Recent questions tagged q5

$\Large\int \frac {\sin^2xdx}{a^2\cos ^2x+b^2\sin^2x \sin^2 x} =$\begin{array}{1 1}(a)\;(b-a)log(a^2\cos ^2x+b^2\sin^2x) & \quad (b)\;\frac{1}{b-a}log(a^2\cos ^2x+b^2\sin^2x) & \\(c)\;\frac{1}{b^2-a^2}log(a^2\cos ^2x+b^2\sin^2x) & \quad(d)\;\frac{1}{a^2+b^2}log(a^2\cos ^2x+b^2\sin^2x)\end{array}

asked Jan 30, 2013 by meena.p

0 answers

At what point on the curve $ y=x^2$ does the tangent make an angle of $ 45^{\circ} $ with the axis.

asked Jan 30, 2013 by thanvigandhi_1

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If $ \begin{bmatrix} 2 & 4 \\ 5 & 1 \end{bmatrix} = \begin{bmatrix} 2x & 4 \\ 6 & x \end{bmatrix} $, then find x.

asked Jan 29, 2013 by thanvigandhi_1

1 answer

The co-ordinates of the point p(x,y) in the first quadrant on the ellipse $\Large\frac{ x^2}{8}+\frac{y^2}{18}$=1 so that the area of the triangle formed by the tangent at P and the co-ordinate axes is the smallest are given by \[(a)\;(2,3)\qquad(b)\;(\sqrt 8,0)\qquad(c)\;(\sqrt {18}, 0)\qquad(d)none\;of\;these\]

asked Jan 28, 2013 by meena.p

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Find the co-factor of $ a_{13}$ in the following : $ \begin{bmatrix} 2 & -3 & 5 \\ 6 & 0 & 4 \\ 1 & 5 & -7 \end{bmatrix} $

asked Jan 28, 2013 by thanvigandhi_1

1 answer

Evaluate : $ \int\large\frac{x^2+\cos 4x}{4x^3+3\sin 4x}$$dx $

asked Jan 27, 2013 by thanvigandhi_1

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If A is a matrix of order 3 x 4 and B is matrix of order 5 x 4, what is the order of matrix (AB)'.

asked Jan 25, 2013 by thanvigandhi_1

1 answer

Evaluate : $ \int\large \frac{x^2+4x}{x^3+6x^2+5}$$dx$

asked Jan 25, 2013 by thanvigandhi_1

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If $ f^1(x)=g(x)\;and\;g^1(x)=-f(x)$ for all n and $f(2)=f^1(2)=4,$ find the value of $f^2(24)+g^2(24)$

asked Jan 24, 2013 by meena.p

1 answer

Three shopkeepers A, B, C are using polythene, handmade bags (prepared by prisoners), and newspaper’s envelope as carry bags. it is found that the shopkeepers A, B, C are using (20,30,40) , (30,40,20,) , (40,20,30) polythene , handmade bags and newspapers envelopes respectively. The shopkeepers A, B, C spent Rs.250, Rs.220 & Rs.200 on these carry bags respectively .Find the cost of each carry bags using matrices. Keeping in mind the social & environmental conditions, which shopkeeper is better? & why?

asked Jan 24, 2013 by shanthinig

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If the function $ f : Q \rightarrow Q$ defined by $ f(x) = 3x+5$ for all $ x \in Q $ is invertible, find $ f^{-1} $.

asked Jan 24, 2013 by thanvigandhi_1

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Prove that $\begin{vmatrix} x-3 & x-4 & x-a \\ x-2 & x-3 & x-b \\ x-1 & x-2 & x-c \end{vmatrix}=0,$ where a,b,c are in A.P

asked Jan 24, 2013 by meena.p

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Considering the principal solutions, find the number of solutions of $ \tan^{-1}2x+\tan^{-1}3x=\frac{\pi}{4}$

asked Jan 23, 2013 by meena.p

1 answer

If $ \begin{vmatrix} 3x & 7 \\ 2 & 4 \end{vmatrix} $= 10, find x.

