Recent questions tagged sec-b

If $\;z_{1}=2-i\;,z_{2}=1+i\;$ find $\;|\large\frac{z_{1}+z_{2}+1}{z_{1}-z_{2}+i}|$

asked Apr 11, 2014 by yamini.v

1 answer

Solve the equation : $\;21x^{2}-28x+10=0\;$

asked Apr 11, 2014 by yamini.v

1 answer

Solve the equation : $\;27x^{2}-10x+1=0\;$

asked Apr 11, 2014 by yamini.v

1 answer

Solve the equation : $\;x^{2}-2x+\large\frac{3}{2}=0\;$

asked Apr 11, 2014 by yamini.v

1 answer

Solve the equation : $\;3x^{2}-4x+\large\frac{20}{3}=0\;$

asked Apr 11, 2014 by yamini.v

1 answer

Convert the following in the polar form : $\;\large\frac{1+3i}{1-2i}$

asked Apr 11, 2014 by yamini.v

1 answer

Convert the following in the polar form : $\;\large\frac{1+7i}{(2-i)^{2}}$

asked Apr 11, 2014 by yamini.v

1 answer

A manufacturer reckons that the value of a machine which costs him $Rs.15,625$, will depreciate each year by $20\%$. find the estimated value at the end of $5$ years.

asked Apr 11, 2014 by rvidyagovindarajan_1

1 answer

For any two complex numbers $\;z_{1}\;$ and $\;z_{2}\;$, what is the value of $\; Re(z_{1} z_{2}) $?

asked Apr 11, 2014 by yamini.v

1 answer

Evaluate : $\;[i^{18} +(\large\frac{1}{i})^{25}]^{3}$

asked Apr 11, 2014 by yamini.v

1 answer

Solve the equation : $\;x^{2}+\large\frac{x}{\sqrt{2}}+1=0\;$

asked Apr 11, 2014 by yamini.v

1 answer

Solve the equation : $\;x^{2}+x+\large\frac{1}{\sqrt{2}}=0\;$

asked Apr 11, 2014 by yamini.v

1 answer

Solve the equation : $\;\sqrt{3}x^{2}-\sqrt{2}x+3\sqrt{3}=0\;$

asked Apr 11, 2014 by yamini.v

1 answer

If $ y=\frac{2}{\Large\sqrt {a^2-b^2}}\tan^{-1}\bigg[\sqrt{\frac{a-b}{a+b}}\tan \frac{x}{2} \bigg],$ prove that $ \Large\frac{dy}{dx}=\frac{1}{a+b \cos x}, \normalsize a>b>0 $

asked Jan 25, 2013 by meena.p

1 answer

Let $\phi(x)\;andh(x)$ be derivable at x = c. Show that necessary and sufficient condition for the function defined as :\[f(x)= \left\{ \begin{array}{1 1} \phi(x), & \quad x \leq c \\ h(x), & \quad x>c \end{array} \right. \]to be derivable at x= c are $(i)\phi(c)=h(c)\quad(ii)\phi'(c)=h'(c)$

asked Jan 25, 2013 by meena.p

1 answer

Let $f(x) = \left\{ \begin{array}{l l} \Large\frac{1-sin^3x}{3cos^2x}, & \quad if\; { x < \Large\frac{\pi}{2}}\\ a, & \quad if\; { x = \Large\frac{\pi}{2}} \\ \Large\frac{b(1-sin x)}{(\pi - 2x)^2}, & \quad if \;{ x > \Large\frac{\pi}{2}} \end{array}. \right.$ If f(x) is continuous function at x $ x = \Large\frac{\pi}{2} $, find a and b.

asked Jan 25, 2013 by meena.p

1 answer

Discuss the continuity of the following function at x = 0 $f(x)= \left\{ \begin{array}{1 1} \Large\frac{x^4+x^3+2x^2}{\tan ^{-1}x} & \quad ,\;x\neq0 \\ 10 & \quad ,\;x=0 \end{array} \right. $

asked Jan 25, 2013 by meena.p

1 answer

Let $ f(x)= \left\{ \begin{array}{1 1} |x|\cos \frac{1}{x} & \quad if\;x\neq0 \\ 0 & \quad if\;x=0 \end{array} \right. $ then discuss the continuity of f(x) at x = 0

