Answers posted by vijayalakshmi_ramakrishnans

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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...

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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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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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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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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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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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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

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$\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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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...

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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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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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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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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...

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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...

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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 $y = mx$ ...

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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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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 ...

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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}\...

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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)^{...

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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...

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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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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...

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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}...

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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...

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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...

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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...

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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...

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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...

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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