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Recent questions tagged q11
Questions
If\( f : P \rightarrow R\) be function defined by \( f(x)=4x^3-7\), show that function f is a bijective function.
cbse
class12
modelpaper
2012
sec-b
q11
math
asked
Jan 25, 2013
by
thanvigandhi_1
0
answers
Let $ f(x) = \large\frac{ax}{x+1}$$, x \neq -1, \: if \: (fof) (x) = x,$ find the value of $a$
cbse
class12
modelpaper
2012
sec-b
q11
math
asked
Jan 25, 2013
by
thanvigandhi_1
0
answers
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
Let A = set of boys of XII class in some school. Let a R b, if and only if a and b use unfair means in the exam, \( a, b \in A\) Is R a transitive relation?
cbse
class12
modelpaper
2012
sec-b
q11
math
asked
Jan 25, 2013
by
thanvigandhi_1
1
answer
Find the matrix X such that :$ \begin{bmatrix} 2 & -1 \\ 0 & 1 \\ -2 & 4 \end{bmatrix}X=\begin{bmatrix} -1 & -8 & -10 \\ 3 & 4 & 0 \\10 & 20 & 10 \end{bmatrix}$
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q11
p7
math
sec-a
asked
Jan 24, 2013
by
meena.p
0
answers
Find the differential equation of the family of ellipses having foci on y- axis and centre at the origin.
cbse
class12
modelpaper
2012
sec-b
q11
math
asked
Jan 24, 2013
by
thanvigandhi_1
1
answer
Prove that $4\tan^{-1}\large\frac{1}{5}-\tan^{-1}\frac{1}{70}+\tan^{-1}\frac{1}{99}=\large\frac{\pi}{4}$
cbse
class12
additionalproblem
kvquestionbank2012
ch2
q11
p5
medium
sec-c
math
asked
Jan 23, 2013
by
meena.p
1
answer
Let R be the relation defined in the set A = {1, 2, 3, 4, 5, 6, 7} by R = {(a, b): both a and b are either odd or even}. Show that R is an equivalence relation. Further, show that all the elements of the subset{1, 3, 5, 7} are related to each other and all elements of the subset {2, 4, 6} are related to each other, but no element of the subset {1, 3, 5, 7}} is related to any element of the subset {2, 4, 6}.
cbse
class12
modelpaper
2012
sec-b
q11
math
asked
Jan 23, 2013
by
thanvigandhi_1
0
answers
Let f, g be two functions defined by \[f(x)=\frac{x}{x+1},g(x)=\frac{x}{1-x},\;then\;find\;(fog)^{-1}(x)\]
cbse
class12
additionalproblem
kvquestionbank2012
ch1
q11
p3
math
sec-b
asked
Jan 23, 2013
by
meena.p
0
answers
For each binary operation * defined below, determine whether * is (i) commutative (ii) associative \( a*b = \large\frac{ab}{2}\) on Q?
cbse
class12
modelpaper
2012
sec-b
q11
math
asked
Jan 22, 2013
by
thanvigandhi_1
0
answers
If y(x) is a solution of $\Large\frac{2-\sin x}{1-y}\bigg(\frac{dy}{dx}\bigg)\normalsize=-\cos x$ and y(0)=1,then find the value of $\frac{1}{2}.$
cbse
class12
ch9
sec-b
q11
p193
short-answer
exemplar
medium
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
Show that the relation R : N \( \rightarrow \) N defined by (a,b)R(c,d) \( \iff \) a+d = b+c for all (a,b), (c,d) \( \in \) N x N is an equivalence relation.
cbse
class12
modelpaper
2012
sec-b
q11
math
asked
Jan 17, 2013
by
thanvigandhi_1
0
answers
Find the sine of the angle between the vectors $\overrightarrow{a}=3\hat i+\hat j+2\hat k$ and $\overrightarrow{b}=-2\hat i+2\hat j+4\hat k.$
cbse
class12
ch10
q11
p215
exemplar
easy
sec-b
math
asked
Jan 17, 2013
by
sreemathi.v
1
answer
'*' is a binary operation defined on Q. Find which of the following binary oprations are associative and which are commutative : $(i) a*b=a-b\: for \: a,b \in Q (ii) a*b = \large\frac{ab}{4}$$\: for \: a,b \in Q.$
cbse
class12
modelpaper
2012
sec-b
q11
math
asked
Jan 16, 2013
by
thanvigandhi_1
0
answers
Show that the relation in the set \( A = { x : x \in W, o \leq x \leq 12} \) given by R = {(a, b) : a-b is a multiple of 4} is an equivalence relation.
