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Recent questions tagged q15
Questions
Discuss the applicability of Roll's theorem for the function \( f(x) = x^{\large\frac{1}{3}} \) on [-1, 1].
cbse
class12
modelpaper
2012
sec-b
q15
math
asked
Jan 16, 2013
by
thanvigandhi_1
0
answers
Find the area bounded by the curve $y=\sqrt x,x=2y+3$ in the first quadrant and $x$-axis.
cbse
class12
ch8
q15
p177
short-answer
exemplar
sec-c
difficult
math
asked
Jan 16, 2013
by
sreemathi.v
1
answer
Verify mean value theorem, if \( f(x)=x^3-5x^2-3x\) in the interval [a, b], where a = 1, b = 3. Find all \( c \in (1, 3)\) for which f' (c) = 0.
cbse
class12
modelpaper
2012
sec-b
q15
math
asked
Jan 15, 2013
by
thanvigandhi_1
0
answers
Prove that every real valued function which is derivable at a point of its domain is also continuous at that point. Is the converse true?
cbse
class12
modelpaper
2012
sec-b
q15
math
asked
Jan 15, 2013
by
thanvigandhi_1
1
answer
Evaluate the following $\int\frac{dt}{\sqrt {3t-2t^2}}$
cbse
class12
ch7
q15
p164
short-answer
exemplar
math
sec-b
asked
Jan 14, 2013
by
sreemathi.v
1
answer
Find the equation of tangent to the curve \( x=sin \: 3t, \: y=cos\: 2t, \: at \: t=\large\frac{\pi}{4}. \)
cbse
class12
modelpaper
2012
sec-b
q15
math
asked
Jan 11, 2013
by
thanvigandhi_1
0
answers
At what point will the tangent to the curve \( y=2x^3-15x^2+36x-21\) be parallel to x - axis? Also, find the equations of tangents to the curve at these points ?
cbse
class12
modelpaper
2012
sec-b
q15
math
asked
Jan 11, 2013
by
thanvigandhi_1
0
answers
Find the angle of intersection of the curves $y=4-x^2$ and $y=x^2$.
cbse
class12
ch6
q15
p136
short-answer
exemplar
medium
sec-b
math
asked
Jan 11, 2013
by
sreemathi.v
1
answer
Using Mathematical Induction prove that $ \large\frac{d}{dx}(x^n)$$=nx^{n-1}, \forall \: n \: \in \: N$ for all positive integers \( n \).
cbse
class12
modelpaper
2012
sec-b
q15
math
asked
Jan 10, 2013
by
thanvigandhi_1
0
answers
Differentiate \( (x^2-5x+8)(x^2+7x+9)\) in three ways mentioned : (i) by using product rule (ii) by expanding the product to obtain a single polynomial (iii) by logarithmic differentiation. Do they all give the same answer?
cbse
class12
modelpaper
2012
sec-b
q15
math
asked
Jan 10, 2013
by
thanvigandhi_1
0
answers
If \( y=x^x-2^{sinx}\) then find \( \frac{\large dy}{\large dx}.\)
cbse
class12
modelpaper
2012
sec-b
q15
math
asked
Jan 9, 2013
by
thanvigandhi_1
0
answers
Suppose 10,000 tickets are sold in a lottery each for Re1.First prize is of Rs 3000 and the second prize is of Rs 2000.There are three third prizes of Rs 500 each.If you buy one ticket,what is your expectation.
cbse
class12
ch13
q15
p273
short-answer
exemplar
sec-a
easy
math
asked
Jan 8, 2013
by
sreemathi.v
1
answer
A man rides his motorcycle at the speed of 50km/hour.He has to speed Rs 2 per km on petrol.If he rides it at at a faster speed of 80km/hour,the petrol cost increases to Rs 3 per km.He has at most Rs120 to spend on petrol and one hour's time.He wishes to find the maximum distance that he can travel.Express this problem as a linear programming problem.
cbse
class12
ch12
q15
p253
short-answer
exemplar
sec-a
easy
math
asked
Jan 7, 2013
by
sreemathi.v
1
answer
If \( y = log \sqrt {\large\frac{1-\cos2x}{1+\cos2x}},\) show that $ \large\frac{dy}{dx} $$= 2 cosec\: 2x.$
cbse
class12
modelpaper
2012
sec-b
q15
math
asked
Jan 7, 2013
by
thanvigandhi_1
0
answers
Differentiate w.r.r. \( x, \cos x . \cos 2x.\cos 3x \).
