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CBSE XII
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Math
Math
Model Papers
Relations and Functions
Inverse Trigonometric Functions
Matrices
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Continuity and Differentiability
Application of Derivatives
Integrals
Application of Integrals
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Vector Algebra
Three Dimensional Geometry
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If $(f:R \to R)$ is defined by $f(x) = x^2$ - $3x+2$. Find $f(f(x))$:
cbse
class12
bookproblem
ch1
misc
q3
p29
sec-a
easy
math
asked
Nov 21, 2012
by
vaishali.a
1
answer
Let \(f:W \to W\) be defined as $f(n)=n$ - $1$, if \(n\;is\;odd\;and\; f(n)=n+1,\;if\;n\;is\; even.\) Show that \(f\) is invertible. Find the inverse of \(f\). Here, \(W\) is the set of all whole numbers.
cbse
class12
bookproblem
ch1
misc
q2
p29
medium
sec-b
math
modelpaper-2014
q15
asked
Nov 21, 2012
by
vaishali.a
1
answer
Let \(f:R \to R\) be defined as \(f(x)=10x+7.\)Find the function \(g:R \to R\) such that \(g\;o\;f = f\;o\;g = I_R.\)
cbse
class12
bookproblem
ch1
misc
q1
p29
sec-b
easy
modelpaper
2012
q11
math
asked
Nov 21, 2012
by
vaishali.a
1
answer
Consider a binary operation $\ast$ on $N$ defined as $a \ast b = a^3 + b^3$. Choose the correct answer:
cbse
class12
bookproblem
ch1
sec4
q13
p26
easy
sec-a
math
asked
Nov 21, 2012
by
vaishali.a
1
answer
If \(( x-a)^2 + (y-b)^2 = c^2\), for some \( c > 0\), prove that $\Large\frac{\begin{bmatrix} 1 + \left(\frac{dy}{dx}\right)^2 \\[0.3em] \end{bmatrix}^{\frac{\Large 3}{\Large 2}}}{\Large\frac{d^2y}{dx^2}}$is a constant independent of \(a\) and \(b\).
cbse
class12
bookproblem
ch5
misc
q15
p191
sec-b
medium
kvquestionbank2012
math
asked
Nov 21, 2012
by
thanvigandhi_1
1
answer
If \( x \sqrt {1+y} + y \sqrt{1+x} = 0\), for, \(-1 < x < 1\), prove that $\large \frac{dy}{dx} = -\frac{1}{(1+x)^2} $
cbse
class12
bookproblem
ch5
misc
q14
p191
sec-b
easy
math
asked
Nov 21, 2012
by
thanvigandhi_1
1
answer
Let $(A=N \times N \,and\, * )$ be the binary operation on $(A)$ defined by $( (a, b) * (c, d) = (a + c, b + d))$. Show that * is commutative and associative. Find the identity element for * on $( A )$, if any.
cbse
class12
bookproblem
ch1
sec4
q11
p25
sec-b
math
asked
Nov 21, 2012
by
vaishali.a
1
answer
Find if the given operation has identity: $\;\; a \ast b = a^2 + b^2$
cbse
class12
bookproblem
ch1
sec4
p25
q10
q10-2
sec-a
math
asked
Nov 21, 2012
by
vaishali.a
2
answers
Let $\ast$ be a binary operation on the set $Q$ of rational numbers as follows: $\;\; a \ast b = a-b$. Find which of the binary operations are commutative and which are associative.
cbse
class12
bookproblem
ch1
sec4
q9
q9-1
p25
easy
sec-a
math
asked
Nov 21, 2012
by
vaishali.a
1
answer
Let $\ast$ be the binary operation on $N$ defined by $a \ast b=H.C.F. $ of a and b. Is $\ast$ commutative? Is $\ast$ associative? Does there exist identity for this binary operation on $N$?
cbse
class12
bookproblem
ch1
sec4
q8
p25
easy
sec-a
math
asked
Nov 21, 2012
by
vaishali.a
1
answer
Differentiate w.r.t. x the function $cot^{-1} \begin{bmatrix} \frac{{\sqrt {1+sin \: x}} + {\sqrt{1-sin \: x}}} {{\sqrt {1+sin \: x}} - {\sqrt{1-sin \: x}}} \\[0.3em] \end{bmatrix}$, where $0 < x < \frac{\pi}{2}$
cbse
class12
bookproblem
ch5
misc
q6
p191
sec-a
medium
math
kvquestionbank2012
asked
Nov 21, 2012
by
thanvigandhi_1
1
answer
Is $\ast$ defined on the set $\{1,2,3,4,5\}$ by $a\ast b=L.C.M$.of $a$ and $b$ a binary operation?
