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Answers posted by vijayalakshmi_ramakrishnans
Questions
51
answers
0
best answers
0
votes
If A and B are independent events such that \( P(A) = 0.2, P(A \cup B)=0.5, \: find \: P(B).\)
answered
Dec 2, 2013
P(AUB) = P(A) + P(B)-P(A intersection B) Since the events are independent P(A intersection B)is 0 Th...
0
votes
Find a, for which \( f(x) = x^2-2ax+6\) is strictly increasing when x > 0.
answered
Nov 30, 2013
If the function is increasing or decreasing f'(x) =0 Given f(x) =x^2-2ax+6 Differentiating w.r.t x w...
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votes
If A is square matrix of order 3 such that | adj.A |=81, find | A |.
answered
Nov 30, 2013
|adjA|^n=|A|^n-1 Given |adjA|=81 81=3^4 Hence |A| =3^3=27 Therefore|A|=27
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votes
Differentiate \( \cos^{-1}x^4\) w.r.t. \( x.\)
answered
Nov 30, 2013
Given y=cos^-1x^4 Differentiating w.r.t x by appying chain rule we get, Dy/dx = (-1/√x^2-1)4x^3 Ther
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votes
Evaluate : $ \int_0^{1.5} [x] \: dx $
answered
Nov 30, 2013
Let I = int of x On integrating we get X^2/2 On applying limits we get 1.5^2/2 - 0 = 2.25/2=1.125
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votes
Find the differential equation that will represent the family of straight lines \( y=mx+c\), where m,c are parameters.
answered
Nov 30, 2013
Since the equation of the straight lines has two parameters, we will hve to differentiate twice. Giv...
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votes
For what values of p, $ \overrightarrow a = (2\hat i + 6\hat j + 3\hat k)$ p is a unit vector.
answered
Nov 30, 2013
Any unit vector in the directiln of a vector.is a vector ÷|avector| |a |vector | is √2^2+6^2+3^2=7 H
0
votes
$\bigg \{ x \in R :\large\frac{2x-1}{x^3+4x^2+3x} \in $$R \bigg \} =$
answered
Nov 3, 2013
$x^3+4x^2+3x= x(x^2+4x+3)$On factorizing this we get $x =0$ and $x = -1$ and $-3.$Hence $R- \{0.-1,-...
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votes
the plane 2x-3y+6z=11 makes and angle arcsin alpha with x axis the value of alpha is
answered
Oct 24, 2013
The angle $\alpha$ made by the plane and the line is given by $sin\alpha =\large\frac{\overri...
0
votes
find the position vector of a point A in space such that A vector is inclined at 60 to OX and at 45 to OY and [OA]= 10 UNITS
answered
Oct 24, 2013
Let cos60 = (x2-x1/))OA . Let O (0,0,0) and A(x1,y1,z1) => 1/2 = (x1-0)/10 => x1 = 5 c0s45 =...
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votes
find the equation of the tangent and normal to the hyperbole s2/a2 - y2/b2 = 1 at the point (x0,y0)
answered
Oct 24, 2013
Given eqn. is $\large\frac{ x^2}{a^2} - \frac{y^2}{b^2}$$ = 1$.....(i) Differentiating on both side...
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votes
let * be a binaray operation on N given by a*b = 1cm (a,b) ,a,b belong to N find 2*4 and is N,* associative?
answered
Oct 24, 2013
(a*b)*c= LCM(a,b)*c and a*(b*c) = a*LCM(b,c)= LCM (a,b,c) Therefore (a*b)*c = a*(b*c) for all a,b,c...
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votes
find the equation of the line passes throught the point (1,2,3) and is parallel to the vector 3i+2j-2k
answered
Oct 24, 2013
Vector Equation of a line passing through the point with position vector $\overrightarrow a$ and pa...
0
votes
A car, traveling with a uniform acceleration, has a velocity of 18 km/hour at a certain time and 54 km/hour after covering a distance of 500m. How much further will it travel to attain a velocity of 72 km/hour?
answered
Aug 18, 2013
v^2-u^2/2s = a given s = 500, u= 18km/hr and v = 54km/hr Now substituting for s,u and v and a we g...
