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Recent questions tagged q14
Questions
Show that: $ii) \qquad \begin{bmatrix} 1 & 2 & 3 \\ 0 & 1 & 0 \\ 1 & 1 & 0 \end{bmatrix} \begin{bmatrix} -1 & 1 & 0 \\ 0 & -1 & 1 \\ 2 & 3 & 4 \end{bmatrix} \: \neq \: \begin{bmatrix} -1 & 1 & 0 \\ 0 & -1 & 1 \\ 2 & 3 & 4 \end{bmatrix} \begin{bmatrix} 1 & 2 & 3 \\ 0 & 1 & 0 \\ 1 & 1 & 0 \end{bmatrix} $
cbse
class12
bookproblem
ch3
sec2
p81
easy
q14
q14-2
math
asked
Feb 27, 2013
by
balaji.thirumalai
1
answer
Show that: $(i) \qquad \begin{bmatrix} 5 & -1 \\ 6 & 7 \end{bmatrix} \begin{bmatrix} 2 & 1 \\ 3 & 4 \end{bmatrix} \: \neq \: \begin{bmatrix} 2 & 1 \\ 3 & 4 \end{bmatrix} \begin{bmatrix} 5 & -1 \\ 6 & 7 \end{bmatrix}$
cbse
class12
bookproblem
ch3
sec2
p81
easy
q14
q14-1
sec-b
math
asked
Feb 27, 2013
by
balaji.thirumalai
1
answer
Solve the following differential equation : $\large \frac{dy}{dx}$$+y=\cos\: x-\sin\: x$
cbse
class12
modelpaper
2012
sec-b
q14
medium
math
asked
Feb 17, 2013
by
thanvigandhi_1
1
answer
Discuss the continuity of the following function at x = 0: $ f(x) = \left\{ \begin{array}{l l}\large\frac{x^4+2x^3+x^2}{\tan^{-1}x}, & \quad if { x \; \neq 2 } \\ 0, & \quad if { x\; = 0 } \end{array} \right. $
cbse
class12
modelpaper
2012
sec-b
q14
easy
math
asked
Feb 15, 2013
by
thanvigandhi_1
1
answer
Verify Lagrange's mean value theorem for the following function: $ f(x)=x^2-2x+3,\: for \: [4,6]$
cbse
class12
modelpaper
2012
sec-b
q14
easy
math
asked
Feb 15, 2013
by
thanvigandhi_1
1
answer
For what value of k is the following function continuous at x = 2?$ f(x) = \left\{ \begin{array}{l l}2x+1, & \quad if { x \: < \: 2 } \\ k, & \quad if { x = 2 } \\ 3x-1, & \quad if { x > 2 } \end{array} \right. $
cbse
class12
modelpaper
2012
sec-b
q14
easy
math
asked
Feb 11, 2013
by
thanvigandhi_1
1
answer
Examine the continuity of the function $ f(x) = \left\{ \begin{array}{l l}\large\frac{| sin\: x |}{x}, & \quad if \;x \; \neq\; 0 \\ 1, & \quad if \;x = 0 \end{array} \right. $
cbse
class12
modelpaper
2012
sec-b
q14
medium
math
asked
Feb 9, 2013
by
thanvigandhi_1
1
answer
Determine the value of k so that the function $ f(x) = \left\{ \begin{array}{l l}kx^2, & \quad if { x \leq 2 } \\ 3, & \quad if { x > 2 } \end{array} \right. $ is continuous
cbse
class12
modelpaper
2012
sec-b
q14
medium
math
asked
Feb 9, 2013
by
thanvigandhi_1
1
answer
If the function defined by $ f(x) = \left\{ \begin{array}{l l}2x-1, & \quad if { x < 2 } \\ a, & \quad if { x = 2 } \\ x+1, & \quad if { x > 2 } \end{array} \right. $ is continuous at x = 2, find the value of a. Also discuss the continuity of f(x) at x = 3.
cbse
class12
modelpaper
2012
sec-b
q14
easy
math
asked
Feb 9, 2013
by
thanvigandhi_1
1
answer
Show that the function = 2x - | x | is continuous at x = 0.