asked Jan 25, 2013 by meena.p

1 answer

Determine the values of a, b and c for which the function :$f(x)= \left\{ \begin{array}{1 1} \Large\frac{\sin (a+1)x+\sin x}{x} & \quad ,\;x<0 \\ c & \quad ,\;x=0 \\ \Large\frac{\sqrt{x+bx^2}-\sqrt x}{b\sqrt{x^3}} & \quad ,\;x>0 \end{array} \right. $ may continuous at x = 0

asked Jan 25, 2013 by meena.p

1 answer

Is the function $ f(x)=\Large\frac{3x+4\tan x}{x}$ continuous at x = 0? If not, how may the function be defined to make it continuous at this point.

asked Jan 25, 2013 by meena.p

1 answer

Show that the function :$f(x)= \left\{ \begin{array}{1 1} \Large\frac{e^{\frac{1}{x}}-1}{e^{\frac{1}{x}}+1}, & \quad when\;x\neq0 \\ 0, & \quad when\; x=0 \end{array} \right. $ is discontinuous at x = 0.

asked Jan 25, 2013 by meena.p

1 answer

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.

asked Jan 25, 2013 by meena.p

1 answer

For any square matrix verify A(adj A) = |A|I

asked Jan 24, 2013 by meena.p

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If $ A=\begin{bmatrix} a & b \\ 0 & 1 \end{bmatrix}\;prove\;that\;A^n=\begin{bmatrix} \Large a^n & \Large\frac{b(a^n-1)}{a-1} \\ \normalsize 0 & 1 \end{bmatrix},n \epsilon N$

asked Jan 24, 2013 by meena.p

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If P and Q are invertible matrices of same order, then show that PQ is also invertible.

asked Jan 24, 2013 by meena.p

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If $ A=\begin{bmatrix} 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{bmatrix} \;find\;A^2\;Hence\;find\;A^6.$

asked Jan 24, 2013 by meena.p

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If $A=\begin{bmatrix} \cos \theta & \sin \theta & \\ -\sin \theta & \cos \theta \end{bmatrix} $ then show that $A^n=\begin{bmatrix} \cos 2\theta & \sin 2\theta & \\ -\sin 2\theta & \cos 2\theta \end{bmatrix} $

asked Jan 24, 2013 by meena.p

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If a, b, c are in A.P. then find the value of: $\begin{vmatrix} 2y+4 & 5y+7 & 8y+a \\ 3y+5 & 6y+8 & 9y+b \\ 4y+6 & 7y+9 & 10y+c \end{vmatrix}$

asked Jan 24, 2013 by meena.p

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If x, y and z all positive, are $p^{th},q^{th}and\;r^{th}$ terms of a G.P. Prove that $\begin{vmatrix} logx & p & 1 \\ logy & q & 1 \\ logz & r & 1 \end{vmatrix}=0$

asked Jan 24, 2013 by meena.p

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If , Y = $ x^4 - \ frac$ {x$^3} ${3} when denotes the number of hours worked and denotes the amount (in Rupees) earned. Then find the value of (in interval) for which the income remains increasing? Explain the importance of earning in life?

asked Jan 24, 2013 by shanthinig

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Find the quadratic function defined by the equation $ f(x)=ax^2+bx+c\;if\;f(0)=6,f(2)=11,f(-3)=6,$ using determinants.

asked Jan 24, 2013 by meena.p

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If $ A+B+C=\large\pi,\;\normalsize show\;that\;\begin{vmatrix} \sin (A+B+C) & \sin B & \cos C \\ -\sin B & 0 & \tan A \\ \cos (A+B) & -\tan A & 0 \end{vmatrix}=0$

asked Jan 24, 2013 by meena.p

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If x, y, z are positive and unequal show that the value of determinant $ \begin{vmatrix} x & y & z \\ y & z & x \\ z & x & y \end{vmatrix}$ is negative.

asked Jan 24, 2013 by meena.p

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If $ p(\alpha)=\begin{bmatrix} \cos \alpha & i\sin \alpha \\ -\sin \alpha & \cos \alpha \end{bmatrix}\;show\;that\;p(\alpha) \times p(\beta)=p(\alpha+\beta)$

asked Jan 24, 2013 by meena.p

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A car parking company has 500 subscribers and collects fixed charges of Rs.300 per subscriber per month. The company proposes to increase the monthly subscription and it is believed that for every increase of Re.1, one subscriber will discontinue the service. What increase will bring maximum income of the company? What values are driven by this problem?

