Recent questions tagged q14

Form the differential equation of all circles which pass through origin and whose centers lie on y-axis as shown below:

asked Jan 18, 2013 by sreemathi.v

1 answer

Using vectors,prove that the parallelogram on the same base and between the same parallels are equal in area.

asked Jan 17, 2013 by sreemathi.v

1 answer

If the function $ f(x) = \left\{ \begin{array}{l l} x^2+3x+a, & \quad { x \leq 1}\\ bx+2, & \quad { x > 1} \end{array}. \right. $ is differentiable for all x. Find a and b.

asked Jan 17, 2013 by thanvigandhi_1

0 answers

If $ y = tan^{-1}x,$ prove that $ (1+x^2)\large\frac{d^2y}{dx^2}$$+2x\large\frac{dy}{dx}$$=0.$

asked Jan 16, 2013 by thanvigandhi_1

0 answers

If $ x^{\large p}.y^{\large q} = (x+y)^{\large p+q}, $ prove that $ \large\frac{dy}{dx}=\large\frac{y}{x}.$

asked Jan 16, 2013 by thanvigandhi_1

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Find the area of the enclosed by the curve $y=-x^2$ and the straight line $x+y+2=0.$

asked Jan 16, 2013 by sreemathi.v

1 answer

If $ y =\large \frac{2}{\sqrt {a^2-b^2}}$$\tan^{-1} \bigg( \sqrt {\large\frac{a+b}{a-b}}\tan\frac{x}{2} \bigg)$. Prove that $\large \frac{dy}{dx}=\frac{1}{a-b\cos x} .$

asked Jan 15, 2013 by thanvigandhi_1

0 answers

Evaluate the following $\displaystyle\int\frac{dx}{\sqrt {16-9x^2}}$

asked Jan 14, 2013 by sreemathi.v

1 answer

If $ x \sqrt {1+y} + y \sqrt{1+x}=0 \: for \: -1 < x < 1$ Prove that : $\large \frac{dy}{dx}=\frac{1}{(1+x)^2} $

asked Jan 11, 2013 by thanvigandhi_1

0 answers

Find the co-ordinates of the point on the curve $\sqrt x\quad \sqrt y=4$ at which tangent is equally inclined to the axes.

asked Jan 11, 2013 by sreemathi.v

1 answer

Find $\large \frac{dy}{dx} $ of following : $ y=(\sin \: x)^x+\sin^{-1} \sqrt x. $

asked Jan 10, 2013 by thanvigandhi_1

0 answers

Prove that : $ \cot^{-1} \bigg[ \large\frac{\sqrt{1+\sin x}+\sqrt{1-\sin x}}{\sqrt{1+\sin x}-\sqrt{1-\sin x}} \bigg]; $$0 < x <\large \frac{\pi}{2} = \large\frac{1}{2} $

asked Jan 10, 2013 by thanvigandhi_1

0 answers

If $ y = \frac{\large sin-x}{\large \sqrt {1-x^2}}$ show that $ (1+x^2) \large\frac{ d^2y}{ dx^2}$$-3x \large\frac{ dy}{ dx}$$ - y=0. $

asked Jan 9, 2013 by thanvigandhi_1

0 answers

Three dice are thrown at the same time.Find the probability of getting three two's,if it is known that the sum of the numbers on the dice was six.

asked Jan 8, 2013 by sreemathi.v

1 answer

A company manufactures two types of sweaters :type A sweaters type B.It costs Rs 360 to make a type A sweater and Rs 120 to make a type B sweater.The company can make at most 300 sweaters and spend at most Rs72,000 a day.The number of sweaters of type B cannot exceed the number of sweaters of type A by more than 100.The company makes a profit of Rs 200 for each sweater of type A and Rs 120 for every sweater of type B.Formulate this problem at a LPP to maximise the profit to the company.

asked Jan 7, 2013 by sreemathi.v

1 answer

For what value of k is the following function continuous at x = 2? $ f(x) = \left\{ \begin{array}{l l} 2x+1, & \quad { x < 2}\\ k, & \quad \text{ $x$ = 2} \\ 3x-1, & \quad \text{ $x$ > 2} \end{array}. \right.$

asked Jan 7, 2013 by thanvigandhi_1

1 answer

If $ y=3 \cos (log\: x) + 4\sin (\log x)$ then show that $ x^2\frac{\large d^2y}{\large dx^2}+x\frac{\large dy}{\large dx}+y=0. $

asked Jan 6, 2013 by thanvigandhi_1

0 answers

Find $\large \frac{dy}{dx}$ if $ (x^2+y^2)^2=xy$

asked Jan 6, 2013 by thanvigandhi_1

0 answers

Prove that : $\large \frac{d}{dx}$$(log_ex)=\large\frac{1}{x}. $

asked Jan 4, 2013 by thanvigandhi_1

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O is the origin and A is (a,b,c).Find the direction cosines of the line OA and the equation of plane through A at right angle to OA.

