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Recent questions tagged q9
Questions
Find the vector and the cartesian equations of the line that passes through the points $(3, -2, -5), (3, -2, 6).$
cbse
class12
bookproblem
ch11
sec2
p478
q9
easy
sec-a
math
asked
Nov 29, 2012
by
balaji.thirumalai
1
answer
Prove that \[tan^{-1} \sqrt{x} = \frac{1}{2} cos^{-1} \;\; \bigg(\frac{1-x}{1+x}\bigg), x\in [0,1]\]
cbse
class12
bookproblem
ch2
misc
q9
p52
medium
sec-b
math
asked
Nov 29, 2012
by
vaishali.a
1
answer
Evaluate $ \begin{vmatrix} x & y & x+y\\ y & x+y & x\\ x+y & x & y \end{vmatrix}$
cbse
class12
bookproblem
ch4
misc
q9
p142
easy
sec-b
math
asked
Nov 29, 2012
by
balaji.thirumalai
1
answer
Solve system of linear equations, using matrix method:<br>$4x-3y=3$ <br> $3x-5y=7$
cbse
class12
bookproblem
ch4
sec6
q9
p136
medium
sec-b
math
asked
Nov 29, 2012
by
balaji.thirumalai
1
answer
Show that the minimum of Z occurs at more than two points. Maximise $z = – x + 2y$, subject to the constraints: $ x \geq 3, x + y \geq 5, x + 2y \geq 6, y \geq 0.$
cbse
class12
bookproblem
ch12
sec1
q9
p514
medium
sec-c
math
asked
Nov 29, 2012
by
fingeazy
1
answer
Find the inverse of the matrix (if it exists): $ \begin{bmatrix} 2 & 1& 3 \\ 4 &- 1 & 0 \\ -7 & 2 & 1 \\ \end{bmatrix} $
cbse
class12
bookproblem
ch4
sec5
q9
p132
medium
sec-b
math
asked
Nov 29, 2012
by
balaji.thirumalai
1
answer
Find the particular solution of the differential equation $(1+e^{2x})dy + (1+y^2)e^xdx$ = 0, given that $y = 1$ when $x = 0$
cbse
class12
bookproblem
ch9
misc
q9
p420
medium
modelpaper
2012
q18
math
sec-a
asked
Nov 29, 2012
by
sreemathi.v
1
answer
By using the properties of determinants show that \[\begin{vmatrix} x&x^2&yz \\ y&y^2&zx \\ z&z^2&xy \end{vmatrix} = (x-y)(y-z)(z-x)(xy+yz+zx) \]
cbse
class12
bookproblem
ch4
sec2
q9
p120
difficult
sec-b
math
asked
Nov 28, 2012
by
balaji.thirumalai
1
answer
Determine order and degree (if defined) of differential equation $y''+(y')^2+2y=0$
cbse
class12
bookproblem
ch9
sec1
q9
p383
easy
math
sec-a
asked
Nov 28, 2012
by
sreemathi.v
1
answer
Find the principal value of the following: $cos^{-1} \bigg( -\frac {1} {\sqrt 2} \bigg) $
cbse
class12
bookproblem
ch2
sec1
q9
p42
sec-a
math
asked
Nov 28, 2012
by
vaishali.a
2
answers
A tank with rectangular base and rectangular sides, open at the top is to be constructed so that its depth is $2 m$ and volume is $8 m^3$. If building of tank costs Rs 70 per sq metres for the base and Rs 45 per square metre for sides. What is the cost of least expensive tank?
cbse
class12
bookproblem
ch6
misc
q9
p242
sec-c
medium
math
asked
Nov 28, 2012
by
thanvigandhi_1
1
answer
Show that the set {[1], [3], [4], [5], [9]} forms an abelian group under multiplication modulo 11.
tnstate
class12
bookproblem
ch9
sec2
exercise9-4
p190
q9
modelpaper
mar-2007
jun-2009
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
Construct the truth tables for the following statement: (p ∨ q) ∨ r
tnstate
class12
bookproblem
ch9
sec1
exercise9-2
p164
q9
asked
Nov 27, 2012
by
balaji.thirumalai
0
answers
An experiment succeeds twice as often as it fails. Find the probability that in the next six trials, there will be at least 4 successes.
cbse
class12
bookproblem
ch13
misc
p583
q9
easy
sec-b
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
On a multiple choice examination with three possible answers for each of the five questions, what is the probability that a candidate would get four or more correct answers just by guessing ?
