
math
sec-b
asked
Jan 24, 2013
by
meena.p
0
answers
If a, b, c are in A.P. then find the value of: $\begin{vmatrix} 2y+4 & 5y+7 & 8y+a \\ 3y+5 & 6y+8 & 9y+b \\ 4y+6 & 7y+9 & 10y+c \end{vmatrix}$
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q42
p10
math
sec-b
asked
Jan 24, 2013
by
meena.p
0
answers
If x, y and z all positive, are $p^{th},q^{th}and\;r^{th}$ terms of a G.P. Prove that $\begin{vmatrix} logx & p & 1 \\ logy & q & 1 \\ logz & r & 1 \end{vmatrix}=0$
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q41
p9
math
sec-b
asked
Jan 24, 2013
by
meena.p
0
answers
Find the quadratic function defined by the equation $ f(x)=ax^2+bx+c\;if\;f(0)=6,f(2)=11,f(-3)=6,$ using determinants.
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q40
p9
math
sec-b
asked
Jan 24, 2013
by
meena.p
0
answers
If $ A+B+C=\large\pi,\;\normalsize show\;that\;\begin{vmatrix} \sin (A+B+C) & \sin B & \cos C \\ -\sin B & 0 & \tan A \\ \cos (A+B) & -\tan A & 0 \end{vmatrix}=0$
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q39
p9
math
sec-b
asked
Jan 24, 2013
by
meena.p
0
answers
If x, y, z are positive and unequal show that the value of determinant $ \begin{vmatrix} x & y & z \\ y & z & x \\ z & x & y \end{vmatrix}$ is negative.
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q38
p9
math
sec-b
asked
Jan 24, 2013
by
meena.p
0
answers
If $ A=\begin{bmatrix} 3 & -4 \\ -1 & 2 \end{bmatrix}$ find Matrix B such that AB= 1
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q37
p9
math
sec-a
asked
Jan 24, 2013
by
meena.p
0
answers
If $A=\begin{bmatrix} \cos \theta & i\sin \theta \\ i\sin \theta & \cos \theta \end{bmatrix}$ then prove by Mathematical Induction that :$A^n=\begin{bmatrix} \cos n\theta & i\sin n\theta \\ i\sin n\theta & \cos n\theta \end{bmatrix}$
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q36
p9
math
sec-c
asked
Jan 24, 2013
by
meena.p
0
answers
If $ p(\alpha)=\begin{bmatrix} \cos \alpha & i\sin \alpha \\ -\sin \alpha & \cos \alpha \end{bmatrix}\;show\;that\;p(\alpha) \times p(\beta)=p(\alpha+\beta)$
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q35
p9
math
sec-b
asked
Jan 24, 2013
by
meena.p
0
answers
Find the values of a and b such that $ A^2+aI=bA\;where\; A=\begin{bmatrix} 3 & 1 \\ 7 & 5 \end{bmatrix}$
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q34
p9
math
sec-b
asked
Jan 24, 2013
by
meena.p
0
answers
If $ A=\begin{bmatrix} 1 & -2 & 1 \\ -2 & 3 & 1 \\ 1 & 1 & 5 \end{bmatrix}$ verify $(AdjA)^{-1}=adj(A^{-1})$
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q33
p9
math
sec-b
asked
Jan 24, 2013
by
meena.p
0
answers
If two matrices $ A^{-1}\;and\;B$ are given how to find $(AB)^{-1}$verify with an example.\[(Find\; B^{-1} then\; find\; B^{-1} \times A^{-1})\]
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q32
p9
math
sec-b
asked
Jan 24, 2013
by
meena.p
0
answers
Check whether the function f (x) =$ x^{100}$ + sin x-1 is strictly increasing or strictly decreasing or none of both on $(-1,1)$ . Should the nature of a man be like this function? Justify your answers
cbse
valuebasedproblems2012
relations-and-functions
ch1
q15
additionalproblem
sec-b
asked
Jan 24, 2013
by
shanthinig
0
answers
If $P(a)=\begin{bmatrix} \cos a & -\sin a & 0 \\ \sin a & \cos a & 0 \\ 0 & 0 & 1 \end{bmatrix}$then show that $[P(x)]^{-1}=[P(-x)]$
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q31
p9
math
sec-b
asked
Jan 24, 2013
by
meena.p
0
answers
Find the matrix x if $ \begin{bmatrix} 2 & 4 \\ 1 & 3 \end{bmatrix} \times \begin{bmatrix} 0 & 2 \\ 1 & 3 \end{bmatrix}=\begin{bmatrix} 1 & 6 \\ 3 & -2 \end{bmatrix}$\[X=-\frac{1}{4}\begin{bmatrix} -53 & 18 \\ 25 & -10 \end{bmatrix}\]
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q30
p9
math
sec-a
asked
Jan 24, 2013
by
meena.p
0
answers
If $A=\begin{bmatrix} 2 & -3 \\ 3 & 4 \end{bmatrix} $satisfies the equation : $ x^2+6x+17=0\;find\;A^{-1}$
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q29
p9
math
sec-b
asked
Jan 24, 2013
by
meena.p
0
answers
If $\begin{vmatrix} x & b & c \\ a & y & c \\ a & b & z \end{vmatrix}=0$ then find the value of $ \large\frac{x}{x-a}+\frac{y}{y-b}+\frac{z}{z-c}$
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q28
p8
math
sec-a
asked
Jan 24, 2013
by
meena.p
0
answers
Given $ A=\begin{bmatrix} a_{11} & a_{12} \\ a_{21} & a_{22} \end{bmatrix}$ such that $ |A|=-10.\;Find\;a_{11}c_{11}+a_{12}c_{12}$
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q27
p8
math
sec-a
asked
Jan 24, 2013
by
meena.p
0
answers
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