cbse
class12
modelpaper
2012
sec-b
q15
math
asked
Jan 6, 2013
by
thanvigandhi_1
0
answers
The length x of a rectangle is decreasing at the rate of 5 cm/minute and the width y is increasing at the rate of 4 cm/minute. When x = 8 cm and y = 6 cm, find the rate of change of (a) the perimeter, (b) the area of the rectangle.
cbse
class12
modelpaper
2012
sec-b
q15
difficult
ch6
math
asked
Jan 4, 2013
by
thanvigandhi_1
1
answer
Find the intervals in which the function f given by $ f(x) =\sin x + \cos x, 0 \leq x \leq 2\pi $ is strictly increasing or strictly decreasing.
cbse
class12
modelpaper
2012
sec-b
q15
difficult
math
asked
Jan 4, 2013
by
thanvigandhi_1
1
answer
Two systems of rectangular axis have the same origin.If a plane cuts them at distances a,b,c and a',b',c',respectively,from the origin,prove that\[\frac{1}{a^2}+\frac{1}{b^2}+\frac{1}{c^2}=\frac{1}{{a'}^2}+\frac{1}{{b'}^2}+\frac{1}{{c'}^2}\]
cbse
class12
ch11
sec-b
q15
p236
exemplar
easy
math
asked
Jan 3, 2013
by
sreemathi.v
1
answer
Find the equation of tangent to the curve \( y = \sqrt {3x-2}\) which is parallel to the line \( 4x-2y+5=0\).
cbse
class12
modelpaper
2012
sec-b
q15
math
asked
Jan 3, 2013
by
thanvigandhi_1
0
answers
Find the intervals in which the function f given by $ f(x) = x^3 + \large\frac{1}{x^3}$$, x \neq 0 $ is, (i) increasing, (ii) decreasing.
cbse
class12
modelpaper
2012
sec-b
q15
math
asked
Jan 3, 2013
by
thanvigandhi_1
0
answers
If \( x = a \bigg( \cos \theta +\ log \tan\large \frac{\theta}{2} \bigg)\) and \( y = a\sin\: \theta\), find the value of \( \large\frac{dy}{dx}\) at \( \theta = \large\frac{\pi}{4} \).
cbse
class12
modelpaper
2012
sec-b
q15
math
asked
Jan 2, 2013
by
thanvigandhi_1
0
answers
Prove that the function f defined by $ f(x)=\left \{\begin{array}{1 1}\large\frac{x}{\mid x\mid+2x^2}, & x\neq 0\\k, &x=0\end{array}\right.$remains discontinuous at x=0,regardless the choice of k.
cbse
class12
ch5
q15
p108
short-answer
exemplar
easy
sec-b
medium
math
asked
Dec 31, 2012
by
sreemathi.v
1
answer
Find all the points of discontinuity of f, where $ f(x) = \left \{ \begin{array}{1 1} \large\frac{sinx}{x}, \quad & if\: x < 0 \\ x+1, \quad & if\: x \geq 0 \end{array}\right \}. $
cbse
class12
modelpaper
2012
sec-b
q15
math
asked
Dec 31, 2012
by
thanvigandhi_1
0
answers
If \( A = \begin{bmatrix} 2 & -3 & 5 \\ 3 & 2 & -4 \\ 1 & 1 & -2 \end {bmatrix} \), find \( A^{-1} \) . Using \( A^{-1} \) , solve the system of equations : $ 2x – 3y + 5z = 11 ,3x + 2y – 4z = –5 ,x + y – 2x = –3. $
cbse
class12
modelpaper
2009
sec-c
q32
ch4
bookproblem
sec6
q15
p137
math
asked
Dec 29, 2012
by
thanvigandhi_1
0
answers
If \( x = a ( cos\: t + t\: sin \: t)\) and \( y = b ( sin\: t - t\: cos\: t )\), find \(\large \frac{d^2y}{dx^2} \)
cbse
class12
modelpaper
2012
sec-b
q15
math
asked
Dec 29, 2012
by
thanvigandhi_1
0
answers
Verify Roll's theorem for the function f, given by \( f(x) = e^x (\sin x - \cos x ) \: on \: \begin{bmatrix} \large\frac{\pi}{4}, & \large\frac{5\pi}{4} \end{bmatrix} \)
cbse
class12
modelpaper
2011
sec-b
q15
math
asked
Dec 28, 2012
by
thanvigandhi_1
0
answers
If \( x^y + y^x = a^b,\) find $\large\frac{dy}{dx} $
cbse
class12
modelpaper
2012
sec-b
q15
math
asked
Dec 25, 2012
by
thanvigandhi_1
0
answers
Verify Rolle's Theorem for the following in the given interval : \( f(x) = (x^2 - 4x + 3 ) e^{2x} \)in [ 1, 3 ]
cbse
class12
modelpaper
2012
sec-b
q15
math
asked
Dec 25, 2012
by
thanvigandhi_1
0
answers
Show that the point(a+5,a-4),(a-2,a+3) and (a,a) do not lie on a straight line for any value of a.