asked Jan 23, 2013 by thanvigandhi_1

1 answer

Let A = {4,5,0}. Find the number of binary operations that can be defined on A.

asked Jan 22, 2013 by meena.p

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If $ y = \sin^{-1}x+\cos^{-1}x, $ then find $\large \frac{dy}{dx} $.

asked Jan 22, 2013 by thanvigandhi_1

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Solve the differential equation$\Large \frac{dy}{dx}\normalsize =2xy-y$

asked Jan 17, 2013 by sreemathi.v

1 answer

Using properties of determinant, prove that $ \begin{bmatrix} 1 & x & y+z \\ 1 & y & z+x \\ 1 & z & x+y \end{bmatrix} = 0 $

asked Jan 17, 2013 by thanvigandhi_1

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Using vectors,find the value of k such that the points $(k,-10,3),(1,-1,3)$ and $(3,5.3)$ are collinear.

asked Jan 17, 2013 by sreemathi.v

1 answer

Let $ \begin{bmatrix} 3 & y \\ x & 1 \end{bmatrix} = \begin{bmatrix} 3 & 2 \\ 4 & 1 \end{bmatrix} $. Find the possible values of x and y, if x, y $ \in $ N.

asked Jan 16, 2013 by thanvigandhi_1

1 answer

Find the area of the region included between $y^2=9x$ and $y=x$.

asked Jan 16, 2013 by sreemathi.v

1 answer

Write the cofactor of elements of third column of the determinant. $ \begin{bmatrix} 4 & -5 & -11 \\ 1 & -3 & 1 \\ 2 & 3 & -7 \end{bmatrix} $

asked Jan 15, 2013 by thanvigandhi_1

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Evaluate the following $\large\int\frac{(1+\cos x)}{x+\sin x}dx$

asked Jan 14, 2013 by sreemathi.v

1 answer

At what points of the ellipse $ 16x^2+9y^2=400$, does the coordinate decrease at the same rate at which the abscissa increases.

asked Jan 11, 2013 by thanvigandhi_1

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Find an angle $\theta$,$0$ <$\;\theta<\Large \frac{1}{2}$,which increases twice as fast as its sine.

asked Jan 11, 2013 by sreemathi.v

1 answer

If $ \begin{bmatrix} x & 2 \\ 18 & x \end{bmatrix} = \begin{bmatrix} 6 & 2 \\ 18 & 6 \end{bmatrix} $ then what is the value of x.

asked Jan 10, 2013 by thanvigandhi_1

1 answer

Find the value of x if : $(i) \begin{bmatrix} 2 & 4 \\ 5 & 1 \end{bmatrix} = \begin{bmatrix} 2x & 4 \\ 6 & x \end{bmatrix} $

asked Jan 10, 2013 by thanvigandhi_1

1 answer

Evaluate : $ \begin{bmatrix} a+ib & c+id \\ -c+id & a-ib \end{bmatrix} $

asked Jan 9, 2013 by thanvigandhi_1

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Two dice are thrown together and the total score is noted.The events E,F and G are 'a total of 4','a total of 9 or more',and 'a total divisible by 5'respectively.Calculate P(E),P(F) and P(G) and decide which pairs of events,if any, are independent.

asked Jan 8, 2013 by sreemathi.v

1 answer

Find the co-factor of $ a_{12}$ in the following $ \begin{bmatrix} 2 & -3 & 5 \\ 6 & 0 & 4 \\ 1 & 5 & -7 \end{bmatrix} $.

asked Jan 6, 2013 by thanvigandhi_1

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Prove that the logatithmic function is strictly increasing on $ ( 0, \infty )$.

asked Jan 4, 2013 by thanvigandhi_1

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The total revenue received from the sale of x units of a product is given by $ R(x) = 13x^2 + 26x + 15 $ Find the marginal revenue when x = 7.