0
votes
find the differential equation of the family of straight lines at a fixed distance p from the origin?
answered
Jun 15, 2013
Toolbox: General equation of a straight line passing through the origin is $y = mx$ ...
0
votes
If A and B are invertible matrices,then which of the following is not correct?\[\begin{array}{1 1}(A)\quad adjA=|A|.A^{-1} & (B)\quad det(A)^{-1}=[det(A)]^{-1}\\(C)\quad (AB)^{-1}=B^{-1}A^{-1} & (D)\quad (A+B)^{-1}=B^{-1}+A^{-1}\end{array}\]
answered
Mar 26, 2013
Toolbox: If $A^{-1}=\frac{1}{|A|}adj( A)$ $A(adj A)=|A|I=(adj A)A$ $(AB)^{-1}=B^{-1}A^{-1}$...
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votes
If $a_1,a_2,a_3,....,a_r$ are in G.P., then prove that the determinant $\begin{vmatrix} a_{r-1} & a_{r-5} & a_{r-9} \\ a_{r-7} & a_{r-11} & a_{r-15} \\ a_{r-13} & a_{r-17} & a_{r-21} \end{vmatrix} is\; independent\; of\; r$
answered
Mar 19, 2013
Toolbox: If each element of a row (or a column) of a determinant is multiplied by constant k,and ...
0
votes
Find the value of $\theta$ satisfying $\begin{bmatrix} 1 & 1 & \sin3\theta \\ -4 & 3 & \cos2\theta \\ 7 & -7 & -2 \end{bmatrix}\;=\;0$
answered
Mar 16, 2013
Toolbox: If $A=\begin{vmatrix}a_{11} & a_{21} & a_{31}\\a_{12} & a_{22} & a_{32}\...
0
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If the coordinates of the vertices of an equilateral triangle with sides of length 'a' are $(x_1,y_1),(x_2,y_2),(x_3,y_3)$ then \[{\begin{vmatrix}x_1 & y_1 &1\\x_2 & y_2 &1\\x_3 & y_3 & 1\end{vmatrix}}^2=\frac{3a^4}{4}.\]
answered
Mar 16, 2013
Toolbox: Area of a triangle ABC is $\Delta=\frac{1}{2}\begin{vmatrix}x_1 & y_1 & 1\\x_2 &...
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Using Cofactors of elements of second row, evaluate $ \Delta = \begin{vmatrix} 5&3&8 \\ 2&0&1 \\ 1&2&3 \end{vmatrix} $
answered
Mar 6, 2013
Toolbox: Expanding the determinant $\bigtriangleup$ along $R_2$ we have $\bigtriangleup=(-1)^{...
0
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Using Cofactors of elements of third column, evaluate $ \Delta = \begin{vmatrix} 1&x&yz \\ 1&y&zx \\ 1&z&xy \end{vmatrix} $
answered
Mar 6, 2013
Toolbox: $\bigtriangleup$=Sum of the product of any row (or column) with their corresponding cofa...
0
votes
Find the adjoint of the matrix: $\begin{bmatrix} 1&2 \\ 3&4 \end{bmatrix} $
answered
Mar 6, 2013
Toolbox: (i)A square matrix is said to be singular if |A|$\neq$ 0. (ii)The adjoint of a square...
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votes
Find the adjoint of the matrix: $\begin{bmatrix} 1&-1&2 \\ 2&3&5 \\ -2&0&1 \end{bmatrix} $
answered
Mar 6, 2013
Toolbox: The adjoint of a square matrix is defined as the transpose of the matrix $[A_{ij}]_n\tim...
0
votes
Verify A (adj A)= (adj A) A = | A | I: \[ \begin{bmatrix} 2&3 \\ - 4&-6 \\ \end{bmatrix} \]
answered
Mar 6, 2013
Toolbox: For a square matrix of order 2,given by $A=\begin{bmatrix}a_{11} & a_{12}\\a_{21}...
0
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Verify A (adj A)= (adj A) A = | A | I: \[ \begin{bmatrix} 1&-1&2 \\ 3&0&-2 \\ 1&0&3 \\ \end{bmatrix} \]
answered
Mar 6, 2013
Toolbox: (i)A square matrix is said to be singular if $|A|$ =0. (ii)The adjoint of a matrix $A...