cbse
class12
bookproblem
ch1
sec4
q7
p25
sec-a
math
asked
Nov 21, 2012
by
vaishali.a
1
answer
Find \(\large \frac{dy}{dx} \), if \( y = \sin^{-1}x + \sin^{-1} \: \sqrt {1-x^2} , -1 \leq x \leq 1 \)
cbse
class12
bookproblem
ch5
misc
q13
p191
sec-a
easy
math
asked
Nov 21, 2012
by
thanvigandhi_1
1
answer
Find \( \large\frac{dy}{dx} \), if \( y = 12 ( 1 - \cos t ) , x = 10 ( t - \sin t ) , -\large\frac{\pi}{2}\normalsize < t <\large \frac{\pi}{2} \)
cbse
class12
bookproblem
ch5
misc
q12
p191
easy
sec-b
math
asked
Nov 21, 2012
by
thanvigandhi_1
1
answer
Let \(\ast\) be the binary operation on \(N\) given by \(a\ast b=L.C.M\,.of\,a\,and\,b\). Find $\begin{array}{1 1}(i)\;\; 5 \ast7,\; 20 \ast 16 & (ii)\;\; Is\; \ast \;commutative?\\(iii)\;\; Is\; \ast \;associative? & (iv)\;\; Find\, the\,identity \, of \ast \, in N\\(v)\;\; Which \, elements\, of \, N\, are\, invertible\, for\, the\, operaation\,\ast ? & \;\end{array}$
cbse
class12
bookproblem
ch1
sec4
q6
p25
sec-b
math
asked
Nov 21, 2012
by
vaishali.a
2
answers
Let $\ast '$ be the binary operation on the set $\{1, 2, 3, 4, 5\}$ defined by $a \ast ' b = H.C.F$ of a and b. Is the operation same as the operation $\ast$ defined in the table below? $\begin{matrix} *&1&2&3&4&5 \\ 1&1&1&1&1&1 \\ 2&1&2&1&2&1 \\ 3&1&1&3&1&1 \\ 4&1&2&1&4&1 \\ 5&1&1&1&1&5 \end{matrix}$
cbse
class12
bookproblem
ch1
sec4
q5
p25
sec-a
easy
math
asked
Nov 21, 2012
by
vaishali.a
1
answer
Differentiate w.r.t. \(x\) the function in \( x^{\large x^2-3} + ( x - 3 )^{\large x^2} \), for \(x > 3\)
cbse
class12
bookproblem
ch5
misc
q11
p191
sec-c
medium
math
asked
Nov 21, 2012
by
thanvigandhi_1
1
answer
Differentiate w.r.t. \(x\) the function in \( x^{\large x} + x^{\large a} + a^{\large x} + a^{\large a} \), for some fixed \( a > 0 \) and \( x > 0 \)
cbse
class12
bookproblem
ch5
misc
q10
p191
sec-b
medium
math
asked
Nov 21, 2012
by
thanvigandhi_1
1
answer
Differentiate w.r.t. \(x\) the function in \( (\sin x - \cos x )^{\large(\sin x - \cos x )} , \large\frac {\pi}{4}\normalsize < x < \large\frac{3\pi}{4} \)
cbse
class12
bookproblem
ch5
misc
q9
p191
sec-b
easy
math
asked
Nov 21, 2012
by
thanvigandhi_1
1
answer
Differentiate w.r.t. \(x\) the function in \( \cos \: (a \cos x + b \sin x) \) , for some constant \(a\) and \(b\)
cbse
class12
bookproblem
ch5
misc
q8
p191
sec-a
easy
math
asked
Nov 21, 2012
by
thanvigandhi_1
1
answer
Differentiate w.r.t. \(x\) the function in \(( \log x )^{\large\log x}, x > 1 \)
cbse
class12
bookproblem
ch5
misc
q7
p191
sec-b
medium
math
asked
Nov 21, 2012
by
thanvigandhi_1
1
answer
Differentiate w.r.t. \(x\) the function in \(\large\frac{\cos^{ -1}\Large\frac{ x}{ 2}}{\sqrt {2x + 7}}, \normalsize-2 < x < 2 \)