cbse
class12
modelpaper
2012
sec-b
q14
easy
math
asked
Feb 8, 2013
by
thanvigandhi_1
1
answer
For what value of k, is the following function continuous at x = 0 ? $ f(x) = \left\{ \begin{array}{l l}\large\frac{1-\cos4x}{8x^2}, & \quad if { x \neq 0 } \\ k, & \quad if { x = 0 } \end{array} \right. $
cbse
class12
modelpaper
2012
sec-b
q14
medium
math
asked
Feb 8, 2013
by
thanvigandhi_1
1
answer
Find the values of x which satisfy the equation \[ sin^{-1}x+sin^{-1}(1-x)=cos^{-1}x.\]
cbse
class12
modelpaper
ch2
2012
sec-b
q14
medium
math
asked
Feb 7, 2013
by
thanvigandhi_1
1
answer
Prove that \( 2sin^{-1}\frac{3}{5}-tan^{-1}\frac{17}{31}=\frac{\pi}{4} \)
cbse
class12
modelpaper
ch2
2012
sec-b
q14
medium
math
asked
Feb 7, 2013
by
thanvigandhi_1
1
answer
Differentiate the following function w.r.t.\( x\) $(x)^{\Large\cos x}+(\sin x)^{\Large\tan \: x} $
cbse
class12
modelpaper
2012
sec-b
q14
difficult
math
asked
Feb 6, 2013
by
thanvigandhi_1
1
answer
Find the probability of throwing almost 2 sixes in 6 throws of a single dice.
cbse
class12
additionalproblem
kvquestionbank2012
ch13
q14
p41
math
asked
Feb 5, 2013
by
meena.p
0
answers
Solve the following differential equation : $ xdy-(y-x^3)dx=0 $
cbse
class12
modelpaper
2012
sec-b
q14
medium
math
asked
Feb 5, 2013
by
thanvigandhi_1
1
answer
Find the perpendicular distance of point (2,3,4) from the line $ \Large\frac{4-x}{2}=\frac{y}{6}=\frac{1-z}{3}$
cbse
class12
additionalproblem
kvquestionbank2012
ch11
q14
p37
math
asked
Feb 5, 2013
by
meena.p
0
answers
Find the relationship between 'a' and 'b' so that the function 'f' defined by $ f(x) = \left\{ \begin{array}{l l}ax+1, & \quad if { x \leq 3} \\ bx+3, & \quad if { x > 3} \end{array} \right. $ is continuous at x = 3.
cbse
class12
modelpaper
2012
sec-b
q14
easy
math
asked
Feb 5, 2013
by
thanvigandhi_1
1
answer
If \( x^y=e^{x-y}\), show that \( \large\frac{dy}{dx}=\frac{logx}{\{log(xe)\}^2} \)
cbse
class12
modelpaper
2012
sec-b
q14
easy
math
asked
Feb 5, 2013
by
thanvigandhi_1
1
answer
Prove that the area of a paralellogram with diagonals $\bar{a}\;and\;\bar{b}\;is\;\frac{1}{2}|\bar{a} \times \bar{b}|$
cbse
class12
additionalproblem
kvquestionbank2012
ch10
q14
p35
difficult
sec-b
math
asked
Feb 4, 2013
by
meena.p
1
answer
Solve:\[\sqrt{1-y^2}dx=[\sin^{-1}y-x]dy\]
cbse
class12
additionalproblem
kvquestionbank2012
ch9
q14
p33
sec-b
math
asked
Feb 4, 2013
by
meena.p
0
answers
If two vectors \( \overrightarrow a \: and \: \overrightarrow b\) are such that \( |\overrightarrow a|=2,|\overrightarrow b|=1\: and \: \overrightarrow a.\overrightarrow b=1\), then find the value of \( (3\overrightarrow a-5\overrightarrow b).(2\overrightarrow a+7\overrightarrow b).\)
cbse
class12
modelpaper
2012
sec-b
q14
math
asked
Feb 4, 2013
by
thanvigandhi_1
0
answers
Sketch the region common to the circle $x^2+y^2=25$ and the parabola $y^2=8x$ also find the area of the region using integration.
cbse
class12
additionalproblem
kvquestionbank2012
ch8
q14
p32
math
asked
Feb 4, 2013
by
meena.p
0
answers
Find the value of 'a' for which the function f defined as $ f(x) = \left\{ \begin{array}{l l}asin\frac{\pi}{2}(x+1), & \quad { x \leq 0} \\ \large \frac{\tan\: x-\sin x}{x^3}, & \quad { x > 0} \end{array} \right. $ is continuous at x = 0.