asked Jan 24, 2013 by shanthinig

0 answers

Find the values of a and b such that $ A^2+aI=bA\;where\; A=\begin{bmatrix} 3 & 1 \\ 7 & 5 \end{bmatrix}$

asked Jan 24, 2013 by meena.p

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If $ A=\begin{bmatrix} 1 & -2 & 1 \\ -2 & 3 & 1 \\ 1 & 1 & 5 \end{bmatrix}$ verify $(AdjA)^{-1}=adj(A^{-1})$

asked Jan 24, 2013 by meena.p

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If two matrices $ A^{-1}\;and\;B$ are given how to find $(AB)^{-1}$verify with an example.\[(Find\; B^{-1} then\; find\; B^{-1} \times A^{-1})\]

asked Jan 24, 2013 by meena.p

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If $P(a)=\begin{bmatrix} \cos a & -\sin a & 0 \\ \sin a & \cos a & 0 \\ 0 & 0 & 1 \end{bmatrix}$then show that $[P(x)]^{-1}=[P(-x)]$

asked Jan 24, 2013 by meena.p

0 answers

If $A=\begin{bmatrix} 2 & -3 \\ 3 & 4 \end{bmatrix} $satisfies the equation : $ x^2+6x+17=0\;find\;A^{-1}$

asked Jan 24, 2013 by meena.p

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let A be the set of all students of class XII in a school and R be the relation, having the same *** on A, and then prove that R is an equivalence relation. Do you think, co-education may be helpful in child development and why?

asked Jan 24, 2013 by shanthinig

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Prove that $f: R → R $ is a bijection given by $f(x) = x^3+3$. Find $f ^{-1} (x)$. Does the truthfulness and honesty may have any relation?

asked Jan 24, 2013 by shanthinig

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If $ A=\begin{bmatrix} 3 & 1 \\ -1 & 2 \end{bmatrix},$ show that $ A^2-5A+7I=0,$ use the result to find $A^4$.

asked Jan 24, 2013 by meena.p

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Let A and B be 3 x 3 matrices such that $ A^T=-A\;and\;B^T=B.$Then the matrix $\lambda(AB+3BA)$ is skew symmetric matrix for $\lambda$.

asked Jan 24, 2013 by meena.p

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Assume X, Y, Z, W and P are matrices of order (2 x n), (3xk), (n x 3) and (p x k) respectively, then the restriction on n, k and p so that py + my will be defined are : (k=3, p=n)

asked Jan 24, 2013 by meena.p

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Find the values of a, b, c if the matrix $\begin{bmatrix} 0 & 2b & c \\ a & b & -c \\ a & -b & c \end{bmatrix}$ satisfy the equation $ A^1A=I_3$

asked Jan 24, 2013 by meena.p

0 answers

If $ A=\begin{bmatrix} 1& 1 & 1 \\ 1& 1 & 1 \\ 1& 1 & 1 \end{bmatrix}$ then prove that $ A^n=\begin{bmatrix} 3^{n-1} & 3^{n-1} & 3^{n-1} \\ 3^{n-1} & 3^{n-1} & 3^{n-1} \\ 3^{n-1} & 3^{n-1} & 3^{n-1} \end{bmatrix}\;n\in N$

asked Jan 24, 2013 by meena.p

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If P and Q are equal matrices of same order such that PQ = QP, then prove by induction that $ PQ^n=Q^nP.$ Further, show that $(PQ)^n=P^n\times Q^n.$

asked Jan 24, 2013 by meena.p

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If $ A=\begin{bmatrix} 3 & 1 \\ 7 & 5 \end{bmatrix}$ find x and y such that $ A^2+xl=yA.\;Find\;A^{-1}.$

asked Jan 24, 2013 by meena.p

1 answer

If $ \begin{bmatrix} \cos^2A & \cos A\sin A \\ \cos A\sin A & \sin^2A \end{bmatrix},Y=\begin{bmatrix} \cos^2B & \cos B\sin B \\ \cos B\sin B & \sin^2B \end{bmatrix}$then show that XY is a zero matrix, provided (A-B) is an odd multiple of $\large\pi/2$

asked Jan 24, 2013 by meena.p

0 answers

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