Recent questions tagged sec-b

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

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If $ y=x^x-2^{sinx}$ then find $ \frac{\large dy}{\large dx}.$

asked Jan 9, 2013 by thanvigandhi_1

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Find the derivaties of the function given by $ f(x)=(1+x)(1+x^2)(1+x^4)(1+x^8)$ and hence find $ f(1) $

asked Jan 9, 2013 by thanvigandhi_1

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Evaluate : $ \int \frac{\large cos(x+a)}{\large sin(x+b)}dx$

asked Jan 9, 2013 by thanvigandhi_1

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Evaluate : $ \int \sin x \sqrt {1+\cos\: x} dx.$

asked Jan 9, 2013 by thanvigandhi_1

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Verify that $ y=A\cos x - B\sin x$, is a solution of the differential equation $ \frac{\large d^2y}{\large dx^2}+y=0.$

asked Jan 9, 2013 by thanvigandhi_1

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Solve the following differential equation : $(y^2-x^2)dy = 3xy\: dx.$

asked Jan 9, 2013 by thanvigandhi_1

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Solve the differential equation : $\large \frac{dy}{dx}-\frac{y}{x}=\bigg( \frac{x-1}{x} \bigg)$$ e^x. $

asked Jan 9, 2013 by thanvigandhi_1

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Show that each of the given three vectors is a unit vector : $\large \frac{1}{7}$$ (2\hat i + 3\hat j + 6\hat k),\large\frac{1}{7} $$(3\hat i - 6\hat j + 2\hat k),\large\frac{1}{7} $$(6\hat i + 2\hat j - 3\hat k)$ (Also show that they are mutually perpendicular to each other).

asked Jan 9, 2013 by thanvigandhi_1

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Find the equation of the $ \bot $ drawn from point (2, 4, -1) to the line $ \frac{\large x+5}{\large 1}=\frac{\large y+3}{\large 4}=\frac{\large z-6}{\large -9}. $

asked Jan 9, 2013 by thanvigandhi_1

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Find the length and the foot of $ \bot $ drawn from point (2, -1, 5) to the line $ \frac{\large x-11}{\large 10}=\frac{\large y+2}{\large -4}=\frac{\large z+8}{\large -11}. $

asked Jan 9, 2013 by thanvigandhi_1

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A speaks truth 8 times out of 10 times. A dice is tossed. He reports that it was 5. What is the probability that it was actually 5?

asked Jan 9, 2013 by thanvigandhi_1

1 answer

Show that the relation R in the set A of points, given by R: {P, Q): distance of the point P from the origin is the same as the distance of Q from the origin }, is an equivalence relation. Further, show that the set of all points related to P = (0, 0) is the circle passing through P with origin as the centre.

asked Jan 8, 2013 by thanvigandhi_1

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Prove that : $ \cot^{-1} \bigg(\large \frac{ \sqrt{1+\sin x}+\sqrt{1-\sin\: x}}{\sqrt{1+\sin\: x}-\sqrt{1-\sin x}} \bigg)=\frac{x}{2}.$

asked Jan 8, 2013 by thanvigandhi_1

0 answers

Using properties of determinants, prove that : $ \begin{bmatrix} a^2+2a & 2a+1 & 1 \\ 2a+1 & a+2 & 1 \\ 3 & 3 & 1 \end{bmatrix} = (a-1)^3. $

asked Jan 8, 2013 by thanvigandhi_1

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Using the properties of determinants, prove that : $ \begin{bmatrix} x-3 & x-4 & x-\alpha \\ x-2 & x-3 & x-\beta \\ x-1 & x-2 & x-\gamma \end{bmatrix} = 0, \: where\: \alpha, \beta, \gamma \: are \: in \ A.P. $

asked Jan 7, 2013 by thanvigandhi_1

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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 = log \sqrt {\large\frac{1-\cos2x}{1+\cos2x}},$ show that $ \large\frac{dy}{dx} $$= 2 cosec\: 2x.$

asked Jan 7, 2013 by thanvigandhi_1

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Find the derivative of $ \sin (3x+2)$ w.r.t $x$ from the first principal.

asked Jan 7, 2013 by thanvigandhi_1

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Evaluate : $\int \large\frac{x^2+1}{x^4+1}$$dx.$

asked Jan 7, 2013 by thanvigandhi_1

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Solve the following differential equation: $ (x^2-y^2)dx+2xy.dy = 0\: given \: that\: y=1\: when \: x = 1.$

asked Jan 7, 2013 by thanvigandhi_1

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Solve the differential equation : $ \large\frac{dy}{dx} $$+y=\cos x - \sin x.$

asked Jan 7, 2013 by thanvigandhi_1

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Solve the differential equation : $ \large\frac{dy}{dx} $$= \log (x+1).$

asked Jan 7, 2013 by thanvigandhi_1

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Find the shortest distance between the following two lines : $ \overrightarrow r = (1+\lambda)\hat i + (2-\lambda)\hat j + (\lambda + 1)\hat k ; \overrightarrow r = (2\hat i -\hat j -\hat k) + \mu (2\hat i + \hat j +\hat k).$

asked Jan 7, 2013 by thanvigandhi_1

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Find the value of $ \lambda $, so that lines $\large \frac{1-x}{3}=\frac{7y-14}{2\lambda}=\frac{5z-10}{11} $ and $ \large \frac{7-7x}{3\lambda}=\large\frac{y-5}{1}=\frac{6-z}{5} $ are perpendicular to each other.

asked Jan 7, 2013 by thanvigandhi_1

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The probability that a student entering an university will graduate is 0.4. Find the probability that out of 3 students of the university: (i) none will graduate (ii) only one will graduate (iii) all will graduate.

asked Jan 7, 2013 by thanvigandhi_1

1 answer

An insurance company issued 2000 scooters and 3000 motor cycles. The probability of an accident involving a scooter is 0.01 and that of a motor cycle is 0.02. An insured vehicle met with an accident. Find the probability that the accident vehicle was a motor cycle.

asked Jan 7, 2013 by thanvigandhi_1

0 answers

Prove that the relation R in the set A = {1, 2, 3, 4, 5}given by R = {(a, b):|a-b) is even }, is an equivalence relation.

asked Jan 6, 2013 by thanvigandhi_1

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Prove that :$ \sin^{-1}\bigg(\large\frac{ 4}{ 5} \bigg) $$+ \sin^{-1}\bigg(\large\frac{ 5}{ 13} \bigg)$$+ \sin^{-1}\bigg(\frac{\large 16}{\large 65}\bigg) = \frac{\large \pi}{\large 2}.$

asked Jan 6, 2013 by thanvigandhi_1

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Solve for : $ x : tan^{-1}3x+tan^{-1}2x=\frac{\large \pi}{\large 4}. $

asked Jan 6, 2013 by thanvigandhi_1

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Using properties of determinants, prove the following : $ \begin{bmatrix} (b+c)^2 & a^2 & a^2 \\ b^2 & (c+a)^2 & b^2 \\ c^2 & c^2 & (a+b)^2 \end{bmatrix} = 2abc(a+b+c)^33 - 3abc. $

asked Jan 6, 2013 by thanvigandhi_1

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Using properties of determinants, prove the following : $ \begin{bmatrix} (b+c)^2 & a^2 & a^2 \\ b^2 & (c+a)^2 & b^2 \\ c^2 & c^2 & (a+b)^2 \end{bmatrix} = 2abc(a+b+c)^3. $

asked Jan 6, 2013 by thanvigandhi_1

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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

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

asked Jan 6, 2013 by thanvigandhi_1

0 answers