cbse
class12
modelpaper
2012
sec-b
q14
medium
math
asked
Feb 4, 2013
by
thanvigandhi_1
1
answer
Show that the function f defined as follows, is continuous at x = 2 but not differentiable $f(x) = \left\{ \begin{array}{l l}3x-2, & \quad { 0 < x \leq 1} \\ 2x^2-x, & \quad { 1 < x \leq 2} \\ 5x-4, & \quad { x > 2 } \end{array} \right. $
cbse
class12
modelpaper
2012
sec-b
q14
math
asked
Feb 4, 2013
by
thanvigandhi_1
0
answers
Find $ \large\frac{dy}{dx},$$ if \: y=\sin^{-1} \bigg[ x \sqrt{1-x}-\sqrt x \sqrt{1-x^2} \bigg] $.
cbse
class12
modelpaper
2012
sec-b
q14
math
asked
Feb 4, 2013
by
thanvigandhi_1
0
answers
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
modelpaper
2012
sec-b
q14
math
asked
Feb 3, 2013
by
thanvigandhi_1
0
answers
Find the point (s) of discountinuity of the function 'f' given by $ f(x) = \left\{ \begin{array}{l l}|x|+3, & \quad { x \leq -3} \\ -2x, & \quad {-3 < x < 3} \\ 6x+2, & \quad { x > 3 } \end{array} \right. $
cbse
class12
modelpaper
2012
sec-b
q14
math
asked
Feb 2, 2013
by
thanvigandhi_1
0
answers
Differentiate : $ \tan^{-1} \bigg( \large\frac{\sqrt{1-x^2}}{x} \bigg)$ w.r.t. \( \cos^{-1} \bigg( 2x\sqrt{1-x^2} \bigg). \)
cbse
class12
modelpaper
2012
sec-b
q14
math
asked
Feb 2, 2013
by
thanvigandhi_1
0
answers
If $ x=a(\cos t+t\sin t), \: y=a(\sin t - t\cos t), \: find \; \large\frac{d^2y}{dx^2}$$ \: at \: t=\large\frac{\pi}{4}. $
cbse
class12
modelpaper
2012
sec-b
q14
math
asked
Jan 31, 2013
by
thanvigandhi_1
0
answers
$\Large\int \frac {dx}{x-X^3}=$\[(a)\;\frac{1}{2}log \frac{x^2}{1-x^2}\qquad (b)\;\frac{1}{2}log \frac{1-x^2}{x^2}\qquad(c)\;log \frac{(1-x)}{x(1+x)}\qquad(d)\;log x(1-x^2)\]
cbse
class12
additionalproblem
kvquestionbank2012
ch7
q14
p24
math
asked
Jan 31, 2013
by
meena.p
0
answers
If the function \( f(x) = \left\{ \begin{array}{l l}3ax+b, & \quad if\: { x > 1} \\ 11, & \quad if \: { x = 1} \\ 5ax-2b, & \quad if \: { x < 1} \end{array} \right. \) is continuous at x = 1, find the values of a and b.
cbse
class12
modelpaper
2012
sec-b
q14
math
asked
Jan 31, 2013
by
thanvigandhi_1
0
answers
Show that the function $ f(x) = \left\{ \begin{array}{l l}\large\frac{x}{|x|+2x^2}, & \quad { x \neq 0} \\ \lambda, & \quad { x = 0} \end{array} \right. $ remains discontinuous at x = 0 regardless of the choice of \( \lambda \).
cbse
class12
modelpaper
2012
sec-b
q14
math
asked
Jan 30, 2013
by
thanvigandhi_1
0
answers
Evaluate: $\int \large\frac{2x -1}{(x-1))(x+2)(x-3)}$$dx$
cbse
class12
modelpaper
2005
sec-a
q14
math
asked
Jan 30, 2013
by
fingeazy
0
answers
Show that the function 'f' given by \( f(x)=|x|+|x+1|, x \in R\) is continuous both at \( x=0 \: and \: x=1.\)
cbse
class12
modelpaper
2012
sec-b
q14
math
asked
Jan 29, 2013
by
thanvigandhi_1
0
answers
The tangent to the curve\[x=a\sqrt{\cos 2\theta} \cos\theta y=a\sqrt{cos2\theta}\sin \theta\]at the point corresponding to $ \theta =\frac{\pi}{6}$ is \begin{array}{1 1}(a)\;Parallel\; to\; the\; x-axis & \qquad (b)\;Parallel\; to\; the\; y-axis \\ (c)\;Parallel\; to\; the\; line\; y = x & \qquad(d)\;none\;of\;these\end{array}
cbse
class12
additionalproblem
kvquestionbank2012
ch6
q14
p17
math
asked
Jan 28, 2013
by
meena.p
0
answers
For what value of k, is the following continuous at x = 0? $ f(x) = \left\{ \begin{array}{l l}\large\frac{\sqrt{1+x}-\sqrt{1-x}}{sin^{-1}x}, & \quad { x \neq 0}\\ k, & \quad { x = 0} \\ \end{array}. \right.$
cbse
class12
modelpaper
2012
sec-b
q14
math
asked
Jan 28, 2013
by
thanvigandhi_1
0
answers
If \( f(x) = \left\{ \begin{array}{l l}x^2, & \quad if\; { x \leq 1}\\ ax+b, & \quad if\; { x > 1} \\ \end{array}. \right.\) is differentiable at x = 1. Find the value of a and b.