0
votes
Find values of $k$ if area of triangle is $4\; sq. units$ and vertices are $(-2, 0), (0, 4), (0, k)$
answered
Mar 6, 2013
Toolbox: The area of a triangle whose vertices are $(x_1,y_1),(x_2,y_2),(x_3,y_3)$ is give...
0
votes
Find the inverse of the matrix (if it exists): $ \begin{bmatrix} 2&-2 \\ 4&3 \\ \end{bmatrix} $
answered
Mar 6, 2013
Toolbox: (i)A square matrix is said to be singular if $|A|$ =0. (ii)A square matrix is inverti...
0
votes
Find the inverse of the matrix (if it exists): $ \begin{bmatrix} -1&5 \\ -3&2 \\ \end{bmatrix} $
answered
Mar 6, 2013
Toolbox: (i)A square matrix is said to be singular if $|A|$ =0. (ii)A square matrix is inverti...
0
votes
Find the inverse of the matrix (if it exists): $ \begin{bmatrix} 1&2&3 \\ 0&2&4 \\ 0&0&5 \\ \end{bmatrix} $
answered
Mar 6, 2013
Toolbox: (i)A matrix is said to be singular if $|A|$ =0. (ii)A square matrix is said to be inv...
0
votes
Find the inverse of the matrix (if it exists): $\begin{bmatrix} 1 & 0 & 0 \\ 3 & 3 & 0 \\ 5 & 2 & -1 \\ \end{bmatrix}$
answered
Mar 6, 2013
Toolbox: (i)A matrix is said to be singular if $|A|$ =0. (ii)A matrix is said to be invertible...
0
votes
Find the inverse of the matrix (if it exists): $ \begin{bmatrix} 2 & 1& 3 \\ 4 &- 1 & 0 \\ -7 & 2 & 1 \\ \end{bmatrix} $
answered
Mar 6, 2013
Toolbox: (i)A matrix is said to be singular if $|A|$ =0. (ii)A matrix is said to be invertible...
0
votes
Find the inverse of the matrix (if it exists): $\begin{bmatrix} 1 & -1 & 2 \\ 0 & 2 & -3 \\ 3 & -2 & 4 \\ \end{bmatrix} $
answered
Mar 6, 2013
Toolbox: (i)A matrix is said to be singular if $|A|$ =0. (ii)A matrix is said to be invertible...
0
votes
Find the inverse of the matrix (if it exists): \[ \begin{bmatrix} 1&0&0 \\ 0&cos\alpha&sin\alpha \\ 0&sin\alpha&-cos\alpha \\ \end{bmatrix} \]
answered
Mar 6, 2013
Toolbox: (i)A matrix is said to be singular if $|A|$ =0. (ii)A matrix is said to be invertible...
0
votes
\[ \text{For the matrix A = } \begin{bmatrix} 1&1&1 \\ 1& 2&- 3 \\ 2 &-1& 3 \end{bmatrix} \] \[ \text{Show that } A^{3} - 6A^{2} + 5A + 11I = O. \text{ Hence, find } A^{-1}\]
answered
Mar 5, 2013
Toolbox: (i)A matrix is said to be singular if $|A|$ =0. (ii)A matrix is said to be invertible...
0
votes
\[ \text{For the matrix A = } \begin{bmatrix} 2&-1&1 \\ -1& 2&- 1 \\ 1 &-1& 2 \end{bmatrix} \] \[ \text{Show that } A^{3} - 6A^{2} + 9A - 4I = O. \text{ Hence, find } A^{-1}\]
answered
Mar 5, 2013
Toolbox: (i)A matrix is said to be singular if $|A|$ =0. (ii)A matrix is said to be invertible...
0
votes
Solve system of linear equations, using matrix method:\[\] \[2x+y+z=1\] \[x-2y-z = \frac{3}{2}\] \[3y-5z=9\]
answered
Mar 5, 2013
Toolbox: A matrix is said to be singular if |A|= 0. A matrix is said to be invertible if |A|$\...
0
votes
Solve system of linear equations, using matrix method:\[\] \[2x+3y+3z=5\] \[x-2y+z=-4\] \[3x-y-2z=3\]
answered
Mar 5, 2013
Toolbox: A matrix is said to be singular if |A|= 0. A matrix is said to be invertible if |A|$\...