asked Jan 3, 2013 by sreemathi.v

1 answer

Differentiate following function w.r.t. $ x$ $ x^{\large \sin x} + ( \sin x )^{\large \cos x} $

asked Jan 3, 2013 by thanvigandhi_1

0 answers

If f(x) , defined by the following, is continuous at x = 0 , find the value of a, b and c. $f(x)=\left \{\begin{array}{1 1}\large\frac{\sin(a+1)x+\sin x}{x}, & if\;x< 0\\c, & if\;x= 0\\ \large\frac{\sqrt{x+bx^2}-\sqrt x}{bx^{\large\frac{3}{2}}}, & if\;x>0\end{array}\right.$

asked Jan 2, 2013 by thanvigandhi_1

0 answers

Prove that : $ (i) \large \frac{d}{dx} $$(a^x) = a^x log_e a. \; (ii) \large\frac{d}{dx}$$ (e^x) = e^x. $

asked Dec 31, 2012 by thanvigandhi_1

0 answers

Find the value of $k$ in the following so that the function $f$ is continuous at the indicated point $f(x)=\left \{\begin{array}{1 1}\large\frac{1-\cos kx}{x\sin x}, & if\;x\neq 0\\\large\frac{1}{2}, & if\;x=0\end{array}\right.\;at\;x=0$

asked Dec 31, 2012 by sreemathi.v

1 answer

Evaluate : $ \int \mathrm \: x \sin^{-1}x \: dx $

asked Dec 29, 2012 by thanvigandhi_1

0 answers

Show that $ f(x) = |x-3|, \large\frac{1}{4} \normalsize \forall \: x\: \in\: R, $ is continuous but not differentiable at $x = 3.$

asked Dec 28, 2012 by thanvigandhi_1

0 answers

Using properties of determinants, prove that : $ \begin{bmatrix} a^2+1 & ab & ac \\ ab & b^2+1 & bc \\ ca & cb & c^2+1 \end{bmatrix} = (1+a^2+b^2+c^2) $

asked Dec 26, 2012 by thanvigandhi_1

0 answers

For what values of a and b, the function f defined as : $ f(x) = \left\{ \begin{array}{l l} 3ax+b, & \quad \text{if $x$ < 1}\\ 11, & \quad \text{ if $x$ = 1} \\ 5ax-2b, & \quad \text{if $x$ > 1} \end{array} is \: continuous\: at\: x=1. \right.$

asked Dec 26, 2012 by thanvigandhi_1

0 answers

Find the value of 'a' for which the function f defined as $ f(x) = \left\{ \begin{array} {l l} a\sin \large\frac{\pi}{{2}(n+1)}, & \quad {x \: \leq \: 0} \\ \large\frac{tanx - sinx}{x^3}, & \quad {x \: > 0} \end{array} \right .$ is continuous at x=0. Differentiate $( x \: cos \: x )^x + ( x\sin\: x )^{\frac{1}{x}}$ w.r.t. $ x $.

asked Dec 25, 2012 by thanvigandhi_1

0 answers

If $a_1,a_2,a_3,....,a_r$ are in G.P., then prove that the determinant $\begin{vmatrix} a_{r-1} & a_{r-5} & a_{r-9} \\ a_{r-7} & a_{r-11} & a_{r-15} \\ a_{r-13} & a_{r-17} & a_{r-21} \end{vmatrix} is\; independent\; of\; r$

asked Dec 24, 2012 by sreemathi.v

1 answer

The integrating factor of the differential equation $ x \frac{dy}{dx} -y = 2x^2 $is \[ \begin{array} (A)\: e^{-x} \quad & (B)\: e^{-y} \\ (C)\: \frac{1}{x} \quad & (D)\: x \end{array} \]