cbse
class12
modelpaper
2012
sec-b
q11
math
asked
Jan 16, 2013
by
thanvigandhi_1
0
answers
Draw a rough sketch of the curve $y=\sqrt{x-1}$ in the interval [1,5].Find the area under the curve and between the lines $x=1$ and $x=5$.
cbse
class12
ch8
q11
p177
short-answer
exemplar
sec-b
medium
math
asked
Jan 16, 2013
by
sreemathi.v
1
answer
Let * be the binary operation on N given by p * q = LCM of p and q. Find (i) 12 * 56 (ii) whether * is commutative? (iii) whether * is associative (iv) identity of * in N.
cbse
class12
modelpaper
2012
sec-b
q11
math
asked
Jan 15, 2013
by
thanvigandhi_1
0
answers
Evaluate the following $\int\sqrt{\frac{a+x}{a-x}}$
cbse
class12
ch7
q11
p164
short-answer
exemplar
sec-b
medium
math
asked
Jan 14, 2013
by
sreemathi.v
1
answer
Let L be the set of all lines in XY - planes and R be the relation in L defined as R = \( { (L_1, L_2 ) : L_1 \: is \: parallel\: to\: L_2} \). Show the R is an equivalence relation. Find the set of all the lines related to the line \( y=2x+4.\)
cbse
class12
modelpaper
2012
sec-b
q11
math
asked
Jan 11, 2013
by
thanvigandhi_1
1
answer
x and y are the sides of two squares such that $y=x-x^2$.Find the rate of change of the area of second square with respect to the area of first square.
cbse
class12
ch6
q11
p136
short-answer
exemplar
easy
sec-b
math
asked
Jan 11, 2013
by
sreemathi.v
1
answer
Show that the relation R in the set \( A = { x \in Z:0 \leq x \leq 12},\) given by (i) R = { a, b : |a-b| is a multiple of 4 } (ii) R = {a, b ; a = b}. is equivalence relation. Find the set of all eleents related to 1 in each case.
cbse
class12
modelpaper
2012
sec-b
q11
math
asked
Jan 10, 2013
by
thanvigandhi_1
0
answers
In each of the follwing cases, state whether the function is one-one, onto or bijective. Justify your answer. $\begin{array}{1 1} (i) \: f: R \rightarrow R\: defined\: by \ f(x)=3-4x \\ (ii)\: f: R \rightarrow R\: defined\: by \ f(x)=1+x^2 .\end{array} $
cbse
class12
modelpaper
2012
sec-b
q11
math
asked
Jan 10, 2013
by
thanvigandhi_1
0
answers
Show that the relation R, defined in the set A of all triangles as \( R = (T_1, T_2):T_2\) is similar to \( T_2\)}, is equivalence relation. Consider three right triangles \( T_1\) , with sides 3, 4, 5; \( T_2\) with sides 5, 12, 13 and \( T_3\) with sides 6, 8, 10. Which triangle among \( T_1, T_2 \: and T_3\) are related?
cbse
class12
modelpaper
2012
sec-b
q11
math
asked
Jan 9, 2013
by
thanvigandhi_1
0
answers
Prove that\begin{array}{1 1}(i)\;P(A)+P(A\cap B)+P(A\cap \bar{B})\\(ii)\;P(A\cup B)=P(A\cap B)+P(A\cap\bar{B})+P(\bar{A}\cap\bar{B})\end{array}
cbse
class12
ch13
q11
p272
short-answer
exemplar
sec-a
easy
math
asked
Jan 8, 2013
by
sreemathi.v
1
answer
Show that the relation R in the set A of points, given by R: {P, Q): distance of the point P from the origin is the same as the distance of Q from the origin }, is an equivalence relation. Further, show that the set of all points related to P = (0, 0) is the circle passing through P with origin as the centre.
cbse
class12
modelpaper
2012
sec-b
q11
math
asked
Jan 8, 2013
by
thanvigandhi_1
0
answers
A manufacture of electronic circuits has a stock of 200 resistors,120 transistors and 150 capacitors and is required to produce two types of circuits A and B .Type A requires 20 resistors,10 transistors and 10 capacitors .Type B requires 10 resistors,20 transistors and 30 capacitors.If the profit on type A circuit is Rs 50 and that an type B circuit is Rs 60,formulate this problem as a LPP so that the manufacturer can maximize his profit.
