Recent questions tagged modelpaper

If $y = x +\tan x$, prove that : $\cos^2x. \large\frac{d^2y}{dx^2}$$-2y+2x = 0. $

asked Jan 3, 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

$ \int \: \frac{\large x^3-x^2+x-1}{\large x-1}dx $

asked Jan 3, 2013 by thanvigandhi_1

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Find the differential equation $y = x \sin x.$

asked Jan 3, 2013 by thanvigandhi_1

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Compute the magnitude of the following vectors : $ \overrightarrow a = \hat i + \hat j + \hat k, \overrightarrow b = 2\hat i - 7\hat j - 3\hat k\: and \: \overrightarrow c = \frac{1}{\sqrt 3}\hat i + \frac{1}{\sqrt 3}\hat j - \frac{1}{\sqrt 3}\hat k $

asked Jan 3, 2013 by thanvigandhi_1

0 answers

If A and B one the events associated with a random experiment and $ P(A) = 0.2, P(B) = 0.3, P (A \cup B ) = 0.4$, find $ (i) P( A \cap B ) and (ii) P( A / B ) $

asked Jan 3, 2013 by thanvigandhi_1

0 answers

In a class having 70% boys, 20% of the boys and 10% of the girls are players. A student is selected at random from the class and is found to be a player. Find the probability that the selected student is a girl.

asked Jan 3, 2013 by thanvigandhi_1

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Show that the relation R defined by (a, b ) R ( c, d ) $ \Rightarrow $ a + b + c on the set N x N is an equivalence relation.

asked Jan 3, 2013 by thanvigandhi_1

0 answers

Using properties of determinants, prove the following : $ \begin{bmatrix} \alpha & \beta & \gamma \\ \alpha^2 & \beta^2 & \gamma^2 \\ \beta+\gamma & \gamma+\alpha & \alpha+\beta \end{bmatrix} $

asked Jan 3, 2013 by thanvigandhi_1

0 answers

Prove, using the properties of determinants $ \begin{bmatrix} a+b & b+c & c+a \\ b+c & c+a & a+b \\ c+a & a+b & b+c \end{bmatrix} = 2 \begin{bmatrix} a & b & c \\ b & c & a \\ c & a & b \end{bmatrix} $

asked Jan 3, 2013 by thanvigandhi_1

0 answers

If $ y = 3e^{2x} + 2e^{3x} $ prove that, $ \large\frac{d^2y}{dx^2} = $$5\large\frac{dy}{dx}$$+6y = 0.$

asked Jan 3, 2013 by thanvigandhi_1

0 answers

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

asked Jan 3, 2013 by thanvigandhi_1

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Find the equation of tangent to the curve $ y = \sqrt {3x-2}$ which is parallel to the line $ 4x-2y+5=0$.

asked Jan 3, 2013 by thanvigandhi_1

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Find the intervals in which the function f given by $ f(x) = x^3 + \large\frac{1}{x^3}$$, x \neq 0 $ is, (i) increasing, (ii) decreasing.

asked Jan 3, 2013 by thanvigandhi_1

0 answers

Evaluate : \[ (i) \int \: \sqrt {x^2+4x+8} dx \] \[ (ii) \int \: \sqrt {(x-5)(7-x)} dx \] \[ (iii) \int \: \sqrt {14x-20-2x^2} dx \] \[ (iv) \int \: \sqrt {4ax-x^2} dx \]

asked Jan 3, 2013 by thanvigandhi_1

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Evaluate $ \int\large\frac{dx}{x[6(\log x)^2+7(\log x)+2]} $

asked Jan 3, 2013 by thanvigandhi_1

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Evaluate $\int\: tan^{-1} \sqrt {\large\frac{1-sinx}{1+sinx}}$$dx.$

asked Jan 3, 2013 by thanvigandhi_1

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Solve the following differential equation : $ \frac{dy}{dx} = \frac{x(2y-x)}{x(2y+x)}, $ if y = 1 when x = 1.

asked Jan 3, 2013 by thanvigandhi_1

0 answers

Find the particular solution, satisfying the given condition for the differential equation $ \large\frac{dy}{dx} - \frac{y}{x} +$$ cosec \bigg(\large \frac{y}{x} \bigg)$$ = 0, y = 0\: when \: x = 1$

asked Jan 3, 2013 by thanvigandhi_1

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If $ \overrightarrow a = \hat i + \hat j + \hat k \: and \: \overrightarrow b = \hat j - \hat k, $ Find a vector $ \overrightarrow c $ such that $ \overrightarrow a $ x $ \overrightarrow c = \overrightarrow b $ and $ \overrightarrow a . \overrightarrow c = 3$.

asked Jan 3, 2013 by thanvigandhi_1

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If $ \overrightarrow a + \overrightarrow b + \overrightarrow c = 0\: and\: | \overrightarrow a | = 3, |\overrightarrow b | = 5\: and \: |\overrightarrow c | = 7 .$Show that the angle between $ \overrightarrow a \: and \overrightarrow b$ is $ 60^{\circ} $

asked Jan 3, 2013 by thanvigandhi_1

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There are two bags I and II. Bag I contains 2 white and 3 red balls and Bag II contains 4 white and 5 red balls. One ball is drawn at random from one of the bags and is found to be red. Find the probability that it was drawn from bag II.

asked Jan 3, 2013 by thanvigandhi_1

1 answer

Find $ \mu$ variance for the following distribution :

asked Jan 3, 2013 by thanvigandhi_1

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Give example of relations which are : \[ \begin{array} (i)\: Symmetric \: but \: neither \: reflexive \: nor\: transitive \\ (ii) \: Transitive\: but\: neither\: reflexive\: nor\: symmetric \\ (iii)\: Reflexive \: and\: symmetric\: but\: not \: transitive \\ (iv)\: Reflexive \: and transitive\: but\: not\: symmetric \\ (v)\: Symmetric\: and\: transitive\: but \: not\: reflexive \end{array}\]

asked Jan 3, 2013 by thanvigandhi_1

0 answers