asked Dec 24, 2012 by thanvigandhi_1

0 answers

If $A=\begin{bmatrix}3 & -4\\1 & 1\\2 & 0\end{bmatrix}\;and\;B=\begin{bmatrix}2 & 1 & 2\\1 & 2 & 4\end{bmatrix} \;$ then verify that $(BA)^2\neq B^2A^2$

asked Dec 22, 2012 by sreemathi.v

1 answer

Evaluate : $ \int \mathrm \: \large\frac{dx}{ \sqrt{5-4x-2x^2}} $

asked Dec 21, 2012 by thanvigandhi_1

0 answers

Prove that $ \sin^{-1}{\frac{8}{17}}+\sin^{-1}{\frac{3}{5}}=\sin^{-1}{\frac{77}{85}}$

asked Dec 20, 2012 by sreemathi.v

1 answer

For what value of $k$ is the following function continuous at $ x=2$? $ f(x) = \left\{ \begin{array}{l l} 2x+1\: \: \: ; & \quad \text{ $x$ < 2}\\ k\: \: \: \: \: \: \: \: \: \:\: \: \: \: ; & \quad \text{ $x$ =2}\\ 3x-1\: \: \: ; & \quad \text{ $x$ >2} \end{array} \right.$

asked Dec 20, 2012 by thanvigandhi_1

0 answers

Let $f\;:\;R\rightarrow R$ be the function defined by $f(x)=\frac{1}{2-\cos x}\forall x\;\in R.$Then,find the range of f.

asked Dec 18, 2012 by sreemathi.v

1 answer

In the following cases,find the distance of each of the given points from the corresponding given plane (a)Point(0,0,0),Plane $3x-4y+12z-3=0$

asked Dec 14, 2012 by thanvigandhi_1

1 answer

Find the shortest distance between the lines $ \overrightarrow r = ( \hat i + 2\hat j + \hat k) + \lambda ( \hat i - \hat j + \hat k )$ and $ \overrightarrow r = 2 \hat i - \hat j - \hat k + \mu (2\hat i + \hat j + 2\hat k )$

asked Dec 14, 2012 by thanvigandhi_1

1 answer

Find the value of $x$ if $ sin \bigg ( sin^{-1} \frac{1}{5} + cos^{-1} \: x \bigg) = 1$.

asked Dec 10, 2012 by thanvigandhi_1

1 answer

Show that the vector $ \hat i + \hat j + \hat k$ is equally inclined to the axes OX, OY and OZ.

asked Dec 6, 2012 by thanvigandhi_1

1 answer

Find the integral $\int(1-x)\sqrt x\;dx$

asked Dec 6, 2012 by sreemathi.v

1 answer

If either vector $\overrightarrow a = \overrightarrow 0$ or $\overrightarrow b = \overrightarrow 0$, then $\overrightarrow a . \overrightarrow b = 0$. But the converse need not be true. Justify your answer with an example.

asked Dec 6, 2012 by thanvigandhi_1

1 answer

Integrate the function $\frac{\large 1}{\large x(log x)^m},x\;>\;0$

asked Dec 6, 2012 by sreemathi.v

1 answer

Find the integrals of the functions\[\frac{\cos x-\sin x}{1+\sin2x}\]

asked Dec 5, 2012 by sreemathi.v

1 answer

Integrate the functions\[\frac{1}{\sqrt{8+3x-x^2}}\]

asked Dec 5, 2012 by sreemathi.v

1 answer

Integrate the rational functions$\;\large\frac{3x-1}{(x+2)^2}$

asked Dec 5, 2012 by sreemathi.v

1 answer

If $ \overrightarrow a, \overrightarrow b, \overrightarrow c, $ are mutually perpendicular vectors of equal magnitudes, show that the vector $ \overrightarrow a + \overrightarrow b + \overrightarrow c$ is equally inclined to $ \overrightarrow a, \overrightarrow b and \overrightarrow c$.

asked Dec 5, 2012 by thanvigandhi_1

1 answer

Integrate the function $x(\log x)^2$

asked Dec 4, 2012 by sreemathi.v

1 answer

Using the method of integration find the area of the region bounded by lines: $2x + y = 4, 3x - 2y = 6$ and $x - 3y + 5 = 0$

asked Dec 4, 2012 by thanvigandhi_1

1 answer

Evaluate the definite integral $\begin{align}\int\limits_0^1\frac{2x+3}{5x^2+1}dx \end{align}$

asked Dec 4, 2012 by sreemathi.v

1 answer

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