cbse
class12
ch4
sec-b
q15
p78
short-answer
exemplar
easy
math
asked
Dec 24, 2012
by
sreemathi.v
1
answer
The vector \( 2\hat i + \propto\hat j + \hat k \) is perpendicular to the vector \( 2\hat i - \hat j - \hat k \) if \[ \begin{array} (A) \: \propto = 5 \quad & (B) \: \propto = -5 \\ (C) \: \propto = -3 \quad & (D) \: \propto = 3 \end{array} \]
cbse
class12
modelpaper
2012
sec-a
q15
math
asked
Dec 24, 2012
by
thanvigandhi_1
0
answers
If possible,find BA and AB,where\[A=\begin{bmatrix}2 & 1 & 2\\1 & 2 & 4\end{bmatrix},B=\begin{bmatrix}4 & 1\\2 & 3\\1 & 2\end{bmatrix}\]
cbse
class12
ch3
q15
p54
short-answer
exemplar
math
sec-a
asked
Dec 22, 2012
by
sreemathi.v
1
answer
If \( y = \frac{\large sin^{-1}x}{\large \sqrt {1-x^2}} \), show that $ (1 - x^2) \large\frac{d^2y}{dx^2} - 3x \large\frac{dy}{dx} $$- y = 0 $
cbse
class12
modelpaper
2009
sec-b
q15
math
asked
Dec 21, 2012
by
thanvigandhi_1
0
answers
Show that $\sin^{-1}{\frac{5}{13}}+\cos^{-1}{\frac{3}{5}}=\tan^{-1}{\frac{63}{16}}$
cbse
class12
ch2
q15
exemplar
medium
sec-b
math
asked
Dec 20, 2012
by
sreemathi.v
1
answer
Let n be a fixed positive integer.Define a relation R in Z as follows: a,b E\inE Z, aRb if and only if a-b is divisible by n. Show that R is an equivalence relation.
cbse
class12
ch1
q15
p12
short-answer
exemplar
sec-a
easy
math
asked
Dec 20, 2012
by
sreemathi.v
1
answer
Differentiate the following with respect to \( x \) : $\tan^-1 \bigg(\large \frac{\sqrt {1+x} - \sqrt {1-x}}{\sqrt {1+x} + \sqrt {1-x}}\bigg) $
cbse
class12
modelpaper
2008-1
sec-b
q15
math
asked
Dec 20, 2012
by
thanvigandhi_1
0
answers
Find the shortest distance between the lines: $ \frac{ \large x + 1 }{ \large 7} = \frac{ \large y + 1}{ \large -6} = \frac{ \large z + 1}{ \large 1}$ and $ \frac{ \large x - 3 }{ \large 1} = \frac{ \large y - 5}{ \large -2} = \frac{ \large z - 7}{ \large 1}$
cbse
class12
bookproblem
ch11
sec2
q15
p478
medium
sec-b
modelpaper
2012
q20
math
asked
Dec 14, 2012
by
thanvigandhi_1
1
answer
Find the equation of the plane passing through the line of intersection of the planes \(\overrightarrow r. (\hat i + \hat j + \hat k)=1\) and \( \overrightarrow r. (2\hat i + 3\hat j - \hat k) + 4 = 0\) and parallel to \(x\) - axis.