cbse
class12
modelpaper
2012
sec-b
q14
math
asked
Jan 27, 2013
by
thanvigandhi_1
0
answers
Verify Lagrange's mean value theorem for the following function : \( f(x) = \sin \: x - \sin\: 2x \: in \: [0, \pi ] \)
cbse
class12
modelpaper
2012
sec-b
q14
math
asked
Jan 27, 2013
by
thanvigandhi_1
1
answer
If \( x^y=e^{y-x}\), show that \( \large\frac{dy}{dx}=\frac{2-logx}{(1-log\:x)^2.} \)
cbse
class12
modelpaper
2012
sec-b
q14
math
asked
Jan 25, 2013
by
thanvigandhi_1
0
answers
Show that the function f(x) = |x-1| is continuous but not differentiable at x=1.
cbse
class12
modelpaper
2012
sec-b
q14
math
asked
Jan 25, 2013
by
thanvigandhi_1
0
answers
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
Let $ f(x) = \left\{ \begin{array}{l l} \large\frac{1-\sin^3x}{3\cos^2x}, & \quad if { x < \large\frac{\pi}{2}}\\ a, & \quad if { x = \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) be a continuous function at \( x =\large \frac{\pi}{2} \), find a and b.
cbse
class12
modelpaper
2012
sec-b
q14
math
asked
Jan 25, 2013
by
thanvigandhi_1
0
answers
A car parking company has 500 subscribers and collects fixed charges of Rs.300 per subscriber per month. The company proposes to increase the monthly subscription and it is believed that for every increase of Re.1, one subscriber will discontinue the service. What increase will bring maximum income of the company? What values are driven by this problem?
cbse
valuebasedproblems2012
relations-and-functions
q14
ch1
sec-b
asked
Jan 24, 2013
by
shanthinig
0
answers
If $ \begin{bmatrix} \cos^2A & \cos A\sin A \\ \cos A\sin A & \sin^2A \end{bmatrix},Y=\begin{bmatrix} \cos^2B & \cos B\sin B \\ \cos B\sin B & \sin^2B \end{bmatrix}$then show that XY is a zero matrix, provided (A-B) is an odd multiple of $\large\pi/2$
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q14
p8
math
sec-b
asked
Jan 24, 2013
by
meena.p
0
answers
Find the vector equation of the plane through the intersection of the plane : $ \overrightarrow r . (\hat i + \hat j + \hat k ) = 6 \: and \: \overrightarrow r . (2\hat i + 3\hat j + 4\hat k ) = -5$ and the point (1, 1, 1).
cbse
class12
modelpaper
2012
sec-b
q14
math
asked
Jan 24, 2013
by
thanvigandhi_1
0
answers
If $ \sin^{-1}x+\sin^{-1}y+\sin^{-1}z=\pi,$ prove that $x\sqrt{1-x^2}+y\sqrt{1-y^2}+z\sqrt{1-z^2}=2xyz$
cbse
class12
additionalproblem
kvquestionbank2012
ch2
q14
p5
difficult
sec-c
math
asked
Jan 23, 2013
by
meena.p
1
answer
If R is a relation on a set $A(A \neq \phi),$ prove that R is symmetric iff $R^{-1} = R$
cbse
class12
additionalproblem
kvquestionbank2012
ch1
q14
p3
math
sec-b
asked
Jan 23, 2013
by
meena.p
0
answers
Solve the following differential equation : $ e^x \sqrt{1-y^2}dx+\large\frac{y}{x}$$dy=0$
cbse
class12
modelpaper
2012
sec-b
q14
math
asked
Jan 23, 2013
by
thanvigandhi_1
0
answers
If \( y = x^{\large\sin x}+(\sin x)^{\large x}, \: find\: \large\frac{dy}{dx}.\)
cbse
class12
modelpaper
2012
sec-b
q14
math
asked
Jan 21, 2013
by
thanvigandhi_1
0
answers
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