cbse
class12
ch12
q11
p252
short-answer
exemplar
sec-a
easy
math
asked
Jan 7, 2013
by
sreemathi.v
1
answer
Prove that the relation R in the set A = {1, 2, 3, 4, 5}given by R = {(a, b):|a-b) is even }, is an equivalence relation.
cbse
class12
modelpaper
2012
sec-b
q11
math
asked
Jan 6, 2013
by
thanvigandhi_1
0
answers
Show that the relation R in the set A = {1, 2, 3, 4, 5} is given by R = {(a, b) : |a-b|is even }, is an equivalence relation. Show that all the elements of {1, 3, 5} are related to each other and all the elements of {2, 4} are related to each other. But no element of {1, 3, 5} is related to any element of {2, 4}.
cbse
class12
modelpaper
2012
sec-b
q11
math
asked
Jan 4, 2013
by
thanvigandhi_1
0
answers
Find the equations of the two lines through the origin which intersect the line $\;\large\frac{x-3}{2}=\frac{y-3}{1}=\frac{z}{1}$ at angles of $\large \frac{\pi}{3}$ each.
cbse
class12
ch11
q11
p236
exemplar
sec-b
difficult
math
asked
Jan 3, 2013
by
sreemathi.v
1
answer
Show that the relation R defined by (a, b ) R ( c, d ) \( \Rightarrow \) a + b + c on the set N x N is an equivalence relation.
cbse
class12
modelpaper
2012
sec-b
q11
math
asked
Jan 3, 2013
by
thanvigandhi_1
0
answers
Let f : N \( \rightarrow \) N be defined by : $ f(n) = \left\{ \begin{array}{l l} \large \frac{n+1}{2} & \quad \text{if $n$ is odd}\\ \large \frac{n}{2} & \quad \text{ if $n$ is even} \end{array} \forall \: n \: \in\: N. \right.$ Find whether the function f is bijective.
cbse
class12
modelpaper
2012
sec-b
q11
math
asked
Jan 2, 2013
by
thanvigandhi_1
0
answers
(i) Is the binary operation * defined on set N, given a * b = \( \large\frac{a+b}{2} \) for all a, b \( \in\) N, comutative? (ii) Is the above binary operation * associative ?
cbse
class12
modelpaper
2012
sec-b
q11
math
asked
Jan 2, 2013
by
thanvigandhi_1
0
answers
Find the value of k in the following so that the function f is continuous at the indicated point $f(x)=\left \{\begin{array}{1 1}3x-8, & if\;x\neq 5\\2k, & if\;x=5\end{array}\right.\;at\;x=5$
cbse
class12
ch5
q11
p108
short-answer
exemplar
sec-a
easy
math
asked
Dec 31, 2012
by
sreemathi.v
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
2009
sec-b
q11
math
asked
Dec 29, 2012
by
thanvigandhi_1
0
answers
Let \( f : N \rightarrow N\) be defined by : $ f(n) = \left\{ \begin{array}{l l} \large \frac{n+1}{2} & \quad \text{if $n$ is odd}\\ \large \frac{n}{2} & \quad \text{ if $n$ is even} \end{array} for \: all\: n\: \in \: N. \right.$
cbse
class12
modelpaper
2012
sec-b
q11
math
asked
Dec 29, 2012
by
thanvigandhi_1
0
answers
Let f, g : R \( \rightarrow \) R be defined as \( f(x) = |x| \: and \: g(x) = [x]\) where [x] denotes the greatest integer less than or equal to x, find the fog \( \bigg(\large \frac{5}{2} \bigg)\) and gof \( (-\sqrt 2) \).
cbse
class12
modelpaper
2011
sec-b
q11
math
asked
Dec 29, 2012
by
thanvigandhi_1
0
answers
Show that the function f : R \( \rightarrow \) R be defined by \( f(x) = 2x^3 - 7\), for \( x \: \in \: R\), is bijective.
cbse
class12
modelpaper
2011
sec-b
q11
math
asked
Dec 28, 2012
by
thanvigandhi_1
0
answers
Let N be the set of all natural numbers and R be the relation on N x N defined by (a, b) R (c, d) if ad = bc. Show that R is an equivalence relation.