asked Jan 3, 2013 by thanvigandhi_1

1 answer

Prove that the line through $A(0,-1,-1)$ and $B(4,5,1)$ intersects the line through $C(3,9,4)$ and $D(-4,4,4)$

asked Jan 3, 2013 by sreemathi.v

1 answer

Write the value of following determinants : $ \begin{vmatrix} a-b & b-c & c-a \\ b-c & c-a & a-b \\ c-a & 2a-b & b-c \end{vmatrix} $

asked Jan 2, 2013 by thanvigandhi_1

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Write the value of the determinant : $\begin{bmatrix} 2 & 3 & 4 \\ 5 & 6 & 8 \\ 6x & 9x & 12x \end{bmatrix} $

asked Jan 2, 2013 by thanvigandhi_1

1 answer

Find whether f(x) is continuous or discontinuous at the indicated point $f(x)=\left \{\begin{array}{1 1}x-4, & if\;x\neq 4\\2(x-4)\\0, & if\;x=4\end{array}\right.$at x=4.

asked Dec 31, 2012 by sreemathi.v

1 answer

If A is a matrix of order 2 x 3 and B is a matrix of order 3 x 5, what is the order of matrix (AB)' or T?

asked Dec 29, 2012 by thanvigandhi_1

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A square matrix A, of order 3, has | A | = 5, find | A.adj.A |.

asked Dec 26, 2012 by thanvigandhi_1

1 answer

Evaluate : $ \begin{bmatrix} \sin10^{\circ} & \quad \cos10^{\circ} \\ \sin80^{\circ} & \quad \cos80^{\circ} \end{bmatrix} $

asked Dec 25, 2012 by thanvigandhi_1

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Using the properties of determinants, evaluate $\begin{vmatrix} x+4 & x & x \\ x & x+4 & x \\ x & x & x+4 \end{vmatrix}$

asked Dec 24, 2012 by sreemathi.v

1 answer

Let A be a square matrix of order 3 × 3, then $ | kA | $ is equal to \[ \begin{array} ((A) \: k | A | \quad & (B)\: k^2 | A | \\ (C) \: k^3 | A | \quad & (D) \: 3k | A | \end{array} \]

asked Dec 24, 2012 by thanvigandhi_1

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Find values of a and b if A=B,where A=$\begin{bmatrix}a + 4 & 3b\\8 & - 6\end{bmatrix},B=\begin{bmatrix}2a + 2 & b^2 + 2\\8 & b^2 - 5b\end{bmatrix}$

asked Dec 22, 2012 by sreemathi.v

1 answer

Write the principal value of $ \cos^{-1} \bigg(\cos \frac{\large 7\pi}{\large 6} \bigg). $

asked Dec 21, 2012 by thanvigandhi_1

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Find the value of $\tan^{-1}\bigg(\tan{\frac{2\pi}{3}}\bigg)$

asked Dec 20, 2012 by sreemathi.v

1 answer

Find the co-factor of $a_{12} $ in the following : $ \begin{bmatrix} 2 & -3 & 5 \\[0.3em] 6 & 0 & 4 \\[0.3em] 1 & 5 & -7 \end{bmatrix}$

asked Dec 20, 2012 by thanvigandhi_1

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Let A={a,b,c,d} and the function f={(a,b),(b,d),(c,a),(d,c)},Write $f^{-1}$.

asked Dec 18, 2012 by sreemathi.v

1 answer

If $ P(A) = \large \frac{6}{11} , P(B) =\large \frac{5}{11}\:$ and $ P(A \cup B) = \large \frac{7}{11}$ , find (i) $P(A \cap B) , (ii) P(A|B) , (iii) P(B|A)$

asked Dec 18, 2012 by thanvigandhi_1

1 answer

Find the vector and cartesian equations of the planes that passes through the point $(1, 0, -2)$ and the normal to the plane is $ \hat i+\hat j - \hat k $

asked Dec 15, 2012 by thanvigandhi_1

1 answer

Write the following function in the simplest form: \[ tan^{-1} \frac{\sqrt {1 + x^2} - 1}{x}, x \neq 0\]

asked Dec 10, 2012 by thanvigandhi_1

1 answer

Construct a 3 x 4 matrix,whose elements are given by: $\;a_{ij}=2i-j$

asked Dec 7, 2012 by sreemathi.v

1 answer

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