cbse
class12
bookproblem
ch11
misc
q15
p498
difficult
sec-b
modelpaper
2012
q21
math
asked
Dec 14, 2012
by
thanvigandhi_1
1
answer
If $ \tan^{-1} \frac{\large x-1}{\large x-2} + \tan^{-1} \frac{\large x+1}{\large x+2} = \frac{\large \pi}{\large 4} $ then find the value of $x$
cbse
class12
bookproblem
ch2
sec2
q15
p48
medium
sec-b
math
asked
Dec 10, 2012
by
thanvigandhi_1
1
answer
Find the position vector of a point $R$ which divides the line joining two points $P$ and $Q$ whose position vectors are $ \hat i + 2\hat j − \hat k$ and $ – \hat i + \hat j + \hat k$ respectively, in the ratio $2 : 1$ internally
cbse
class12
bookproblem
ch10
sec2
q15
q15-1
p440
medium
sec-b
math
asked
Dec 6, 2012
by
thanvigandhi_1
1
answer
Find the integral $\int\sqrt x\;(3x^2+2x+3)\;dx$
cbse
class12
bookproblem
ch7
sec1
q15
p299
sec-a
medium
math
asked
Dec 6, 2012
by
sreemathi.v
1
answer
If the vertices $A, B, C$ of a triangle $ABC$ are $(1, 2, 3), (-1, 0, 0), (0, 1, 2)$ respectively, then find $ \angle ABC. \angle ABC$ is the angle between the vectors $ \overline {BA}$ and $\overline {BC}$.
cbse
class12
bookproblem
ch10
sec3
q15
p448
medium
sec-b
math
asked
Dec 6, 2012
by
thanvigandhi_1
1
answer
Integrate the function $\frac{\large x}{\large 9-4x^2}$
cbse
class12
bookproblem
ch7
sec2
q15
p304
sec-b
easy
math
asked
Dec 6, 2012
by
sreemathi.v
1
answer
Find the integrals of the functions\[\tan^32x\sec2x\]
cbse
class12
bookproblem
ch7
sec3
q15
p307
sec-b
medium
math
asked
Dec 5, 2012
by
sreemathi.v
1
answer
Integrate the functions $\frac{1}{\sqrt{(x-a)(x-b)}}$
cbse
class12
bookproblem
ch7
sec4
q15
p316
sec-a
easy
math
asked
Dec 5, 2012
by
sreemathi.v
1
answer
Integrate the rational functions $\frac{1}{x^4-1}$
cbse
class12
bookproblem
ch7
sec5
q15
p322
sec-b
difficult
math
asked
Dec 5, 2012
by
sreemathi.v
1
answer
Prove that \( (\overrightarrow a + \overrightarrow b) ⋅ (\overrightarrow a + \overrightarrow b) =| \overrightarrow a |^2 + |\overrightarrow b |^2\), if and only if \(\overrightarrow a,\: \overrightarrow b\) are perpendicular, given \(\overrightarrow a ≠ 0, \overrightarrow b ≠ 0\).
cbse
class12
bookproblem
ch10
misc
q15
p459
easy
sec-b
math
asked
Dec 5, 2012
by
thanvigandhi_1
1
answer
Integrate the function $\;\int\;(x^2+1)\;log\;x$
cbse
class12
bookproblem
ch7
sec6
q15
p327
sec-b
easy
math
asked
Dec 4, 2012
by
sreemathi.v
1
answer
Find the area of the region ${(x, y) : y^2\: \leq \: 4x, 4x^2 + 4y^2\: \leq\: 9}$
cbse
class12
bookproblem
ch8
misc
q15
p376
sec-c
difficult
modelpaper
2012
q26
math
asked
Dec 4, 2012
by
thanvigandhi_1
1
answer
Evaluate the definite integral\[\int\limits_0^1x\;e^{x^2}dx\]
cbse
class12
bookproblem
ch7
sec9
q15
p338
sec-a
easy
math
asked
Dec 4, 2012
by
sreemathi.v
1
answer
By using the properties of definite integrals,evaluate the integral $\begin{align*}\int\limits_0^\frac{\Large \pi}{\Large 2}\frac{\sin x-\cos x}{1+\sin x\cos x}\;dx \end{align*}$
cbse
class12
bookproblem
ch7
sec11
q15
p347
sec-a
easy
math
asked
Dec 3, 2012
by
sreemathi.v
1
answer
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