cbse
class12
bookproblem
ch5
misc
q5
p191
sec-b
medium
math
asked
Nov 21, 2012
by
thanvigandhi_1
1
answer
Differentiate w.r.t. \(x\) the function in \( sin^{-1}(x \: \sqrt x ), 0 \leq x \leq 1 \)
cbse
class12
bookproblem
ch5
misc
q4
p191
sec-b
medium
math
asked
Nov 21, 2012
by
thanvigandhi_1
1
answer
Differentiate w.r.t. $x$ the function in $(5x)^{\large 3 \cos 2x} $
cbse
class12
bookproblem
ch5
misc
q3
p191
sec-a
easy
math
asked
Nov 21, 2012
by
thanvigandhi_1
1
answer
Differentiate w.r.t. \(x\) the function in \( sin^3x + cos^6x \)
cbse
class12
bookproblem
ch5
misc
q2
p191
sec-c
medium
math
asked
Nov 21, 2012
by
thanvigandhi_1
1
answer
Differentiate w.r.t. \(x\) the function in \( (3x^2 - 9x + 5)^9 \)
cbse
class12
bookproblem
ch5
misc
q1
p191
sec-b
easy
math
asked
Nov 21, 2012
by
thanvigandhi_1
1
answer
Examine the applicability of Mean Value Theorem for all three functions given in $(i)\;f (x) = [x] \;for\; x \: \in [5,9]$
cbse
class12
bookproblem
ch5
sec8
q6
q6-1
p186
sec-a
easy
math
asked
Nov 21, 2012
by
thanvigandhi_1
1
answer
Verify Mean Value Theorem, if \( f (x) = x^3 - 5x^2 - 3x \) in the interval \( [a,b]\), where \( a = 1\) and \( b = 3\). Find all \( c \in (1,3) \) for which \( f'(c) = 0\).
cbse
class12
bookproblem
ch5
sec8
q5
p186
sec-b
medium
math
asked
Nov 21, 2012
by
thanvigandhi_1
1
answer
Verify Mean Value Theorem, if \( f (x) = x^2 - 4x - 3 \) in the interval \( [a,b]\), where \( a = 1 \) and \(b = 4 \).
cbse
class12
bookproblem
ch5
sec8
q4
p186
sec-b
easy
math
asked
Nov 21, 2012
by
thanvigandhi_1
1
answer
If \( f : [ -5,5] \rightarrow R \) is a differentiable function and if \( f' (x) \) does not vanish anywhere, then prove that \( f (-5) \: \neq \: f (5)\).
cbse
class12
bookproblem
ch5
sec8
q3
p186
sec-b
medium
math
asked
Nov 21, 2012
by
thanvigandhi_1
1
answer
Examine if Rolle's theorem is applicable to any of the following functions. Can you say some thing about the converse of Rolle's theorem from these example? $(i)\;f (x) = [x] \;for\; x \: \in [5,9] $
cbse
class12
bookproblem
ch5
sec8
q2
p186
math
sec-a
asked
Nov 20, 2012
by
thanvigandhi_1
1
answer
Verify Rolle's theorem for the function \( f (x) =x^2 + 2x - 8, x \: \in [ -4 , 2 ]. \)
cbse
class12
bookproblem
ch5
sec8
q1
p186
sec-a
easy
math
asked
Nov 20, 2012
by
thanvigandhi_1
1
answer
If \( y = ( tan^{-1}x )^2\), show that \( (x^2 + 1 )^2 \: y_2 + 2x (x^2 +1 ) \: y_1 = 2 \)
cbse
class12
bookproblem
ch5
sec7
q17
p184
sec-a
medium
math
asked
Nov 20, 2012
by
thanvigandhi_1
1
answer
Consider the binary operation \( \wedge\) on the set \(\{1, 2, 3, 4, 5\}\) defined by \(a \wedge b = min \{a, b\}\). Write the multiplication table of the operation \( \wedge\) .