0
votes
Solve system of linear equations, using matrix method:\[\] \[x-y+z=4\] \[2x+y-3z=0\] \[x+y+z=2\]
answered
Mar 5, 2013
Toolbox: A matrix is said to be singular if |A|= 0. A matrix is said to be invertible if |A|$\...
0
votes
Solve system of linear equations, using matrix method:\[\] \[x-y+2z=7\] \[3x+4y-5z=-5\] \[2x-y+3z=12\]
answered
Mar 5, 2013
Toolbox: A matrix is said to be singular if |A|= 0. A matrix is said to be invertible if |A|$\...
0
votes
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: \[2x-3y+5z=11\] \[3x+2y-4z = -5\] \[x+y-2z = -3\]
answered
Mar 5, 2013
Toolbox: A matrix is said to be singular if |A|= 0. A matrix is said to be invertible if |A|$\...
0
votes
The cost of 4 kg onion, 3 kg wheat and 2 kg rice is Rs 60. The cost of 2 kg onion, 4 kg wheat and 6 kg rice is Rs 90. The cost of 6 kg onion 2 kg wheat and 3 kg rice is Rs 70. Find cost of each item per kg by matrix method.
answered
Mar 5, 2013
Toolbox: A matrix is said to be singular if |A|= 0. A matrix is said to be invertible if |A|$\...
0
votes
$If \; A^{-1}=\begin{bmatrix} 3 &-1 & 1\\ -15&6 &-5 \\ 5& -2&2 \end{bmatrix} \; and \; B = \begin{bmatrix} 1 & 2 & -2\\ -1 & 3 & 0\\ 0 & -2 & 1 \end{bmatrix}, \; find \; (AB)^{-1} $
answered
Mar 5, 2013
Toolbox: A matrix is said to be singular if|A|=0. A matrix is said to be invertible if $|A|\ne...
0
votes
Let A = $\begin{bmatrix} 1 & -2 & 1\\ -2 & 3 & 1\\ 1 & 1 & 5 \end{bmatrix}$. Verify that \[\] $(i)\ \; \left [adj A \right ]^{-1} = adj(A^{-1}) \;\;\;\; $
answered
Mar 5, 2013
Toolbox: A matrix is said to be singular if|A|=0. A matrix is said to be invertible if $|A|\ne...
0
votes
Using properties of determinants, prove that: $ \begin{vmatrix} x &x^2 &1 & px^3\\ y &y^2 &1 & py^3\\ z &z^2 &1 & pz^3 \end{vmatrix}= (1+pxyz) (x-z) (y-z)(z-x), $ where p is any scalar.
answered
Mar 5, 2013
Toolbox: If each element of a row(or a column) of a determinant is multiplied by a constan...
0
votes
Using properties of determinants, prove that: $\begin{vmatrix} 3a&-a+b&-a+c\\ -b+a&3b&-b+c\\ -c+a&-c+b&3c \end{vmatrix}= 3(a+b+c)(ab+bc+ca)$
answered
Mar 5, 2013
Toolbox: If each element of a row(or a column) of a determinant is multiplied by a constan...
0
votes
Find equation of line joining (3, 1) and (9, 3) using determinants.
answered
Feb 24, 2013
The area of a triangle whose vertices are $(x_1,y_1),(x_2,y_2),(x_3,y_3)$ is given by ...
0
votes
Which of the following is a homogeneous differential equation?
answered
Dec 25, 2012
Toolbox:A differential equation of the form $dy/dx = F(x,y)$ is said to be homogenous, if $F(x,y)$ i...
0
votes
Show that the differential equation is homogeneous and solve\[(x-y)\;dy-(x+y)\;dx=0\]
answered
Dec 24, 2012
Solution: $tan^{-1}(y/x) = (1/2)log(x^2+y^2) + C$ Toolbox: A dif...
0
votes
Show that the differential equation is homogeneous and solve\[y'=\frac{x+y}{x}\]
answered
Dec 24, 2012
Solution: $y = x. logx + C.x$ Tool Box: ...
0
votes
Determine order and degree (if defined) of differential equation $y'+5y=0$
answered
Dec 24, 2012
Toolbox:The highest order derivative present in the differential equation determines the order of th...
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