cbse
class12
bookproblem
ch13
sec5
p577
q9
sec-b
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
The random variable X has a probability distribution P(X) of the following form, where k is some number : \[ P(X) = \left\{ \begin{array}{l l} k & \quad \text{if $x$ = 0}\\ 2k & \quad \text{if $x$ = 1} \\ 3k & \quad \text{if $x$ = 2} \\ 0 & \quad \text{otherwise} \end{array} \right. \] (a) Determine the value of k. (b) Find $P (X \lt 2), P (X \leq 2), P(X \geq 2).$
cbse
class12
bookproblem
ch13
sec4
p571
q9
sec-b
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
Two groups are competing for the position on the Board of directors of a corporation. The probabilities that the first and the second groups will win are 0.6 and 0.4 respectively. Further, if the first group wins, the probability of introducing a new product is 0.7 and the corresponding probability is 0.3 if the second group wins. Find the probability that the new product introduced was by the second group.
cbse
class12
bookproblem
ch13
sec3
p556
q9
sec-b
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
If A and B are two events such that $P (A) = \large \frac{1}{4} , P (B) = \large\frac{1}{2} $ and $P(A \cap B) = \large \frac{1}{8} $ , find $P$ (not A and not B).
cbse
class12
bookproblem
ch13
sec2
p546
q9
sec-a
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
What is the maximum value of the function $\sin \: x + \cos x$?
cbse
class12
bookproblem
ch6
sec5
q9
p232
sec-b
medium
math
asked
Nov 27, 2012
by
thanvigandhi_1
1
answer
Determine P(E|F) . Mother, father and son line up at random for a family picture E : son on one end, F : father in middle
cbse
class12
bookproblem
ch13
sec1
q9
p539
sec-a
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
Find $x$ and $y$, if $ 2\begin{bmatrix} 1 & 3 \\ 0 & x \end{bmatrix} + \begin{bmatrix} y & 0 \\ 1 & 2 \end{bmatrix} = \begin{bmatrix} 5 & 6 \\ 1 & 8 \end{bmatrix} $
cbse
class12
bookproblem
ch3
sec2
q9
p81
easy
shortanswer
sec-a
math
asked
Nov 26, 2012
by
pady_1
1
answer
The approximate change in the volume of a cube of side $x$ metres caused by increasing the side by $3\%$ is
cbse
class12
bookproblem
ch6
sec4
q9
p216
sec-a
medium
math
asked
Nov 26, 2012
by
thanvigandhi_1
1
answer
Find $ \frac{1}{2}(A + A')$ and $\frac{1}{2}(A - A')$ , when $ A = \begin{bmatrix} 0 & a & b \\ -a & 0 & c \\ -b & -c & 0 \end{bmatrix} $
cbse
class12
bookproblem
ch3
sec3
q9
p89
medium
shortanswer
sec-b
math
asked
Nov 25, 2012
by
pady_1
1
answer
Using elementary transformations, find the inverse of the matrix if it exists - $ \begin{bmatrix} 3 & 10 \\ 2 & 7 \end{bmatrix} $
cbse
class12
bookproblem
ch3
sec4
q9
p97
medium
shortanswer
sec-b
math
asked
Nov 23, 2012
by
pady_1
1
answer
Find the point on the curve $y = x^3 - 11x + 5$ at which the tangent is $y = x -11$.
cbse
class12
bookproblem
ch6
sec3
q9
p212
sec-a
easy
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
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
bookproblem
ch3
misc
q9
p100
medium
shortanswer
sec-b
math
asked
Nov 23, 2012
by
pady_1
1
answer
Prove that \( y =\large { \frac{4\sin\theta}{(2+\cos\theta)}}-\normalsize \theta\) is an increasing function of \(\theta\) in $\left[0, \: \large {\frac{\pi}{2}}\right]$
cbse
class12
bookproblem
ch6
sec2
q9
p205
sec-b
easy
modelpaper
2012
q15
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
A balloon, which always remains spherical has a variable radius. Find the rate at which its volume is increasing with the radius when the later is $10\; cm$.
cbse
class12
bookproblem
ch6
sec1
q9
p198
sec-a
easy
math
asked
Nov 22, 2012
by
thanvigandhi_1
1
answer
Given a non-empty set \(X\), consider the binary operation \(\ast : P(X) × P(X) \to P(X)\) given by \(A \ast B=A \cap B\; \forall A, \) \( B \;in\; P(X),\) where \(P(X)\) is the power set of \(X\). Show that \(X\) is the identity element for this operation and \(X\) is the only invertible element in \(P(X)\) with respect to the operation \(\ast\).
cbse
class12
bookproblem
ch1
misc
q9
p30
sec-a
math
asked
Nov 22, 2012
by
vaishali.a
1
answer
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
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
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
If $x$ and $y$ are connected parametrically by the equations given in $x = a \sec \theta, y = b \tan \theta $ without eliminating the parameter, Find $\frac{\large dy}{\large dx}$.