cbse
class12
bookproblem
ch1
sec4
q3
p24
sec-a
easy
modelpaper
2012
q11
math
asked
Nov 20, 2012
by
vaishali.a
1
answer
For each operation $\ast$ defined below, determine whether $\ast$ is binary, commutative or associative. $\begin{array}{1 1}(i) \;\;\; On\, Z,\, define \,a*b\, = a-b & \;\\(ii) \;\;\; On\, Q,\, define \,a*b\, = ab+1 & \;\\(iii) \;\;\; On\, Q,\, define \,a*b\, = \frac {ab} {2} & \;\\(iv) \;\;\; On\, Z^+, \, define\, a*b= 2^{ab} & \;\\(v) \;\;\; On\, Z^+,\, define \,a*b\, = a^b & \;\\(vi) \;\;\; On R - \{ -1\},\, define\, a*b= \frac {a} {b+1} & \;\end{array}$
cbse
class12
bookproblem
ch1
sec4
q2
p24
sec-b
math
asked
Nov 20, 2012
by
vaishali.a
5
answers
If \( e^y ( x + 1 ) = 1\), show that \( \large\frac{d^2y}{dx^2} = \left(\frac{dy}{dx}\right)^2\)
cbse
class12
bookproblem
ch5
sec7
q16
p184
sec-b
easy
math
asked
Nov 20, 2012
by
thanvigandhi_1
1
answer
If \( y = 500e^{\large 7x} + 600e^{\large -7x}\), show that \( \large\frac{d^2y}{dx^2}\normalsize = 49y\)
cbse
class12
bookproblem
ch5
sec7
q15
p184
sec-a
easy
math
asked
Nov 20, 2012
by
thanvigandhi_1
1
answer
If \( y = Ae^{mx} + Be^{nx}\), show that \( \large\frac{d^2y}{dx^2} -\normalsize ( m + n ) \large\frac{dy}{dx} +\normalsize mny = 0 \)
cbse
class12
bookproblem
ch5
sec7
q14
p184
sec-b
easy
math
asked
Nov 20, 2012
by
thanvigandhi_1
1
answer
If \( y = 3 \cos \: (\log x ) + 4 \sin ( \log x )\), show that \(x^2y_2 + xy_1 + y = 0\)
cbse
class12
bookproblem
ch5
sec7
q13
p184
sec-a
easy
math
asked
Nov 20, 2012
by
thanvigandhi_1
1
answer
If \( y =\cos^{-1}x \) , find \( \large\frac{d^2y}{dx^2}\) in terms of \( y \) alone.
cbse
class12
bookproblem
ch5
sec7
q12
p184
sec-b
medium
math
asked
Nov 20, 2012
by
thanvigandhi_1
1
answer
If \( y = 5 \cos x - 3 \sin x \) , prove that \( \large\frac{d^2y}{dx^2}\normalsize + y = 0\)
cbse
class12
bookproblem
ch5
sec7
q11
p183
sec-a
easy
math
asked
Nov 20, 2012
by
thanvigandhi_1
1
answer
Find the second order derivatives of the functions given in $ \sin (\log x) $
cbse
class12
bookproblem
ch5
sec7
q10
p183
sec-a
easy
math
asked
Nov 20, 2012
by
thanvigandhi_1
1
answer
Find the second order derivatives of the functions given in $\log ( \log x) $
cbse
class12
bookproblem
ch5
sec7
q9
p183
sec-a
easy
math
asked
Nov 20, 2012
by
thanvigandhi_1
1
answer
Find the second order derivatives of the functions given in $ \tan^{-1} x $
cbse
class12
bookproblem
ch5
sec7
q8
p183
sec-a
easy
math
asked
Nov 20, 2012
by
thanvigandhi_1
1
answer
Find the second order derivatives of $ e^{6x} \cos 3x$
cbse
class12
bookproblem
ch5
sec7
q7
p183
sec-a
easy
math
asked
Nov 20, 2012
by
thanvigandhi_1
1
answer
Find the second order derivatives of the function $(e^{\large x} \sin 5x)$
cbse
class12
bookproblem
ch5
sec7
q6
p183
sec-a
medium
math
asked
Nov 20, 2012
by
thanvigandhi_1
1
answer
Find the second order derivatives of the functions given in $ x^3 \log x $
cbse
class12
bookproblem
ch5
sec7
q5
p183
sec-a
easy
math
asked
Nov 20, 2012
by
thanvigandhi_1
1
answer
Find the second order derivatives of the functions given in $\log x $
cbse
class12
bookproblem
ch5
sec7
q4
p183
sec-a
easy
math
asked
Nov 20, 2012
by
thanvigandhi_1
1
answer
Find the second order derivatives of the functions given in $ x \; \cos x$
cbse
class12
bookproblem
ch5
sec7
q3
p183
sec-a
easy
math
asked
Nov 20, 2012
by
thanvigandhi_1
1
answer
Find the second order derivatives of the functions given in $ x^{\large 20} $
cbse
class12
bookproblem
ch5
sec7
q2
p183
sec-a
easy
math
asked
Nov 20, 2012
by
thanvigandhi_1
1
answer
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