cbse
modelpaper
2012
sec-b
q11
asked
Dec 26, 2012
by
thanvigandhi_1
1
answer
Consider \( f : R_+ \rightarrow [ -5, \infty ] \) given by \( f(x) = 9x^2 + 6x - 5\). Show that f is invertible with \( f^{-1} (y) = \bigg[\large \frac{\sqrt {y+6} - 1}{3} \bigg] \)
cbse
class12
modelpaper
2012
sec-b
q11
math
asked
Dec 25, 2012
by
thanvigandhi_1
0
answers
\( \int \: e^x \bigg(\frac{1}{x} - \frac{1}{x^2} \bigg) dx\) is equal to \[ \begin{array} ((A)\: \frac{-e^x}{x^2}+C \quad & (B)\: \frac{e^x}{x^2}+C \\ (C) \: \frac{-e^x}{x^2} \quad & (D) \: \frac{e^x}{x} \end{array} \]
cbse
class12
modelpaper
2012
sec-a
q11
math
asked
Dec 24, 2012
by
thanvigandhi_1
0
answers
Does $A=\begin{bmatrix}5 & 3\\1 & 2\end{bmatrix}$ satisfy the equation $\;A^2-3A-7I=0$ and hence find $\;A^{-1}$
class12
cbse
ch3
q11
p54
short-answer
exemplar
sec-c
medium
math
asked
Dec 22, 2012
by
sreemathi.v
1
answer
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 a change of (a) the perimeter, (b) the area of the rectangle.
cbse
class12
modelpaper
2009
sec-b
q11
math
asked
Dec 21, 2012
by
thanvigandhi_1
0
answers
Solve the following equation $\cos\big(\tan^{-1}x\big)=\sin\bigg(\cot^{-1}{\frac{3}{4}}\bigg)$
cbse
class12
ch2
q11
p36
exemplar
medium
sec-b
math
asked
Dec 20, 2012
by
sreemathi.v
1
answer
(i) Is the binary operation * , defined on set N, given by \(a*b =\large \frac{a+b}{2}\) for all \( a,b \in\: N\), commutative? \[ \] (ii) Is the above binary operation * associative?
cbse
class12
modelpaper
2008-1
sec-b
q11
math
asked
Dec 20, 2012
by
thanvigandhi_1
0
answers
Let the function $f\;:\;R \rightarrow R$ be defined by$ f(x)=\cos x,\forall \;x\;\in R$.Show that f is neither one-one nor onto
cbse
class12
ch1
q11
p11
short-answer
exemplar
sec-a
easy
math
asked
Dec 18, 2012
by
sreemathi.v
1
answer
Find the equation of the plane through the line of intersection of the planes $x + y + z = 1$ and $2x + 3y + 4z = 5$ which is perpendicular to the plane$x -y + z = 0.$
cbse
class12
bookproblem
ch11
sec3
q11
p493
sec-b
medium
math
asked
Dec 15, 2012
by
thanvigandhi_1
1
answer
Find the angle between the following pair of lines: $ \frac{\large x-2}{\large 2} = \frac{\large y-1}{\large 5} = \frac{\large z + 3}{\large -3} \: and\: \frac{\large x+2}{\large -1} = \frac{\large y-4}{\large 8} = \frac{\large z - 5}{\large 4} $
cbse
class12
bookproblem
ch11
sec2
q11
p478
easy
sec-b
q11-1
math
asked
Dec 14, 2012
by
thanvigandhi_1
1
answer
Find the value of $ \tan^{-1} \bigg[ 2\cos \bigg(2\sin^{-1}\frac{1}{2}\bigg) \bigg] $
cbse
class12
bookproblem
ch2
sec2
q11
p48
medium
sec-b
math
asked
Dec 10, 2012
by
thanvigandhi_1
1
answer
Show that the vectors \(2\hat i − 3\hat j + 4\hat k\) and \(− 4\hat i + 6\hat j − 8\hat k\) are collinear.
class12
bookproblem
ch10
sec2
q11
p440
easy
sec-a
asked
Dec 6, 2012
by
thanvigandhi_1
1
answer
Find the integral $\displaystyle\int\frac{\large x^3+5x^2-4}{\large x^2}\;dx$
cbse
class12
bookproblem
ch7
sec1
q11
p299
sec-a
easy
math
asked
Dec 6, 2012
by
sreemathi.v
1
answer
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