cbse
class12
bookproblem
ch5
sec6
q9
p181
easy
sec-a
math
asked
Nov 20, 2012
by
thanvigandhi_1
1
answer
Differentiate the functions given in w.r.t. $x : $ $ x ^{\large\sin x} + (\sin x)^{\large\cos x} $
cbse
class12
bookproblem
ch5
sec5
q9
p178
difficult
sec-c
math
asked
Nov 17, 2012
by
thanvigandhi_1
1
answer
Differentiate the following w.r.t. $x: \large \frac {\cos x}{\log x}$,$\; x > 0 $
cbse
class12
bookproblem
ch5
sec4
q9
p174
easy
sec-a
math
asked
Nov 16, 2012
by
thanvigandhi_1
1
answer
A diet is to contain at least 80 units of vitamin A and 100 units of minerals. Two foods $F_{1} $ and $F_{2} $ are available. Food $F_1$ costs Rs 4 per unit food and $F_2$ costs Rs 6 per unit. One unit of food $F_{1} $ contains 3 units of vitamin A and 4 units of minerals. One unit of food $F_{2} $ contains 6 units of vitamin A and 3 units of minerals. Formulate this as a linear programming problem. Find the minimum cost for diet that consists of mixture of these two foods and also meets the minimal nutritional requirements.
cbse
class12
bookproblem
ch12
sec2
q9
p520
sec-c
medium
math
asked
Nov 16, 2012
by
fingeazy
1
answer
A fruit grower can use two types of fertilizer in his garden, brand P and brand Q. Tests indicate that the garden needs at least 240 kg of phosphoric acid, at least 270 kg of potash and at most 310 kg of chlorine. The amounts (in kg) of nitrogen, phosphoric acid, potash, and chlorine in a bag of each brand are given in the table below. \[\] $\begin{matrix} \text{kg per bag:}& \text{Brand P} &\text{Brand Q} \\ \text {Nitrogen} &3 & 3.5\\ \text {Phosphoric Acid}& 1 & 2\\ \text {Potash}&3 &1.5 \\ \text {Chlorine}& 1.5 & 2 \end{matrix}$ \[\] If the grower wants to maximise the amount of nitrogen added to the garden, how many bags of each brand should be added? What is the maximum amount of nitrogen added?
cbse
class12
bookproblem
ch12
misc
q9
p528
sec-c
difficult
math
asked
Nov 16, 2012
by
fingeazy
1
answer
Find $ \frac {dy}{dx} $ in the following: $ y = sin^{-1} \left(\frac{2x}{1 + x^2}\right) $
cbse
class12
bookproblem
ch5
sec3
q9
p169
easy
sec-a
exercise5-3
math
asked
Nov 15, 2012
by
thanvigandhi_1
1
answer
Consider \(f:R_+ \to [\;\text{–5}, \infty )\)given by \(f(x)=9x^2 +6x\)-\(5\).Show that \(f\) is invertible with \( f^{-1} (y) = \bigg(\frac{(\sqrt{y+6}) -1} { 3}\bigg) \)
cbse
class12
bookproblem
ch1
sec3
q9
p19
medium
sec-b
math
asked
Nov 15, 2012
by
vaishali.a
1
answer
Find all points of discontinuity of $f$, where $f$ is defined by $f(x) = \left\{ \begin{array} {1 1} \large \frac x { |\;x\;| },& \quad\text{ if \(x\) < 0 }\\ -1 ,& \quad \text{if $x$ \( \geq 0\)}\\ \end{array} \right. $
cbse
class12
bookproblem
ch5
sec1
q9
p159
sec-b
medium
math
asked
Nov 9, 2012
by
thanvigandhi_1
1
answer
Prove that the function \( f \) given by $f(x) = | x - 1 |, x \in R\;$ is not differentiable at $\; x = 1$.
cbse
class12
bookproblem
ch5
sec2
q9
p166
exercise5-2
sec-b
medium
math
asked
Nov 8, 2012
by
thanvigandhi_1
1
answer
Show that each of 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 $\}$ is an equivalence relation. Find the set of all elements related to 1.
cbse
class12
bookproblem
ch1
ex1-1
q9
p6
easy
sec-a
modelpaper
2012
q13
math
asked
Nov 7, 2012
by
vaishali.a
1
answer
Find the shortest distance between lines $\hat{r} = 6\hat{i} + 2\hat{j} + 2\hat{k} + \lambda ( \hat{i} - 2\hat{j} + 2\hat{k} )$ and $\hat{r} = - 4\hat{i} - \hat{k} + \mu (3\hat{i} - 2\hat{j} - 2\hat{k} )$
cbse
class12
bookproblem
ch11
misc
p498
q9
sec-b
easy
math
asked
Nov 2, 2012
by
balaji.thirumalai
1
answer
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